DOCSLIB.ORG

SOLUTIONS Chapter 1 Problem 1.1. Problem 1.2. Because |/0 ^0

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
SOLUTIONS Chapter 1 Problem 1.1. Problem 1.2. Because |/0 ^0 SOLUTIONS Chapter 1 Problem 1.1. 2,t-i) = —#2,t-i and Problem 1.2. Because |/0^0. Problem 1.3. a) No, because the deviations do not converge to zero, b) Yes, because the deviations remain bounded. Problem 1.4. a) P = 4 and b) yt = -j/t-i, 2/o = -1: P = 2. Problem 1.5. Prom (1.13) 1 1 + a (7-M)" =« X = i where 5 = 1/(1-a/3). Problem 1.6. A characteristic vector 5 and the corresponding characteristic value A are determined by Xs = Ms, that is, coordi- natewise XjSij = ctS2j and XjS2j — Psij. After multiplication: X'JSIJS2J = a(3sijS2,j- No characteristic vector may have coordinate zero, because then the other coordinate would also be zero. Therefore A^ = a(3. Thus we may normalize as siy3; = 1, that is, AjS2,j = A that is, 52,i = ^/®/f3 and 52,2 = -y/a//3. From (1.20) x0 = £isi + 6^2, whence the given initial state x0 = (#i,o>£2,o) yields ^-. (1.21) pro- vides the solution. 283 284 Solutions Problem 1.7. First we solve the scalar equation #1>t = rriiiXi^-i +wi. We substitute the solution obtained into the scalar equation X2,t = ™>22%i,t-i + ^2i^i,t-i + ^2, and so on. The only complication arises from the exponential terms on the R.H.S., which can be tackled, see (1.36). Problem 1.8. Column j of matrix M shows the image of the unit vector e^, thus magnification and rotation are combined. The characteristic equation is P(X) = A2 - 2p(coscp)A + p2 = 0 [(1.27)- (1.28)], yielding the foregoing characteristic roots. The geometric meaning also suggests this result. Problem 1.9. According to Problem 1.6, Mi has two character- istic values: 1 and -1. According to Problem 1.7, both characteristic values of Mi are equal to 1, however, there exists only a single inde- pendent characteristic vector: s = (0,1). Problem 1.10. Xt = Xxt-i 4- w where #*, A and w are scalars. Theorem 1.1: if A ^ 1, then x° = w/(l - A). Theorem 1.2: trivial. Theorem 1.3: empty. Theorem 1.4: stability — 1 < A < 1. Theorem 1.5: 0 < A < 1. Theorem 1.6: $ = 1/|A|. Theorem 1.7: xt = xt-i is meaningless. Theorem 1.8 reduces to Theorem 1.4. Problem 1.11. a) Ai = A2 > 0. b) at least one sign-change, at least two sign-changes. Problem 1.12. a) 0 l/a 0 **•( b) 6n = 0. c) Example 1.15. d) Similarly to Problem 1.6, the characteristic equation of matrix / — B(k) is P(X) = (A — I)2 — af3kik2 = 0, whence A = 1 ± y/aflkik2, Ai > 1. Chapter 2 Problem 2.1. Programming. Problem 2.2. Insert the stationary values into (2.18)-(2.19). Equations y° = Y°l+c and Y° = A{y°) yield the traditional equation l y° = Ay° + c, whence y° = (/ - A)~ c, Y° = A{y°). Considering the stationary conditions (2.20)-(2.21): system y° + (d)z° = y*,Y° + Dx Z° = Y* has a positive solution in (z°,Z°), assuming that y° < y* and Y° < Y* hold. Solutions 285 Problem 2.3. For |A| = 1, expression + e2 - is denned for all -1 < SftA < 1. The hyperbolic function |TT(A)|2 reaches its maximum at one end point. Since TT(1) = (/? — «)/(l — e) and TT(—1) = ((3 + a)/(l + s), under our assumptions, 0 < TT(1) < TT(—1) hold. Problem 2.4. (See Lovell, 1962 and Martos, 1990.) For uniform norms and reactions, b = (1 + 7e)l = /Jl holds, that is, matrix (2.43) is a rational function of AT, that is, A is a likewise function of v. A = 1 - (1 - u)e - (1 - i/)/?(l - vP)~lve. Problem 2.5. Let now fa = bi + fc^, a; = 6; and si = 1 - &;, 7rt = pi, z = 1,... ,n. On the basis of Problem 2.3 one can prove again that, due to 7Ti(—1) < 0, p[iV(—p(—1))] < 1 is sufficient but generally not necessary. If, however, N is 2-cyclic, then —p(N) is also a dominant characteristic value, that is, p[N(—p(—l))] < 1 is also necessary. Chapter 3 Problem 3.1. a) f(x) > x holds, though 0 < f'(x) = 1 - (1 + ex)~2ex < 1. b) Interval (—00,00) is not compact. Problem 3.2. a) The map is indeed not a contraction, since for (3 = 1 and x0 = 0.01, x\ = 50.005, while for y0 = 1, yx = 1. b) Comparing the arithmetic and geometric means yields xt > y//5 (t > 1). Then 0 < f'(x) = 1/2 - p/(2x2) < 1, that is, contrac- tion. Note that /'(>//?) = 0, that is, the convergence is very fast. Problem 3.3.