Economics 140A Hypothesis Testing in Regression Models

Save this PDF as:

Size: px
Start display at page:

Transcription

1 Economics 140A Hypohesis Tesing in Regression Models While i is algebraically simple o work wih a populaion model wih a single varying regressor, mos populaion models have muliple varying regressors 1 + X + + k X k + U The classic assumpions are virually una eced by he presence of muliple varying regressors. The only change is ha we now assume ha here is no mulicollineariy among he regressors. The coe ciens have he inerpreaion of parial derivaives The coe cien measures he e ec on of a one uni change in X holding all oher regressors consan. Esimaion of he model is exacly as before (here is no simpliciy gained by working in deviaion-from-means form), so he OLS coe cien esimaors are (B 1 B k ) arg min ~B 1 ~ B k ~ B1 ~ B X ~ Bk X k As we discussed earlier, he probabiliy ha B i i is zero, so we do no rely on poin esimaes alone. Raher we focus on inerval esimaes, which conain informaion boh abou he variance and he shape of he disribuion of he esimaor. There is an ineresing parallel beween he model wih one regressor and he model wih muliple regressors. For he model wih one regressor he variance of he esimaor of he coe cien on X 1 is V (B 1 ) X 1 X 1 For he model wih muliple regressors V (B 1 ) S 1

2 where S 1 is he sum of squared residuals afer regressing X 1 on a consan and he oher regressors. We see ha he denominaor of he variance for he single regressor model is simply he sum of squared residuals from regressing X 1 on a consan. Con dence Inervals To make clear ha a con dence inerval depends on he shape of he esimaor s disribuion consider a con dence inerval for he esimaor of he regression error variance. The esimaor of is S 1 n n k U. Noe (n k) S n k From he abulaed values of n a k (n k) S c 95 Sep 1 Sep 1 c (n k) S 1 95 a (n k) S (n c a k) S Thus, 95 percen of he random inervals of he form (n k) S (n k) S c a 95 conain. How should one choose he criical values a and c? Because he n k disribuion is skew, here are wo ways o choose he criical values. The rs way is o choose equal-ailed criical values for which (n k)s (n k)s a c 05. The second way is o selec he criical values o minimize he disance c a. (The wo ways are idenical for a symmeric disribuion.) Inser he picure from page 7 of he noes. To undersand he impor of criical value selecion, consider he following

3 Example. Le n k 18 and s 36. From he abulaed values of 18 we deermine he equal-ailed criical values (n k) S (n k) S wih Also (by grid search) we deermine he criical values ha minimize heir di erence (n k) S (n k) S and wih The logic ha we wish o consruc he shores con dence inerval seems o poin o he second way. Wha are he wo con dence inervals? For he equal-ailed criical values, he con dence inerval is (06 790) wih lengh For he shores disance criical values, he con - dence inerval is (17 913) wih lengh The shorer inerval is obained wih he equalailed criical values! Why? Because he con dence inerval is no a linear funcion of he criical values ( 1 and 1 appear raher han a and c), so he shores criical a c value inerval does no yield he shores con dence inerval. Hypohesis Tesing While inerval esimaion is ofen done wihou a speci c hypohesis in mind, he esimaed inerval is easily used o es a hypohesis. Recall ha for hypohesis esing we rs deermine he null hypohesis and he alernaive in such a way ha rejecion of he null hypohesis (in favor of he alernaive hypohesis) is a conclusion of ineres. Consider he populaion regression model in which he dependen variable is consumpion of a paricular good and he regressor of ineres is income. We wish o esablish if increases in income a ec consumpion of he good, bu we are fairly cerain ha increases in income do no decrease consumpion of he good. The null hypohesis H 0 0 3

4 is esed agains he one-sided alernaive H 1 > 0 Coe cien Esimaor Tes Saisics As we have seen, we examine he sample daa o see if he esimae is large enough ha we may rejec he null hypohesis. How large is large enough o be saisically persuasive? We mus deermine a bound, such ha if he esimae is a leas as large as he bound, he esimae would cause us o rejec he null hypohesis. Again B N (0 1) B where B is he variance of B. Recall ha we begin by deermining a region for which we do no rejec he null hypohesis (for he wo-sided alernaive, ( )). For he one-sided alernaive a es, he region for which we do no rejec he null will be ( 1 c), where c is he larges value we feel is consisen wih he null hypohesis. From abulaed values of N (0 1), an upper bound for is obained from B B Sep 1 Sep Sep 3 (B 165 B ) 95 ( B B ) 95 (B 165 B ) 95 Thus, 95 percen of random inervals of he form (B 165 B 1) conain. In oher words, 95 percen of he random values B 165 B are less han or equal o. Because is very likely o be a leas as large as he lower bound, we are con den ha if he esimaed lower bound is larger han zero hen he null hypohesis is false. 4

