Lecture 18 GMM:IV, Nonlinear Models
|
|
- Francine Lester
- 5 years ago
- Views:
Transcription
1 Lecure 8 :IV, Nonlinear Models Le Z, be an rx funcion of a kx paraeer vecor, r > k, and a rando vecor Z, such ha he r populaion oen condiions also called esiain equaions EZ, hold for all, where is he rue value of. For exaple, in he linear case we considered earlier, Z [y x w ] and Z, w *y -x, where r is equal o he diensionaliy of w. Anoher exaple nonlinear reression odel y fx, + ε Ew ε In his case, Z [y x w ] and Z, w *y -fx,
2 Ye anoher exaple Hansen and Sinleon Econoerica, 982 In he consupion-based asse pricin odel developed by Lucas Econoerica, 978, he represenaive household chooses a consupion plan in period o axiize expeced discouned uiliy subec o a sequence of bude consrains. In addiion o purchasin a consupion ood he nueraire ood, he aen can purchase N asses which differ accordin o he nuber of periods unil auriy,2,,n. hese providin he fuure incoe ha suppor fuure consupion. Wih a consan relaive risk aversion uiliy funcion, his opiizaion proble urns ou o produce he followin Euler equaions for he aen s opial consupion pah E[ δ r / p c / c γ, +, + I ] for,,n, where c is period consupion, r +, is he period + payoff fro a uni of asse purchased in period, and p, is he period price of a uni of asse. δ and γ are he paraeers of he odel δ he discoun rae, γ he paraeer ha
3 specifies he paricular CRRA uiliy funcion. I denoes he aen s inforaion se in period. We are ineresed in esiain he paraeers δ and γ. We can rewrie he Euler equaions as E[ δ r / p c / c I ] γ, +, + and, applyin he law of ieraed expecions, E[ δ r / p c / c w ] γ, +, + where w is an n-diensional vecor conained in I. r / p,, c / c E..,,, or any oher acroeconoic and/or financial variables ha ih be in I.
4 I follows ha he followin n oen condiions us hold for all : E[ w δ r, + / p, c + / c γ ] which is of he for EZ, Wha is he alernaive o o esiae his odel? MLE. Bu MLE requires specifyin he sequence of oin condiional disribuions for r / p, c / c,, + + hen axiizin he lo likelihood funcion subec o he sequence of Euler equaions. Excep in special cases e.., lonoral disribuion, his is a very essy proble copuaionally. [However, subec o he correc specificaion of he relevan disribuions, he MLE will be ore efficien asypoically han. is seiparaerically efficien bu he MLE is a fully paraeric esiaor and is ore efficien han.] he CAPM exaple and oher econoic exaples which ive rise o oen condiions of his for are provided in Chaper of Hall s exbook
5 he saple analoues of he r populaion oens EZ, are he r saple oens Z, he efficien esiaor of is: ar in Q where Q is he weihin arix Q ] ~ ~ / [ where ~ is any consisen esiaor of.
6 Noes. his esiaor will enerally have o be calculaed nuerically. See Ch. 3 of Hall s book for ore discussion of his. 2. o obain a preliinary consisen esiaor of we can apply inefficien. ha is, apply wih any p.d. Q, e.., Q I. An ieraive version of his esiaor ay work beer in applicaions alhouh here will be no asypoic ain o ierain.
7 Under suiable reulariy condiions, Ω G G N D where E and E G Ω Consisen esiaors of G and Ω: Ω and G
8 Overidenificaion es Assue r > k Under H : E, J where Χ D 2 r k J J Q Noe ha and Q are evaluaed here a.
9 esin Linear and/or Nonlinear Resricions on Consider a se of q linear and/or nonlinear resricions on. Le J J saisic fro he unresriced reression J,R J saisic fro he resriced s.. he sae Q arix used in forin J is also used in forin J,R. hen under he null hypohesis ha he q resricions are correc J 2, R J Χ q D
Lecture 10 Estimating Nonlinear Regression Models
Lecure 0 Esimaing Nonlinear Regression Models References: Greene, Economeric Analysis, Chaper 0 Consider he following regression model: y = f(x, β) + ε =,, x is kx for each, β is an rxconsan vecor, ε is
More informationIntroduction to Numerical Analysis. In this lesson you will be taken through a pair of techniques that will be used to solve the equations of.
