An RBC Model with Additive Technology Shocks. <<89516CF18641B843BA67FEDA6AB81D07>]>> That is, the agent seeks to maximize: 00 Eo L /3tu(ct - >.Ct), t=O ... Write down the consumer's Bellman equation and find his optimality conditions. %����P��L��P�V�h�����A������YUZ�D�(��?�������)&q�+� �Sb� When doing so, you need to be very clear on what the state variables are, what the control variables are etc. Habit persistence: Boldrin, Christiano, and Fisher (2001) The intensive and extensive margin: Hansen (1985) and Cho and Cooley (1994) Raul Santaeul alia-Llopis(Wash.U.) ... related to the Hamilton-Jacobi-Bellman equation for asset pricing. Econ 714: Macroeconomic Theory II1 Assignment 4: Answer Key2 1 Habit persistence Consider the problem of choosing a In general let the original problem be max ut X∞ t=0 βtr(x t,u t) subject to (3.14) x t+1 = g(x t,u t) x 0 given Then the associated Bellman equation takes the form: V(x t) = max ut {r(x t,u t)+βV[g(x t,u t)]} where r and g are known functions • … Part of the free Move 37 Reinforcement Learning course at The School of AI. The solution to the deterministic growth model can be written as a Bellman equation as follows: V(k) = max c ˆ c1 ˙ 1 1 ˙ + V(k0) ˙ s.t. b.For each of the following examples, if possible, assume that the initial con-ditions are such that yt is covariance stationary. So the policy functions in cases with and without habit persistence are the same, meaning the the saving rates in the two cases are equal. Problem 3 (Habit Persistence) Consider following dynamic problem with habit persistence preferences: max X∞ t=0 βt(lnC t+γlnCt−1) s.t Ct+Kt+1 6 AK α t Ct,Kt+1 > 0 k0,C−1 > 0 given Formulate the Bellman equation for this problem and clearly specify the state and control variables. xref Outline • The Model • The Habit-Forming Maximization Problem • Optimal Policies • The Role of Stochastic PDE’s • Feedback Formulae • Dynamic Programming • Stochastic Hamilton-Jacobi-Bellman Equation • Deterministic Coeﬃcients • An Example • Open Problems • Basic References 1 0000009395 00000 n that rule-of-thumb behavior and habit persistence are both important in accounting for predictable consumption growth. Persistence and determination alone are omnipotent. The value function can be obtained by the usual algorithm defined by the operator provided by the Bellman equation. 0000052233 00000 n %PDF-1.3 y��,ñ�n A�W�\$SwS�T�gw�qd��t^�����no4ElV��q�g�}�\$����j�l®���I+SK�}��"\$�ۀ�C�ݷ�y a�G�������&�Z�.�u� ͯ�����]�U� A����s�����O�W*�6 ��U�\$�%4�F�l�Tס��%��lޠԯ�b��͗R�)�=U�]�a��������W�v9t�7�Qm]�U]�#h�ht懘�L��;� Firstly, habit persistence may indicate that the tax system is inequitable and provides an argument for tax reform. equation implied by the model with habits and found no statistically signiﬁcant evidence for habit formation. 0000008821 00000 n %%EOF (b) Define a recursive competitive equilibrium in this environmeut. Econ 714: Macroeconomic Theory II1 Assignment 4: Answer Key2 1 Habit persistence Consider the problem of choosing a 0000003434 00000 n 0000001470 00000 n Under habit persistence, an increase in current consumption lowers the marginal utility of consumption in the current period and increases it in the next period. 0000001789 00000 n Linearized Euler Equation Methods Spring 20162 / 61 In order to ﬁnd the dynamics of c∗, consider the change in the term h W(t)− x(t) r+a−b i. Further, the parameter restrictions implied by the habit persistence model and the standard model are rejected decisively, View Notes - econ714hw4sol-2012 from ECON 714 at University of Wisconsin. 0000001299 00000 n This comes with a lot of practice. A dynamic panel approach is adopted to investigate if an entity’s ETR this year is related to its ETR next year. By using the dynamic programming arguments, he … startxref Key words. 0000004020 00000 n (2001), and Augeraud-Veron and Bambi (2015). endstream endobj 135 0 obj<>/Size 106/Type/XRef>>stream It is solved using a Bellman equation Time=lnseparalble Utility Chapter Idl 0000006783 00000 n 3 The consumption function with habit persistence 15 3.1 Aggregate consumption with Infinitely living households 16 3.2 Aggregate consumption with finitely lived overlapping generations 18 4 Empirical results 20 4.1 Data 20 4.2 Estimation results 20 5 Conclusions 26 References 27 APPENDIX 1. ��4�4�x�FM���. Moreover, this setting is a simple example of Cox, Ingersoll, and Ross general equilibrium pro-duction economy model with assets’ supply perfectly elastic (i.e., constant return technologies). 0000002319 00000 n Special attention is given to the role of habit persistence in explaining the equity premium puzzle, observed business-cycle fluctuations and inflation dynamics, and in generating a theory of counter-cyclical markups of prices over marginal costs. 0000007415 00000 n That is, the agent seeks to maximize: 00 Eo L /3tu(ct - >.Ct), t=O where the initial values e0 is given, and Ct is aggregate consumption. 0000003976 00000 n This comes with a lot of practice. An internal habit persistence model by George Constantinides (Conžianiinid€ 1990) ia a simple example of a Cox, Ingersoll, and Ross production economy where auppliež are perfectly elutic. Of AI to a certain growth condition the system dynamics [ 1 ] of no habit in! 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