* Draw the diagram known from the cobweb -cycle. After some trials one can discover the following case by case approach. a) Figure 3.1:Ifl<a<2, then the fixed point f(x°) - x° lies in (0;l/2). Due to symmetry, for x* = 1 - x°, f(x*) = x°. If x* < x0 < 1, then x± < x°; if 1/2 <x0 < x*, then x° < xi < 1/2. We have demonstrated that the system can stay to the right from 1/2 for at most one time-period. If x° < xt < 1/2, then x° < xt+i < xt\ 286 Solutions if 0 < xt < x°, then Xt < Xt+i < 1/2. Because of monotonicity, the limit exists, which is naturally a fixed point, that is, is equal to x°. b) Figure 3.2: If 2 < a < 3, then there exists such a number 0 < x\ < 1/2, for which f{xl) = 1/2. Because of symmetry, x\ = 1 — xj, f\x\) = 1/2. If xl < x0 < 1, then xx < x\. If 1/2 < x0 < z$, then x\ < xi < 1/2. If xt < x\, then xt < xt+i < x\. If x\ < xt < 1/2, then xt < #t+i < x2; that is, sooner or later the system arrives to the open interval (xJjXj) and stays there. Then the contraction map theorem is applicable, because * 1 =*= c) For a = 2, there is a borderline case between a) and b). Problem 3.4.* If matrix A (or B) is invertible, then the proof of the Lemma is elementary: ABx = Ax, y = A~xx => BAy = Ay. Hence via a limit-argument the Lemma applies for any matrix P A. Thus p(AB--C) = p(B--CA), that is, matrix D/ (x2) = D/(xi)D/(xP) • • -D/(x2) is stable. Problem 3.5. a) x° = 2 - 2x° => x° = 2/3. b) x2 = 2xi and xi = 2 - 2x2 = 2 - 4xi => xi = 2/5 => x2 = 4/5. c) Out of three, either two points are less than 1/2 or two points are greater than 1/2. Then continue as in b). d) Unstable, because |/'(-)| > 2, or 4,8 > 1. Problem 3.6. sin2<p = 2 sin </? cos </? implies <pt = 2<pt-i, and so on. Problems 3.7-3.9. Programming. Chapter 4 Problems 4.1—4.3. Programming. Problem 4.4. In fact, we used (4.28') rather than the time- invariance of At at (4.29). Problem 4.5.* Introducing the general control-theoretic frame- work with bounds, we have the state space equation xt = xt-i + But, and the planned control equation u\ = — {k)xt and the actual control equation u\ \iv?it<u\\ u?t \iu\<v?it<v%', i = l,...,n. { a ll a a i i,t — i' where u\ and uf are lower and upper control bounds, respectively. Solutions 287 Similarly to Section 2.2, we can generalize the analysis not only to the extended stock signalling model but to any Metzlerian control model. Chapter 5 Problem 5.1. Because of f(t,x) — \x, with notation h — t/k, the xk{ti,k) = Xk(U-i,k) + \xk(U-i,k)h = (1 + \h)xk(U-i,k). According to the formula of the geometric series, the solution is Xk(t) = #fc(0)(l + Xt/k)k, therefore for k —• oo, xu{t) converges to ext. Problem 5.2. Due to f[r,x(r)] = XX(T), the fcth integral equa- tion is xk+1{t) = x(0) + X / xk{r)dT. Jo For approximation 0, xo(t) = 1, the formula holds. Mathematical induction: Plug in approximation k and integrate by terms: the inte- gral of term j is equal to XXH^ 1/[(j + l)j!], which is just term j + 1, j = 0,1,..., fc, and term 0 remains 1. Problem 5.3. For function f(x) = x2/3, the difference-quotient [f(x) - f(0)]/(x - 0) = rc"1/3 is unbounded around x « 0. Problem 5.4. a) dx/dt = Xx =>• x~ldx = Xdt => logx = A£ -f xt+c c Xt c => x(t) = e ^ x(0) = e => x(t) = xoe . b) dx/dt = x2lz => x~2lzdx = dt => 3x^3 = t => x(0 = (^/3)3. c) dx/dt = x2 => x~2dx = dt => -x~l = t + c => x(t) = -l/(t H- c) => x(0) = -1/c and so on. Problem 5.5. Using (5.17*)-(5.18*) and Theorem 5.7, we have A = i and s = (1, —i)/2. Then 5Rs = (l,0)/2 and Ss = -(0,l)/2. Problem 5.6. We shall apply Theorem 5.8. According to the relation among the roots and coefficients, Ai + A2 = —a and Ai A2 = /?. a) If a system is stable, then the real parts of both roots are negative, that is, a > 0 and (3 > 0 (either real or complex), b) Assume a > 0 and 0 > 0.