Inroducion o Nuerical Analysis oion In his lesson you will be aen hrough a pair of echniques ha will be used o solve he equaions of and v dx d a F d for siuaions in which F is well nown, and he iniial
More informationDecision Tree Learning. Decision Tree Learning. Decision Trees. Decision Trees: Operation. Blue slides: Mitchell. Orange slides: Alpaydin Humidity
Decision Tree Learning Decision Tree Learning Blue slides: Michell Oulook Orange slides: Alpaydin Huidiy Sunny Overcas Rain ral Srong Learn o approxiae discree-valued arge funcions. Sep-by-sep decision
More informationOutline. lse-logo. Outline. Outline. 1 Wald Test. 2 The Likelihood Ratio Test. 3 Lagrange Multiplier Tests
Ouline Ouline Hypohesis Tes wihin he Maximum Likelihood Framework There are hree main frequenis approaches o inference wihin he Maximum Likelihood framework: he Wald es, he Likelihood Raio es and he Lagrange
More informationFINM 6900 Finance Theory
FINM 6900 Finance Theory Universiy of Queensland Lecure Noe 4 The Lucas Model 1. Inroducion In his lecure we consider a simple endowmen economy in which an unspecified number of raional invesors rade asses
More informationTesting the Random Walk Model. i.i.d. ( ) r
he random walk heory saes: esing he Random Walk Model µ ε () np = + np + Momen Condiions where where ε ~ i.i.d he idea here is o es direcly he resricions imposed by momen condiions. lnp lnp µ ( lnp lnp
More information1 Widrow-Hoff Algorithm
COS 511: heoreical Machine Learning Lecurer: Rob Schapire Lecure # 18 Scribe: Shaoqing Yang April 10, 014 1 Widrow-Hoff Algorih Firs le s review he Widrow-Hoff algorih ha was covered fro las lecure: Algorih
More informationIntroduction D P. r = constant discount rate, g = Gordon Model (1962): constant dividend growth rate.
Inroducion Gordon Model (1962): D P = r g r = consan discoun rae, g = consan dividend growh rae. If raional expecaions of fuure discoun raes and dividend growh vary over ime, so should he D/P raio. Since
More informationState-Space Models. Initialization, Estimation and Smoothing of the Kalman Filter
Sae-Space Models Iniializaion, Esimaion and Smoohing of he Kalman Filer Iniializaion of he Kalman Filer The Kalman filer shows how o updae pas predicors and he corresponding predicion error variances when
More informationProblem Set 5. Graduate Macro II, Spring 2017 The University of Notre Dame Professor Sims
Problem Se 5 Graduae Macro II, Spring 2017 The Universiy of Nore Dame Professor Sims Insrucions: You may consul wih oher members of he class, bu please make sure o urn in your own work. Where applicable,
More informationSZG Macro 2011 Lecture 3: Dynamic Programming. SZG macro 2011 lecture 3 1
SZG Macro 2011 Lecure 3: Dynamic Programming SZG macro 2011 lecure 3 1 Background Our previous discussion of opimal consumpion over ime and of opimal capial accumulaion sugges sudying he general decision
More informationACE 564 Spring Lecture 7. Extensions of The Multiple Regression Model: Dummy Independent Variables. by Professor Scott H.
ACE 564 Spring 2006 Lecure 7 Exensions of The Muliple Regression Model: Dumm Independen Variables b Professor Sco H. Irwin Readings: Griffihs, Hill and Judge. "Dumm Variables and Varing Coefficien Models
More informationBU Macro BU Macro Fall 2008, Lecture 4
Dynamic Programming BU Macro 2008 Lecure 4 1 Ouline 1. Cerainy opimizaion problem used o illusrae: a. Resricions on exogenous variables b. Value funcion c. Policy funcion d. The Bellman equaion and an
More information3.1.3 INTRODUCTION TO DYNAMIC OPTIMIZATION: DISCRETE TIME PROBLEMS. A. The Hamiltonian and First-Order Conditions in a Finite Time Horizon
3..3 INRODUCION O DYNAMIC OPIMIZAION: DISCREE IME PROBLEMS A. he Hamilonian and Firs-Order Condiions in a Finie ime Horizon Define a new funcion, he Hamilonian funcion, H. H he change in he oal value of
More informationMath 10B: Mock Mid II. April 13, 2016
Name: Soluions Mah 10B: Mock Mid II April 13, 016 1. ( poins) Sae, wih jusificaion, wheher he following saemens are rue or false. (a) If a 3 3 marix A saisfies A 3 A = 0, hen i canno be inverible. True.
More informationProblem set 2 for the course on. Markov chains and mixing times
J. Seif T. Hirscher Soluions o Proble se for he course on Markov chains and ixing ies February 7, 04 Exercise 7 (Reversible chains). (i) Assue ha we have a Markov chain wih ransiion arix P, such ha here
More informationE β t log (C t ) + M t M t 1. = Y t + B t 1 P t. B t 0 (3) v t = P tc t M t Question 1. Find the FOC s for an optimum in the agent s problem.