5 For a given sample, we have he esimae b. If we replace he random esimaor wih he xed esimae, hen he 95 percen (one-sided) con dence inerval is (b 165 B 1) or he 95 percen lower con dence bound is b 165 B. To es he null hypohesis, we check o see if he lower con dence bound is posiive. If he lower con dence bound is posiive, we rejec he null hypohesis. We do so because we have 95 percen con dence ha he populaion value is larger han he lower con dence bound, so we have 95 percen con dence ha he populaion value is posiive. If he lower con dence bound is no posiive, hen he null value of zero lies in our con dence inerval and so we fail o rejec he null hypohesis. I is also sraighforward o perform hypohesis ess on sums (or di erences) of coe ciens. Consider a es ha wo coe ciens are equal ( 1 ) H agains H The null hypohesis is rejeced if he con dence inerval formed from 195 B 1 B B1 B does no conain 0. Noe B 1 B V (B 1 ) + V (B ) C (B 1 B ) Likelihood Tes Saisics While con dence inervals are one way of esing hypoheses, oher ess are available. For wo-sided alernaives here is also he likelihood-raio es saisic. Consider a es of H 0 0 agains H The likelihood-raio es saisic is consruced by esimaing he model under he null and alernaive hypoheses. Le L be he likelihood funcion wih in he model and le L R be he likelihood funcion wih excluded from he model (ha is, H 0 0 is imposed). The likelihood-raio es saisic LR ln L 1 5

6 where he single degree-of-freedom re ecs he fac ha only one resricion is imposed on he resriced model. If he null hypohesis is correc, hen L R ' L and he es saisic is close o zero. If he null hypohesis is false, hen L R < L and he es saisic will be larger han zero. We rejec he null hypohesis if he esimaed es saisic exceeds he criical value. Finally, one should noe he di erence beween saisical signi cance and economic signi cance. I may be he case ha an esimaed coe cien is saisically signi can, ye he magniude of he erm is so small ha i has lile or no e ec on he dependen variable. Sum of Squares Decomposiion While speci caion of a model is mos ofen based on heoreical grounds, i is imporan o have some measure of he overall adequacy of he model in explaining he movemens in he dependen variable. The baseline for comparison is he model wihou heoreical regressors 0 + U For such a model, he predicion for each value of is he consan 0, where he OLS esimaor of 0 is B 0 1 Y n 1 Any improvemen aribued o heoreical regressors requires ha we explain he variaion Yn. The oal variaion in he sample, ofen ermed he oal sum-of-squares, is Yn To derive an expression for he oal sum-of-squares, we consider he model wih a single regressor. The unexplained sum-of-squares, which is he variaion no explained by he model, is Y ( B 0 B 1 X ) Yn B 1 X Xn Yn B 1 6 Yn X Xn + B 1 X Xn

7 From he de niion of B 1, he las erm cancels wih par of he middle erm, hus Y Yn B 1 Yn X Xn where he las erm on he righ is he variaion explained by he heoreical regressors (ermed he explained sum-of-squares). We have ha he oal sumof-squares is equal o he explained sum-of-squares plus he unexplained sum-ofsquares. One of he mos common measures of model adequacy is he raio of explained variaion o oal variaion, ofen ermed R squared, R Y Because he OLS esimaors minimize he sum of squared residuals, hey maximize R. Tha is, he OLS esimaors are he esimaors ha resul in he highes degree of explained variaion. As indicaed by he above derivaion, 0 R 1. Ye i is possible o have compuer oupu wih a negaive esimae of R. How so? Consider a regression model wih he inercep omied. A correc program calculaes R as R 1 Y which is conained in [0 1]. Ye some programs err by including an inercep in he oal sum of squares calculaion R 1 Y for which i is possible ha Y Y > n Y. Include graph from aached yellow ruled shee numbered page 8 Because 1 + X + + K X K 1 + U will exacly any sample of K observaions of (X ), inclusion of heoreically irrelevan regressors will increase R. Mos regression model esimaes repor 7