Load more

Recommended publications
  • Complexity and Bounded Rationality in Individual Decision Problems
    Complexity and Bounded Rationality in Individual Decision Problems Theodoros M. Diasakos Working Paper No. 90 December 2008 www.carloalberto.org THE CARLO ALBERTO NOTEBOOKS Complexity and Bounded Rationality in Individual Decision Problems¤ Theodoros M. Diasakosy December 2008z ¤I am grateful to Chris Shannon for invaluable advice on this and earlier versions. Discussions with David Ahn, Bob Anderson, Paolo Ghirardato, Shachar Kariv, Botond Koszegi, Matthew Rabin, Jacob Sagi, and Adam Szeidl were of signi¯cant bene¯t. I also received helpful comments from Art Boman, Zack Grossman, Kostis Hatzitaskos, Kristof Madarasz, George Petropoulos, Florence Neymotin, and participants in the Xth Spring Meeting of Young Economists, the 2005 Conference of the Southwestern Economic Association, the 3rd and 5th Conference on Research in Economic Theory and Econometrics, and the 2007 SAET conference. Needless to say, all errors are mine. This research was supported by a fellowship from the State Scholarship Foundation of Greece. yCollegio Carlo Alberto E-mail: [email protected] Tel:+39-011-6705270 z°c 2008 by Theodoros M. Diasakos. Any opinions expressed here are the author's, not of the CCA. Abstract I develop a model of endogenous bounded rationality due to search costs, arising implicitly from the decision problem's complexity. The decision maker is not required to know the entire structure of the problem when making choices. She can think ahead, through costly search, to reveal more of its details. However, the costs of search are not assumed exogenously; they are inferred from revealed preferences through choices. Thus, bounded rationality and its extent emerge endogenously: as problems become simpler or as the bene¯ts of deeper search become larger relative to its costs, the choices more closely resemble those of a rational agent.
    [Show full text]
  • Physics of Risk and Uncertainty in Quantum Decision Making VI Yukalov
    Physics of risk and uncertainty in quantum decision making V.I. Yukalov1,2,a and D. Sornette1,3,b 1Department of Management, Technology and Economics, Swiss Federal Institute of Technology, ETH Zurich, Kreuzplatz 5, Zurich 8032, Switzerland 2Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia 3Swiss Finance Institute, University of Geneva, CH-1211 Geneva 4, Switzerland Abstract The Quantum Decision Theory, developed recently by the authors, is applied to clarify the role of risk and uncertainty in decision making and in particular in relation to the phe- nomenon of dynamic inconsistency. By formulating this notion in precise mathematical terms, we distinguish three types of inconsistency: time inconsistency, planning para- dox, and inconsistency occurring in some discounting effects. While time inconsistency is well accounted for in classical decision theory, the planning paradox is in contradiction with classical utility theory. It finds a natural explanation in the frame of the Quan- tum Decision Theory. Different types of discounting effects are analyzed and shown to enjoy a straightforward explanation within the suggested theory. We also introduce a gen- eral methodology based on self-similar approximation theory for deriving the evolution equations for the probabilities of future prospects. This provides a novel classification of possible discount factors, which include the previously known cases (exponential or hyperbolic discounting), but also predicts a novel class of discount factors that decay to a strictly positive constant for very large future time horizons. This class may be useful to deal with very long-term discounting situations associated with intergenerational public policy choices, encompassing issues such as global warming and nuclear waste disposal.