Noes, M. Krause.. Problem Se 9: Exercise on FTPL Same model as in paper and lecure, only ha one-period govenmen bonds are replaced by consols, which are bonds ha pay one dollar forever. I has curren marke
More informationAffine term structure models
Affine erm srucure models A. Inro o Gaussian affine erm srucure models B. Esimaion by minimum chi square (Hamilon and Wu) C. Esimaion by OLS (Adrian, Moench, and Crump) D. Dynamic Nelson-Siegel model (Chrisensen,
More informationMacroeconomic Theory Ph.D. Qualifying Examination Fall 2005 ANSWER EACH PART IN A SEPARATE BLUE BOOK. PART ONE: ANSWER IN BOOK 1 WEIGHT 1/3
Macroeconomic Theory Ph.D. Qualifying Examinaion Fall 2005 Comprehensive Examinaion UCLA Dep. of Economics You have 4 hours o complee he exam. There are hree pars o he exam. Answer all pars. Each par has
More informationDecision Tree Learning. Decision Tree Learning. Decision Trees. Decision Trees: Operation. Blue slides: Mitchell. Turquoise slides: Alpaydin Humidity
Decision Tree Learning Decision Tree Learning Blue slides: Michell Oulook Turquoise slides: Alpaydin Huidiy Sunny Overcas Rain ral Srong Learn o approxiae discree-valued arge funcions. Sep-y-sep decision
More informationDecision Tree Learning. Decision Tree Learning. Example. Decision Trees. Blue slides: Mitchell. Olive slides: Alpaydin Humidity
Decision Tree Learning Decision Tree Learning Blue slides: Michell Oulook Olive slides: Alpaydin Huidiy Sunny Overcas Rain Wind High ral Srong Weak Learn o approxiae discree-valued arge funcions. Sep-y-sep
More informationEstimates and Forecasts of GARCH Model under Misspecified Probability Distributions: A Monte Carlo Simulation Approach
Journal of Modern Applied Saisical Mehods Volue 3 Issue Aricle 8-04 Esiaes and Forecass of GARCH Model under Misspecified Probabiliy Disribuions: A Mone Carlo Siulaion Approach OlaOluwa S. Yaya Universiy
More information13.3 Term structure models
13.3 Term srucure models 13.3.1 Expecaions hypohesis model - Simples "model" a) shor rae b) expecaions o ge oher prices Resul: y () = 1 h +1 δ = φ( δ)+ε +1 f () = E (y +1) (1) =δ + φ( δ) f (3) = E (y +)
More informationPolynomial Adjustment Costs in FRB/US Flint Brayton, Morris Davis and Peter Tulip 1 May 2000
Polynoial Adjusen Coss in FRB/US Flin Brayon, Morris Davis and Peer Tulip 1 May 2000 The adjusen dynaics of os ajor nonfinancial variables in FRB/US are based on a fraework of polynoial adjusen coss, or
More informationErrata (1 st Edition)
P Sandborn, os Analysis of Elecronic Sysems, s Ediion, orld Scienific, Singapore, 03 Erraa ( s Ediion) S K 05D Page 8 Equaion (7) should be, E 05D E Nu e S K he L appearing in he equaion in he book does
More informationIntroduction to choice over time
Microeconomic Theory -- Choice over ime Inroducion o choice over ime Individual choice Income and subsiuion effecs 7 Walrasian equilibrium ineres rae 9 pages John Riley Ocober 9, 08 Microeconomic Theory
More informationThus the force is proportional but opposite to the displacement away from equilibrium.