8 anoher measure, he adjused R in which he explanaory power of an addiional regressor is raded o agains he loss of one degree-of-freedom R A (Y n K ) ( Yn) A imes i is useful o sudy he signi cance of he proposed populaion regression model. The signi cance of he proposed model is under es wih n 1 H 0 3 K 0 agains H 1 no H 0 where he alernaive hypohesis is ha a leas one coe cien is no zero. If K, hen we have only a single coe cien o es and a naural es saisic is he coe cien esimaor es saisic B 0 S B wih S B h n S X i 1 X We could, equivalenly, use he square of he coe cien esimaor es saisic B n X X S which has an F 1n disribuion. (Fac If he random variable Z has a disribuion wih n degrees-of-freedom, hen Z has an F 1n disribuion.) If K >, hen a single coe cien esimaor is no available (nor or ransformaions as B B 3 0 does no impose he resricion ha boh coe ciens are zero). Raher we noe ha he numeraor of he squared coe cien esimaor es saisic is simply Y, which can be consruced for K >. In deail, because he ed values conain he sample mean, so Y (B1 + B X + + B K X K ) B 1 + B X + + B KXK KX k1 B k X k Xk 8

9 Hence he coe cien esimaor es saisic is (Y ) K 1 S If he null hypohesis is rue, hen he numeraor of he es saisic will be close o zero, so we rejec he null hypohesis if he es saisic exceeds he criical value from he F K 1n K disribuion. As one would surmise, he es saisic can be wrien in erms of R as (Y K 1 ) n K S K 1 n K K 1 (U ) n K R K 1 1 R The es saisic is an increasing funcion of R. redicion Y Y A goal of regression esimaion is predicion of he dependen variable. Consider a model wih K. Given a value of he regressor (eiher from he sample or ou of he sample) X, he corresponding predicion of he dependen variable is Y B 1 + B X. To be useful, he poin predicion mus be accompanied by a measure of uncerainy. The variance of he predicion is V Y V (B1 ) + V (B ) X + C (B 1 B ) X + V (U ) X n X " 1 n + + X n X n + X Xn X # + X! X Xn n X X X Xn n X X + X + Thus a 95 percen con dence inerval for he prediced values is no parallel o he regression line, bu raher increases in widh as he disance from he sample mean 9

10 increases. Noe, if here is more han one regressor, hen he con dence inerval does no necessarily increase as he disance from he sample means increases. This follows because he variance of he predicion conains he covariance beween he regressors, which can be negaive. Noe, ha if one wished o remove he e ec of he idiosyncraic error U, which implies ha we are predicing E ( jx ) raher han jx, he variance is lowered by he amoun (he quaniy V (U ) is eliminaed because EU 0). 10

Chapter 8: Regression with Lagged Explanatory Variables

Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One

Chapter 7. Response of First-Order RL and RC Circuits

Chaper 7. esponse of Firs-Order L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural

Cointegration: The Engle and Granger approach

Coinegraion: The Engle and Granger approach Inroducion Generally one would find mos of he economic variables o be non-saionary I(1) variables. Hence, any equilibrium heories ha involve hese variables require

Vector Autoregressions (VARs): Operational Perspectives

Vecor Auoregressions (VARs): Operaional Perspecives Primary Source: Sock, James H., and Mark W. Wason, Vecor Auoregressions, Journal of Economic Perspecives, Vol. 15 No. 4 (Fall 2001), 101-115. Macroeconomericians

Stability. Coefficients may change over time. Evolution of the economy Policy changes

Sabiliy Coefficiens may change over ime Evoluion of he economy Policy changes Time Varying Parameers y = α + x β + Coefficiens depend on he ime period If he coefficiens vary randomly and are unpredicable,

Appendix A: Area. 1 Find the radius of a circle that has circumference 12 inches.

Appendi A: Area worked-ou s o Odd-Numbered Eercises Do no read hese worked-ou s before aemping o do he eercises ourself. Oherwise ou ma mimic he echniques shown here wihou undersanding he ideas. Bes wa

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is \$613.

Graduae School of Business Adminisraion Universiy of Virginia UVA-F-38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised

Mathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)

Mahemaics in Pharmacokineics Wha and Why (A second aemp o make i clearer) We have used equaions for concenraion () as a funcion of ime (). We will coninue o use hese equaions since he plasma concenraions

Issues Using OLS with Time Series Data. Time series data NOT randomly sampled in same way as cross sectional each obs not i.i.d

These noes largely concern auocorrelaion Issues Using OLS wih Time Series Daa Recall main poins from Chaper 10: Time series daa NOT randomly sampled in same way as cross secional each obs no i.i.d Why?