    [Show full text]
  • A Model of Time-Inconsistent Misconduct: the Case of Lawyer Misconduct
    Fordham Law Review Volume 74 Issue 3 Article 8 2005 A Model of Time-Inconsistent Misconduct: The Case of Lawyer Misconduct Manuel A. Utset Follow this and additional works at: https://ir.lawnet.fordham.edu/flr Part of the Law Commons Recommended Citation Manuel A. Utset, A Model of Time-Inconsistent Misconduct: The Case of Lawyer Misconduct, 74 Fordham L. Rev. 1319 (2005). Available at: https://ir.lawnet.fordham.edu/flr/vol74/iss3/8 This Article is brought to you for free and open access by FLASH: The Fordham Law Archive of Scholarship and History. It has been accepted for inclusion in Fordham Law Review by an authorized editor of FLASH: The Fordham Law Archive of Scholarship and History. For more information, please contact [email protected]. A Model of Time-Inconsistent Misconduct: The Case of Lawyer Misconduct Cover Page Footnote Professor of Law, University of Utah, S.J. Quinney College of Law. I would like to thank Nancy McLaughlin, Daniel Medwed, and Linda Smith fo their comments. This article is available in Fordham Law Review: https://ir.lawnet.fordham.edu/flr/vol74/iss3/8 A MODEL OF TIME-INCONSISTENT MISCONDUCT: THE CASE OF LAWYER MISCONDUCT Manuel A. Utset* INTRODUCTION The recent corporate scandals resulted from systematic violations of federal securities laws and state corporate law by managers over long periods of time. This type of systematic managerial misconduct requires the active participation of lawyers or at least their turning a blind eye to manager actions that should arouse their suspicion and a desire to investigate further. Thus, corporate scandals invariably lead scholars and regulators to question the effectiveness of existing regulations of corporate lawyers.
    [Show full text]
  • Lectures on Political Competition and Welfare
    GV 507: Lectures on Political Competition and Welfare Professor Timothy Besley∗ Michaelmas Term 1999 Contents 1 TheEconomicEnvironment........................ 3 2 RepresentativeDemocracy......................... 5 2.1PolicyChoice............................. 5 2.2Voting................................. 6 2.3Campaigning............................. 7 2.4Entry................................. 7 2.5 Equilibrium .............................. 8 2.6TheDownsianModel......................... 9 2.7TheCitizen-CandidateModel.................... 10 2.8Assessment.............................. 16 3 Normative Analysis of Political Equilibria . ............. 16 3.1 Efficiency............................... 20 3.2DistributionalIssues......................... 23 4 DynamicAnalysis.............................. 28 4.1Anapproachtopolitico-economicequilibrium........... 28 4.2PolicyMakingintheDynamicModel................ 33 4.2.1 FailuretoCommittoFutureCompensation........ 33 4.2.2 StrategicPolicyMaking................... 35 4.2.3 Aggregate Capital Accumulation and Political Equilibrium 36 ∗Disclaimer: These notes are not guaranteed to be error free. Please bring any problems that you notice to the attention of the lecturer. 4.3Assessment.............................. 39 5 AppendixA:Proofs............................. 44 2 1. The Economic Environment There are N citizens who have to make a social decision about a set policies de- noted by x ,where denotes the set of feasible policies. Citizen’s preferences over policy∈ areA denotedAV i (x, j)(wherei =1, ...,
    [Show full text]
  • Dynamic Inconsistency and Inefficiency of Equilibrium Under
    Dynamic Inconsistency and Inefficiency of Equilibrium under Knightian Uncertainty∗ Patrick Beissnery Michael Zierhutz March 14, 2019 Abstract This paper extends the theory of general equilibrium with Knightian uncertainty to economies with more than two dates. Agents have incomplete preferences with multiple priors `ala Bewley. These priors are updated in light of new informa- tion. Contrary to the two-date model, the market outcome varies with choice of updating rule. We document two phenomena: First, agents may find it optimal to deviate from their initial trading plans. This dynamic inconsistency may result in Pareto inefficiency, even if the market is dynamically complete. Second, ambiguous probability mass may spread; new information may create new uncertainty. Ei- ther phenomenon is avoided under certain updating rules: Full Bayesian updating guarantees dynamic consistency and Pareto efficiency, while maximum-likelihood updating prevents ambiguity spillovers. We ask whether it is possible to design updating rules that combine both properties. The answer is negative: No