Chaper 3 : Siple Haronic Moion Hooe s law saes ha he force (F) eered by an ideal spring is proporional o is elongaion l F= l where is he spring consan. Consider a ass hanging on a he spring. In equilibriu
More informationLecture Notes 5: Investment
Lecure Noes 5: Invesmen Zhiwei Xu (xuzhiwei@sju.edu.cn) Invesmen decisions made by rms are one of he mos imporan behaviors in he economy. As he invesmen deermines how he capials accumulae along he ime,
More informationEXPONENTIAL PROBABILITY DISTRIBUTION
MTH/STA 56 EXPONENTIAL PROBABILITY DISTRIBUTION As discussed in Exaple (of Secion of Unifor Probabili Disribuion), in a Poisson process, evens are occurring independenl a rando and a a unifor rae per uni
More informationThis document was generated at 1:04 PM, 09/10/13 Copyright 2013 Richard T. Woodward. 4. End points and transversality conditions AGEC
his documen was generaed a 1:4 PM, 9/1/13 Copyrigh 213 Richard. Woodward 4. End poins and ransversaliy condiions AGEC 637-213 F z d Recall from Lecure 3 ha a ypical opimal conrol problem is o maimize (,,
More informationOptimal Stopping of Partially Observable Markov Processes: A Filtering-Based Duality Approach
1 Opial Sopping of Parially Observable Marov Processes: A Filering-Based Dualiy Approach Fan Ye, and Enlu Zhou, Meber, IEEE Absrac In his noe we develop a nuerical approach o he proble of opial sopping
More informationANSWERS TO EVEN NUMBERED EXERCISES IN CHAPTER 6 SECTION 6.1: LIFE CYCLE CONSUMPTION AND WEALTH T 1. . Let ct. ) is a strictly concave function of c
John Riley December 00 S O EVEN NUMBERED EXERCISES IN CHAPER 6 SECION 6: LIFE CYCLE CONSUMPION AND WEALH Eercise 6-: Opimal saving wih more han one commodiy A consumer has a period uiliy funcion δ u (
More information1 Consumption and Risky Assets
Soluions o Problem Se 8 Econ 0A - nd Half - Fall 011 Prof David Romer, GSI: Vicoria Vanasco 1 Consumpion and Risky Asses Consumer's lifeime uiliy: U = u(c 1 )+E[u(c )] Income: Y 1 = Ȳ cerain and Y F (
More informationLicenciatura de ADE y Licenciatura conjunta Derecho y ADE. Hoja de ejercicios 2 PARTE A
Licenciaura de ADE y Licenciaura conjuna Derecho y ADE Hoja de ejercicios PARTE A 1. Consider he following models Δy = 0.8 + ε (1 + 0.8L) Δ 1 y = ε where ε and ε are independen whie noise processes. In
More informationHypothesis Testing in the Classical Normal Linear Regression Model. 1. Components of Hypothesis Tests
ECONOMICS 35* -- NOTE 8 M.G. Abbo ECON 35* -- NOTE 8 Hypohesis Tesing in he Classical Normal Linear Regression Model. Componens of Hypohesis Tess. A esable hypohesis, which consiss of wo pars: Par : a
More informationEcon Autocorrelation. Sanjaya DeSilva
Econ 39 - Auocorrelaion Sanjaya DeSilva Ocober 3, 008 1 Definiion Auocorrelaion (or serial correlaion) occurs when he error erm of one observaion is correlaed wih he error erm of any oher observaion. This
More informationGeneralized Least Squares
Generalized Leas Squares Augus 006 1 Modified Model Original assumpions: 1 Specificaion: y = Xβ + ε (1) Eε =0 3 EX 0 ε =0 4 Eεε 0 = σ I In his secion, we consider relaxing assumpion (4) Insead, assume
More information1. Consider a pure-exchange economy with stochastic endowments. The state of the economy
Answer 4 of he following 5 quesions. 1. Consider a pure-exchange economy wih sochasic endowmens. The sae of he economy in period, 0,1,..., is he hisory of evens s ( s0, s1,..., s ). The iniial sae is given.
More informationForecasting optimally
I) ile: Forecas Evaluaion II) Conens: Evaluaing forecass, properies of opimal forecass, esing properies of opimal forecass, saisical comparison of forecas accuracy III) Documenaion: - Diebold, Francis
More informationFinal Spring 2007
.615 Final Spring 7 Overview The purpose of he final exam is o calculae he MHD β limi in a high-bea oroidal okamak agains he dangerous n = 1 exernal ballooning-kink mode. Effecively, his corresponds o
More informationT. J. HOLMES AND T. J. KEHOE INTERNATIONAL TRADE AND PAYMENTS THEORY FALL 2011 EXAMINATION
ECON 841 T. J. HOLMES AND T. J. KEHOE INTERNATIONAL TRADE AND PAYMENTS THEORY FALL 211 EXAMINATION This exam has wo pars. Each par has wo quesions. Please answer one of he wo quesions in each par for a
More informationWEEK-3 Recitation PHYS 131. of the projectile s velocity remains constant throughout the motion, since the acceleration a x
WEEK-3 Reciaion PHYS 131 Ch. 3: FOC 1, 3, 4, 6, 14. Problems 9, 37, 41 & 71 and Ch. 4: FOC 1, 3, 5, 8. Problems 3, 5 & 16. Feb 8, 018 Ch. 3: FOC 1, 3, 4, 6, 14. 1. (a) The horizonal componen of he projecile
More informationTwo Coupled Oscillators / Normal Modes
Lecure 3 Phys 3750 Two Coupled Oscillaors / Normal Modes Overview and Moivaion: Today we ake a small, bu significan, sep owards wave moion. We will no ye observe waves, bu his sep is imporan in is own
More informationx y θ = 31.8 = 48.0 N. a 3.00 m/s
4.5.IDENTIY: Vecor addiion. SET UP: Use a coordinae sse where he dog A. The forces are skeched in igure 4.5. EXECUTE: + -ais is in he direcion of, A he force applied b =+ 70 N, = 0 A B B A = cos60.0 =
More informationProblem set 3: Endogenous Innovation - Solutions
Problem se 3: Endogenous Innovaion - Soluions Loïc Baé Ocober 25, 22 Opimaliy in he R & D based endogenous growh model Imporan feaure of his model: he monopoly markup is exogenous, so ha here is no need
More informationChapter 14 Wiener Processes and Itô s Lemma. Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull
Chaper 14 Wiener Processes and Iô s Lemma Copyrigh John C. Hull 014 1 Sochasic Processes! Describes he way in which a variable such as a sock price, exchange rae or ineres rae changes hrough ime! Incorporaes
More informationRobust estimation based on the first- and third-moment restrictions of the power transformation model
h Inernaional Congress on Modelling and Simulaion, Adelaide, Ausralia, 6 December 3 www.mssanz.org.au/modsim3 Robus esimaion based on he firs- and hird-momen resricions of he power ransformaion Nawaa,
More informationThis document was generated at 7:34 PM, 07/27/09 Copyright 2009 Richard T. Woodward
his documen was generaed a 7:34 PM, 07/27/09 Copyrigh 2009 Richard. Woodward 15. Bang-bang and mos rapid approach problems AGEC 637 - Summer 2009 here are some problems for which he opimal pah does no
More informationUnit Root Time Series. Univariate random walk
Uni Roo ime Series Univariae random walk Consider he regression y y where ~ iid N 0, he leas squares esimae of is: ˆ yy y y yy Now wha if = If y y hen le y 0 =0 so ha y j j If ~ iid N 0, hen y ~ N 0, he
More informationFinancial Econometrics Jeffrey R. Russell Midterm Winter 2009 SOLUTIONS
Name SOLUTIONS Financial Economerics Jeffrey R. Russell Miderm Winer 009 SOLUTIONS You have 80 minues o complee he exam. Use can use a calculaor and noes. Try o fi all your work in he space provided. If
More informationLast exit times for a class of asymptotically linear estimators
Las exi ies for a class of asypoically linear esiaors M. Alagh, M. Broniaowski 2, and G. Celan 3 Dépareen de Mahéaiques, Universié Louis Paseur, 4 Rue René Descares, 67000 Srasbourg, France 2 LSTA, Universié
More informationRiemann Hypothesis and Primorial Number. Choe Ryong Gil
Rieann Hyohesis Priorial Nuber Choe Ryong Gil Dearen of Maheaics Universiy of Sciences Gwahak- dong Unjong Disric Pyongyang DPRKorea Eail; ryonggilchoe@sar-conek Augus 8 5 Absrac; In his aer we consider
More informationA Consistent Nonparametric Test for Causality in Quantile
SFB 649 Discussion Paper 8-7 A Consisen Nonparaeric es for Causaliy in Quanile Kiho Jeong* Wolfgang Härdle** * Kyungpook Naional Universiy Daegu, Korea ** Hubold-Universiä zu Berlin, Gerany SFB 6 4 9 E
More informationGMM - Generalized Method of Moments
GMM - Generalized Mehod of Momens Conens GMM esimaion, shor inroducion 2 GMM inuiion: Maching momens 2 3 General overview of GMM esimaion. 3 3. Weighing marix...........................................