such rule exists. JEL Classification: D52; D53; D81 Keywords: Knightian uncertainty, Dynamic consistency, General equilibrium, In- complete markets ∗The authors thank Pablo Beker, Federico Echenique, Georgios Gerasimou, Christian Kellner, Fabio Maccheroni, Filipe Martins-da-Rocha, Frank Riedel, Ronald Stauber, Georg Weizs¨acker, and Jan Werner, as well as participants in the 2018 North American Summer Meeting of the Econometric Society and the workshop on Mathematics of Behavioral Economics and Knightian Uncertainty in Financial Markets at ZiF Bielefeld for helpful comments. M. Zierhut gratefully acknowledges financial support by the German Research Foundation (DFG) under project ZI 1673/1-1. yResearch School of Economics, ANU, 26012 Canberra, Australia, [email protected] zInstitute of Financial Economics, Humboldt University, 10099 Berlin, Germany, michael.zierhut@hu- berlin.de.
    [Show full text]
  • Dynamic (Time) Inconsistency
    First introduced by Kydland and Prescott in 1977, “Rules rather than Discretion: The Inconsistency of Optimal Plans” Let’s look at the Nobel prize description of this work: Time-consistent Policy In the late 1950s and early 1960s, the conventional wisdom, summarized in the so-called Phillips curve, was that economic policy could permanently reduce Dynamic (Time) unemployment by allowing for high inflation. In the late 1960s and early 1970s, however, several researchers had begun to question this view. Milton Friedman (Laureate in 1976) and Edmund Phelps showed that there exists a long-run equilibrium level of unemployment independently of the Inconsistency rate of inflation. Unemployment can be reduced below this equilibrium level through higher inflation, but only in the short run. In the long run, inflationary expectations and wage increases adjust to actual inflation, which in turn “Dynamic Inconsistency, Cooperation, and brings unemployment back to its equilibrium level. In the article from 1977, Kydland and Prescott extended the theory of economic the Benevolent Dissembling Government” policy. They showed that economic policymakers who cannot commit to a rule in advance often will conduct a policy that gives rise to high inflation, By Stanley Fischer despite their stated objective of low inflation. The Laureates presented this as one of several examples of a general problem in economic policymaking: the time consistency problem. Since then, this concept has been at the forefront of research on – and the formulation of – economic policy. Desirable Policies Often not Implemented A noteworthy example of the time consistency problem can be found in monetary policy. Assume that the objective The essence of the time consistency problem is as follows: of policymakers is low inflation and that they announce a policy which economic policymakers regard as the best such a policy.
    [Show full text]
  • Behavioral Economics: from Theory to Practice Dr
    Behavioral economics: from theory to practice dr. Nadezhda Shilova, Faculty of Economics Schiences, NRU HSE Pre-requisites: Students are supposed to be acquainted with the very basic economic concepts taught within the course of microeconomics; some basic knowledge on game theory is also welcomed but not obligatory. Course Type (compulsory, elective, optional) elective/optional Abstract: A usual complaint about economic theory courses we hear from students sounds like "but it does not work like this in real life!" Unfortunately, studying general cases takes too much time to explain that life is a special case of a general rule. During the suggested course we will try to reconcile theory and practice: we will see how mental and emotional filters shape the choice people make personally and as a group. We will also try to understand what is rational choice and you will formulate for yourself what rational patterns to follow (or not to follow) in real life whenever you'll have to make a decision - as a consumer or as a producer or even as a governor. Learning Objectives: Deeper and broader understanding of behavioral patterns; improving own decision making schemes and making better decisions. Course Plan: № Topics Academic/Contact Hours Self-study Lectures Labs Hours 1. Homo Economicus: the concept of rationality in 2 2 2 economics. Rationality VS egoistic behavior. 2. Why economics needed psychologists. Reshaping 4 2 4 cognitive schemes. Heuristics. 3. What also influences our choice: emotions, 2 - 2 institutions, what else? 4. Decisions under uncertainty. Probabilistic 2 2 2 mistakes. 5. Well-being and happiness: what is everything for? 4 2 4 Notion of rationality – again.
    [Show full text]
  • Adam Smith, Behavioral Economist
    Journal of Economic Perspectives—Volume 19, Number 3—Summer 2005—Pages 131–145 Adam Smith, Behavioral Economist Nava Ashraf, Colin F. Camerer and George Loewenstein n The Wealth of Nations, published in 1776, Adam Smith famously argued that economic behavior was motivated by self-interest. But 17 years earlier in 1759, I Smith had proposed a theory of human behavior that looks anything but self- interested. In his first book, The Theory of Moral Sentiments, Smith argued that behavior was determined by the struggle between what Smith termed the “passions” and the “impartial spectator.” The passions included drives such as hunger and sex, emotions such as fear and anger, and motivational feeling states such as pain. Smith viewed behavior as under the direct control of the passions, but believed that people could override passion-driven behavior by viewing their own behavior from the perspective of an outsider—the impartial spectator—a “moral hector who, looking over the shoulder of the economic man, scrutinizes every move he makes” (Grampp, 1948, p. 317).1 1 A long-standing dispute has raged over whether Adam Smith’s view of human motivation as expressed in The Theory of Moral Sentiments complements or contradicts the view of human motivation expressed in The Wealth of Nations. Although much has been written about “das Adam Smith problem” of reconciling these texts, most modern Smith scholarship asserts that there is no essential contradiction between the texts. As the editors of the Glasgow Edition of the Works and Correspondence of Adam Smith edition of The Theory of Moral Sentiments write (Raphael and Macfie, 1976, p.
    [Show full text]
  • Dynamic Inconsistency and Monetary Policy Management
    Munich Personal RePEc Archive Dynamic Inconsistency and Monetary Policy Management Balaban, Georgiana and Vîntu, Denis Bucharest Academy of Economic Studies 23 June 2010 Online at https://mpra.ub.uni-muenchen.de/56042/ MPRA Paper No. 56042, posted 17 May 2014 18:26 UTC Dynamic inconsistency and monetary policy management Georgiana Balaban Junior teaching assistant, PhD Candidate The Bucharest Academy of Economic Studies, Departament of Economics & Economic Policies, 6, Romana Square, district 1, Bucharest, 010374, PO 22, Romania, e-mail: [email protected] , phone: 0040743100150 Denis Vîntu PhD Candidate The Bucharest Academy of Economic Studies, Doctoral School, 6, Romana Square, district 1, Bucharest, 010374, PO 22, Romania, e-mail: [email protected], phone 0040754937695 Abstract This paper studies the importance of the dynamic inconsistency of monetary policy. The paper is organized as follows: in the first part the concept of dynamic inconsistency is explained; the next sections analyse the the rules versus discretion dilemma and some solutions to counteract the dynamic inconsistency of monetary policy - delegate monetary policy to an independent and conservative central banker; offering to the central banker a performance contract, in which his salary is directly linked to the performance of some important macroeconomic variables such as GDP and inflation rate; inflation targeting strategy. The last section briefly presents the management of monetary policy in Romania after adoption of inflation targeting strategy. Keywords:
    [Show full text]
  • WORKING OVER TIME: DYNAMIC INCONSISTENCY in REAL EFFORT TASKS* Ned Augenblick Muriel Niederle Charles Sprenger
    WORKING OVER TIME: DYNAMIC INCONSISTENCY IN REAL EFFORT TASKS* Ned Augenblick Muriel Niederle Charles Sprenger Experimental tests of dynamically inconsistent time preferences have lar- gely relied on choices over time-dated monetary rewards. Several recent studies have failed to find the standard patterns of present bias. However, such mon- etary studies contain often-discussed confounds. In this article, we sidestep Downloaded from these confounds and investigate choices over consumption (real effort) in a longitudinal experiment. We pair this effort study with a companion monetary discounting study. We confirm very limited time inconsistency in monetary choices. However, subjects show considerably more present bias in effort. Furthermore, present bias in the allocation of work has predictive power for demand