More information1. Calibration factor
Annex_C_MUBDandP_eng_.doc, p. of pages Annex C: Measureen uncerainy of he oal heigh of profile of a deph-seing sandard ih he sandard deviaion of he groove deph as opography er In his exaple, he uncerainy
More informationSeminar 4: Hotelling 2
Seminar 4: Hoelling 2 November 3, 211 1 Exercise Par 1 Iso-elasic demand A non renewable resource of a known sock S can be exraced a zero cos. Demand for he resource is of he form: D(p ) = p ε ε > A a
More informationVectorautoregressive Model and Cointegration Analysis. Time Series Analysis Dr. Sevtap Kestel 1
Vecorauoregressive Model and Coinegraion Analysis Par V Time Series Analysis Dr. Sevap Kesel 1 Vecorauoregression Vecor auoregression (VAR) is an economeric model used o capure he evoluion and he inerdependencies
More informationSection 4.4 Logarithmic Properties
Secion. Logarihmic Properies 59 Secion. Logarihmic Properies In he previous secion, we derived wo imporan properies of arihms, which allowed us o solve some asic eponenial and arihmic equaions. Properies
More informationEstocástica FINANZAS Y RIESGO
Sochasic discoun facor for Mexico and Chile... Esocásica Sochasic discoun facor for Mexico and Chile, a coninuous updaing esimaion approach Humbero Valencia Herrera Fecha de recepción: 2 de diciembre de
More informationComparing Means: t-tests for One Sample & Two Related Samples
Comparing Means: -Tess for One Sample & Two Relaed Samples Using he z-tes: Assumpions -Tess for One Sample & Two Relaed Samples The z-es (of a sample mean agains a populaion mean) is based on he assumpion
More informationREVIEW OF MAXIMUM LIKELIHOOD ESTIMATION
REVIEW OF MAXIMUM LIKELIHOOD ESIMAION [] Maximum Likelihood Esimaor () Cases in which θ (unknown parameer) is scalar Noaional Clarificaion: From now on, we denoe he rue alue of θ as θ o hen, iew θ as a
More informationMixed-frequency VAR models with Markov-switching dynamics
Mixed-frequency VAR odels wih Markov-swiching dynaics Maxio Caacho * Universidad de Murcia Absrac: This paper exends he Markov-swiching vecor auoregressive odels o accoodae boh he ypical lack of synchroniciy
More informationDISCRETE GRONWALL LEMMA AND APPLICATIONS
DISCRETE GRONWALL LEMMA AND APPLICATIONS JOHN M. HOLTE MAA NORTH CENTRAL SECTION MEETING AT UND 24 OCTOBER 29 Gronwall s lemma saes an inequaliy ha is useful in he heory of differenial equaions. Here is
More information) were both constant and we brought them from under the integral.
YIELD-PER-RECRUIT (coninued The yield-per-recrui model applies o a cohor, bu we saw in he Age Disribuions lecure ha he properies of a cohor do no apply in general o a collecion of cohors, which is wha
More informationEconomics 8105 Macroeconomic Theory Recitation 6
Economics 8105 Macroeconomic Theory Reciaion 6 Conor Ryan Ocober 11h, 2016 Ouline: Opimal Taxaion wih Governmen Invesmen 1 Governmen Expendiure in Producion In hese noes we will examine a model in which
More informationEnergy Storage Benchmark Problems
Energy Sorage Benchmark Problems Daniel F. Salas 1,3, Warren B. Powell 2,3 1 Deparmen of Chemical & Biological Engineering 2 Deparmen of Operaions Research & Financial Engineering 3 Princeon Laboraory
More information1 Answers to Final Exam, ECN 200E, Spring
1 Answers o Final Exam, ECN 200E, Spring 2004 1. A good answer would include he following elemens: The equiy premium puzzle demonsraed ha wih sandard (i.e ime separable and consan relaive risk aversion)
More information20. Applications of the Genetic-Drift Model
0. Applicaions of he Geneic-Drif Model 1) Deermining he probabiliy of forming any paricular combinaion of genoypes in he nex generaion: Example: If he parenal allele frequencies are p 0 = 0.35 and q 0
More informationAn Extension to the Tactical Planning Model for a Job Shop: Continuous-Time Control
An Exension o he Tacical Planning Model for a Job Shop: Coninuous-Tie Conrol Chee Chong. Teo, Rohi Bhanagar, and Sephen C. Graves Singapore-MIT Alliance, Nanyang Technological Univ., and Massachuses Insiue
More informationThe consumption-based determinants of the term structure of discount rates: Corrigendum. Christian Gollier 1 Toulouse School of Economics March 2012
The consumpion-based deerminans of he erm srucure of discoun raes: Corrigendum Chrisian Gollier Toulouse School of Economics March 0 In Gollier (007), I examine he effec of serially correlaed growh raes