of a meaningfully binding commitment device. Therefore our findings http://qje.oxfordjournals.org/ validate a key implication of models of dynamic inconsistency, with correspond- ing policy implications. JEL Codes: C91, D12, D81. I. Introduction Models of dynamically inconsistent time preferences (Strotz 1956; Laibson 1997; O’Donoghue and Rabin 1999, 2001) are pil- lars of modern behavioral economics, having added generally to at Law Library on July 13, 2015 economists’ understanding of the tensions involved in consump- tion-savings choices, task performance, temptation, and self- control beyond the standard model of exponential discounting (Samuelson 1937). Given the position of present-biased prefer- ences in the behavioral literature,
    [Show full text]
  • Dynamic Games and Contracts Insights from a Decade of Research
    Dynamic Games and Contracts Insights from a Decade of Research, and Recent Directions Susan Athey SED Plenary Talk, July 2010 Motivating Examples Collusion with private information about costs, repeated auctions • — Athey, Bagwell, Sanchirico (2004); Athey and Bagwell (2001); Athey and Bagwell (2008); Hopenhayn and Skrzypacz (2004); Harrington and Skrzypacz (2008) Public good problems • Trading favors (academic department hiring, within-firm cooperation, legis- • latures, families) (Hauser and Hopenhayn (2008), Abdulkadiroglu and Bag- well (2005)) Bilateral bargaining (Athey and Miller, 2007) • Monetary authority (Athey, Atkeson, Kehoe, 2008) • Individual dynamic inconsistency problem (Amador, Angeletos, Werning • (2005) Relational Contracts (Levin (2003), Rayo (2007), • Repeated procurement • Dynamic Public Finance (Golosov, Tsyvinski, and Werning (2006) survey) • Class of Dynamic Problems Efficient decision depends on private information dispersed among agents • (never publicly observed or audited) Information changes over time • — i.i.d. v. correlated over time — Affected by decisions (learning by doing, experimentation, capacity) Transfers of money/utility (?) • — None/wasteful (single agent with objective aligned with principal; agents anonymous; strongly symmetric equilibria) — Transfer utility but not money (asymmetric equilibria, trading favors) — Leaky bucket (inefficient gift giving, bribes with detection probability) — Transfer money Commitment? • — Far-sighted agents with self-enforcing agreements — Formal contracts (participation constraints?) General Economic Questions Efficiency: can it be sustained? Is it optimal for agents? • — Cases w/o a principal, includes budget balanced transfers or perfectly efficient transfers of utility — Tradeoffs between efficiency in one period and efficiency in future periods (inefficient rewards and punishments) — What kinds of inefficiency occur, and when does it happen? — Collusion case: want to get most efficient firm to produce in each period, but all firms like market share.
    [Show full text]
  • Multiple Solutions Under Quasi-Exponential Discounting Nicolas Vieille, Jörgen Weibull
    Multiple solutions under quasi-exponential discounting Nicolas Vieille, Jörgen Weibull To cite this version: Nicolas Vieille, Jörgen Weibull. Multiple solutions under quasi-exponential discounting. 2008. hal- 00354231 HAL Id: hal-00354231 https://hal.archives-ouvertes.fr/hal-00354231 Preprint submitted on 19 Jan 2009 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. ECOLE POLYTECHNIQUE CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE MULTIPLE SOLUTIONS UNDER QUASI-EXPONENTIAL DISCOUNTING Nicolas VIEILLE Jörgen W. WEIBULL March 2008 Cahier n° 2008-26 DEPARTEMENT D'ECONOMIE Route de Saclay 91128 PALAISEAU CEDEX (33) 1 69333033 http://www.enseignement.polytechnique.fr/economie/ mailto:[email protected] MULTIPLE SOLUTIONS UNDER QUASI-EXPONENTIAL DISCOUNTING Nicolas VIEILLE1 Jörgen W. WEIBULL2 March 2008 Cahier n° 2008-26 Abstract: We consider a group or committee that faces a binary decision under uncertainty. Each member holds some private information. Members agree which decision should be taken in each state of nature, had this been known, but they may attach different values to the two types of mistake that may occur. Most voting rules have a plethora of uninformative equilibria, and informative voting may be incompatible with equilibrium.
    [Show full text]