More informationSolutions to Odd Number Exercises in Chapter 6
1 Soluions o Odd Number Exercises in 6.1 R y eˆ 1.7151 y 6.3 From eˆ ( T K) ˆ R 1 1 SST SST SST (1 R ) 55.36(1.7911) we have, ˆ 6.414 T K ( ) 6.5 y ye ye y e 1 1 Consider he erms e and xe b b x e y e b
More informationR t. C t P t. + u t. C t = αp t + βr t + v t. + β + w t
Exercise 7 C P = α + β R P + u C = αp + βr + v (a) (b) C R = α P R + β + w (c) Assumpions abou he disurbances u, v, w : Classical assumions on he disurbance of one of he equaions, eg. on (b): E(v v s P,
More informationChapter 5. Heterocedastic Models. Introduction to time series (2008) 1
Chaper 5 Heerocedasic Models Inroducion o ime series (2008) 1 Chaper 5. Conens. 5.1. The ARCH model. 5.2. The GARCH model. 5.3. The exponenial GARCH model. 5.4. The CHARMA model. 5.5. Random coefficien
More informationChapter 2. Models, Censoring, and Likelihood for Failure-Time Data
Chaper 2 Models, Censoring, and Likelihood for Failure-Time Daa William Q. Meeker and Luis A. Escobar Iowa Sae Universiy and Louisiana Sae Universiy Copyrigh 1998-2008 W. Q. Meeker and L. A. Escobar. Based
More informationOn Edgeworth Expansions in Generalized Urn Models
On Edgeworh Expansions in Generalized Urn Models Sh M Mirahedov Insiue of Maheaics and Inforaion Technologies Uzbeisan (E- ail: shirahedov@yahooco S Rao Jaalaadaa Universiy of California Sana Barbara USA
More informationA Bayesian Approach to Spectral Analysis
Chirped Signals A Bayesian Approach o Specral Analysis Chirped signals are oscillaing signals wih ime variable frequencies, usually wih a linear variaion of frequency wih ime. E.g. f() = A cos(ω + α 2
More information12: AUTOREGRESSIVE AND MOVING AVERAGE PROCESSES IN DISCRETE TIME. Σ j =
1: AUTOREGRESSIVE AND MOVING AVERAGE PROCESSES IN DISCRETE TIME Moving Averages Recall ha a whie noise process is a series { } = having variance σ. The whie noise process has specral densiy f (λ) = of
More informationLeast Favorable Compressed Sensing Problems for First Order Methods
eas Favorable Copressed Sensing Probles for Firs Order Mehods Arian Maleki Deparen of Elecrical and Copuer Engineering Rice Universiy Richard Baraniuk Deparen of Elecrical and Copuer Engineering Rice Universiy
More informationEcon107 Applied Econometrics Topic 7: Multicollinearity (Studenmund, Chapter 8)
I. Definiions and Problems A. Perfec Mulicollineariy Econ7 Applied Economerics Topic 7: Mulicollineariy (Sudenmund, Chaper 8) Definiion: Perfec mulicollineariy exiss in a following K-variable regression
More informationThe Brock-Mirman Stochastic Growth Model
c December 3, 208, Chrisopher D. Carroll BrockMirman The Brock-Mirman Sochasic Growh Model Brock and Mirman (972) provided he firs opimizing growh model wih unpredicable (sochasic) shocks. The social planner
More informationESTIMATION OF DYNAMIC PANEL DATA MODELS WHEN REGRESSION COEFFICIENTS AND INDIVIDUAL EFFECTS ARE TIME-VARYING
Inernaional Journal of Social Science and Economic Research Volume:02 Issue:0 ESTIMATION OF DYNAMIC PANEL DATA MODELS WHEN REGRESSION COEFFICIENTS AND INDIVIDUAL EFFECTS ARE TIME-VARYING Chung-ki Min Professor
More informationVehicle Arrival Models : Headway
Chaper 12 Vehicle Arrival Models : Headway 12.1 Inroducion Modelling arrival of vehicle a secion of road is an imporan sep in raffic flow modelling. I has imporan applicaion in raffic flow simulaion where
More informationModern Dynamic Asset Pricing Models
Modern Dynamic Asse Pricing Models Teaching Noes 6. Consumpion, Porfolio Allocaion and Equilibrium wih Consrains 1 Piero Veronesi Universiy of Chicago CEPR, NBER 1 These eaching noes draw heavily on Cuoco
More informationBias in Conditional and Unconditional Fixed Effects Logit Estimation: a Correction * Tom Coupé
Bias in Condiional and Uncondiional Fixed Effecs Logi Esimaion: a Correcion * Tom Coupé Economics Educaion and Research Consorium, Naional Universiy of Kyiv Mohyla Academy Address: Vul Voloska 10, 04070
More informationRational Bubbles in Non-Linear Business Cycle Models. Robert Kollmann Université Libre de Bruxelles & CEPR
Raional Bubbles in Non-Linear Business Cycle Models Rober Kollmann Universié Libre de Bruxelles & CEPR April 9, 209 Main resul: non-linear DSGE models have more saionary equilibria han you hink! Blanchard
More informationHow to Deal with Structural Breaks in Practical Cointegration Analysis
How o Deal wih Srucural Breaks in Pracical Coinegraion Analysis Roselyne Joyeux * School of Economic and Financial Sudies Macquarie Universiy December 00 ABSTRACT In his noe we consider he reamen of srucural
More information1 Price Indexation and In ation Inertia
Lecures on Moneary Policy, In aion and he Business Cycle Moneary Policy Design: Exensions [0/05 Preliminary and Incomplee/Do No Circulae] Jordi Galí Price Indexaion and In aion Ineria. In aion Dynamics
More informationDEPARTMENT OF STATISTICS
A Tes for Mulivariae ARCH Effecs R. Sco Hacker and Abdulnasser Haemi-J 004: DEPARTMENT OF STATISTICS S-0 07 LUND SWEDEN A Tes for Mulivariae ARCH Effecs R. Sco Hacker Jönköping Inernaional Business School
More informationUnderwater vehicles: The minimum time problem
Underwaer vehicles: The iniu ie proble M. Chyba Deparen of Maheaics 565 McCarhy Mall Universiy of Hawaii, Honolulu, HI 968 Eail: chyba@ah.hawaii.edu H. Sussann Deparen of Maheaics Rugers Universiy, Piscaaway,
More informationModeling Economic Time Series with Stochastic Linear Difference Equations
A. Thiemer, SLDG.mcd, 6..6 FH-Kiel Universiy of Applied Sciences Prof. Dr. Andreas Thiemer e-mail: andreas.hiemer@fh-kiel.de Modeling Economic Time Series wih Sochasic Linear Difference Equaions Summary:
More informationα = relative risk aversion
BRAV CONSTANTNDES AND GECZY (BCG) Lucas model [ ] E R = Whils providin rea inuiion has enerally been rejeced by he empirical sudies. BCG do wo hins. ) Relax assumpion of complee consumpion insurance No
More informationStatistics and Probability Letters
Saisics and Probabiliy Leers 82 (2012) 998 1004 Conens liss available a SciVerse ScienceDirec Saisics and Probabiliy Leers journal hoepage: www.elsevier.co/locae/sapro Fiing birh-and-deah queueing odels
More informationConduction Equation. Consider an arbitrary volume V bounded by a surface S. Let any point on the surface be denoted r s
Conducion Equaion Consider an arbirary volue V bounded by a surface S. Le any poin on he surface be denoed r s and n be he uni ouward noral vecor o he surface a ha poin. Assue no flow ino or ou of V across
More informationLecture 23 Damped Motion
Differenial Equaions (MTH40) Lecure Daped Moion In he previous lecure, we discussed he free haronic oion ha assues no rearding forces acing on he oving ass. However No rearding forces acing on he oving
More informationLecture 4 Notes (Little s Theorem)
Lecure 4 Noes (Lile s Theorem) This lecure concerns one of he mos imporan (and simples) heorems in Queuing Theory, Lile s Theorem. More informaion can be found in he course book, Bersekas & Gallagher,
More informationCooperative Ph.D. Program in School of Economic Sciences and Finance QUALIFYING EXAMINATION IN MACROECONOMICS. August 8, :45 a.m. to 1:00 p.m.
Cooperaive Ph.D. Program in School of Economic Sciences and Finance QUALIFYING EXAMINATION IN MACROECONOMICS Augus 8, 213 8:45 a.m. o 1: p.m. THERE ARE FIVE QUESTIONS ANSWER ANY FOUR OUT OF FIVE PROBLEMS.
More informationLecture 20: Riccati Equations and Least Squares Feedback Control
34-5 LINEAR SYSTEMS Lecure : Riccai Equaions and Leas Squares Feedback Conrol 5.6.4 Sae Feedback via Riccai Equaions A recursive approach in generaing he marix-valued funcion W ( ) equaion for i for he
More informationTesting for a Single Factor Model in the Multivariate State Space Framework
esing for a Single Facor Model in he Mulivariae Sae Space Framework Chen C.-Y. M. Chiba and M. Kobayashi Inernaional Graduae School of Social Sciences Yokohama Naional Universiy Japan Faculy of Economics
More informationKalman filtering for maximum likelihood estimation given corrupted observations.
alman filering maimum likelihood esimaion given corruped observaions... Holmes Naional Marine isheries Service Inroducion he alman filer is used o eend likelihood esimaion o cases wih hidden saes such
More information2. Nonlinear Conservation Law Equations
. Nonlinear Conservaion Law Equaions One of he clear lessons learned over recen years in sudying nonlinear parial differenial equaions is ha i is generally no wise o ry o aack a general class of nonlinear
More information