AP Calculus AB 2013 Scoring Guidelines

AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a mission-driven no-for-profi organizaion ha connecs sudens o college success and opporuniy. Founded in 19, he College Board was

Multiple Structural Breaks in the Nominal Interest Rate and Inflation in Canada and the United States

Deparmen of Economics Discussion Paper 00-07 Muliple Srucural Breaks in he Nominal Ineres Rae and Inflaion in Canada and he Unied Saes Frank J. Akins, Universiy of Calgary Preliminary Draf February, 00

Fakultet for informasjonsteknologi, Institutt for matematiske fag

Page 1 of 5 NTNU Noregs eknisk-naurviskaplege universie Fakule for informasjonseknologi, maemaikk og elekroeknikk Insiu for maemaiske fag - English Conac during exam: John Tyssedal 73593534/41645376 Exam

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)

Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer

Chapter 2 Problems. s = d t up. = 40km / hr d t down. 60km / hr. d t total. + t down. = t up. = 40km / hr + d. 60km / hr + 40km / hr

Chaper 2 Problems 2.2 A car ravels up a hill a a consan speed of 40km/h and reurns down he hill a a consan speed of 60 km/h. Calculae he average speed for he rip. This problem is a bi more suble han i

Revisions to Nonfarm Payroll Employment: 1964 to 2011

Revisions o Nonfarm Payroll Employmen: 1964 o 2011 Tom Sark December 2011 Summary Over recen monhs, he Bureau of Labor Saisics (BLS) has revised upward is iniial esimaes of he monhly change in nonfarm

Chabot College Physics Lab RC Circuits Scott Hildreth

Chabo College Physics Lab Circuis Sco Hildreh Goals: Coninue o advance your undersanding of circuis, measuring resisances, currens, and volages across muliple componens. Exend your skills in making breadboard

Permutations and Combinations

Permuaions and Combinaions Combinaorics Copyrigh Sandards 006, Tes - ANSWERS Barry Mabillard. 0 www.mah0s.com 1. Deermine he middle erm in he expansion of ( a b) To ge he k-value for he middle erm, divide

A Probability Density Function for Google s stocks

A Probabiliy Densiy Funcion for Google s socks V.Dorobanu Physics Deparmen, Poliehnica Universiy of Timisoara, Romania Absrac. I is an approach o inroduce he Fokker Planck equaion as an ineresing naural

Part 1: White Noise and Moving Average Models

Chaper 3: Forecasing From Time Series Models Par 1: Whie Noise and Moving Average Models Saionariy In his chaper, we sudy models for saionary ime series. A ime series is saionary if is underlying saisical

Journal Of Business & Economics Research September 2005 Volume 3, Number 9

Opion Pricing And Mone Carlo Simulaions George M. Jabbour, (Email: jabbour@gwu.edu), George Washingon Universiy Yi-Kang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo

Chapter 2 Kinematics in One Dimension

Chaper Kinemaics in One Dimension Chaper DESCRIBING MOTION:KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings moe how far (disance and displacemen), how fas (speed and elociy), and how

RESTRICTIONS IN REGRESSION MODEL

RESTRICTIONS IN REGRESSION MODEL Seema Jaggi and N. Sivaramane IASRI, Library Avenue, New Delhi-11001 seema@iasri.res.in; sivaramane@iasri.res.in Regression analysis is used o esablish a relaionship via

Hedging with Forwards and Futures

Hedging wih orwards and uures Hedging in mos cases is sraighforward. You plan o buy 10,000 barrels of oil in six monhs and you wish o eliminae he price risk. If you ake he buy-side of a forward/fuures

The Transport Equation

The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be

Chapter 4: Exponential and Logarithmic Functions

Chaper 4: Eponenial and Logarihmic Funcions Secion 4.1 Eponenial Funcions... 15 Secion 4. Graphs of Eponenial Funcions... 3 Secion 4.3 Logarihmic Funcions... 4 Secion 4.4 Logarihmic Properies... 53 Secion

4. International Parity Conditions

4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency

Chapter 8 Student Lecture Notes 8-1

Chaper Suden Lecure Noes - Chaper Goals QM: Business Saisics Chaper Analyzing and Forecasing -Series Daa Afer compleing his chaper, you should be able o: Idenify he componens presen in a ime series Develop

Supplementary Appendix for Depression Babies: Do Macroeconomic Experiences Affect Risk-Taking?

Supplemenary Appendix for Depression Babies: Do Macroeconomic Experiences Affec Risk-Taking? Ulrike Malmendier UC Berkeley and NBER Sefan Nagel Sanford Universiy and NBER Sepember 2009 A. Deails on SCF

A Mathematical Description of MOSFET Behavior

10/19/004 A Mahemaical Descripion of MOSFET Behavior.doc 1/8 A Mahemaical Descripion of MOSFET Behavior Q: We ve learned an awful lo abou enhancemen MOSFETs, bu we sill have ye o esablished a mahemaical

COMPUTATION OF CENTILES AND Z-SCORES FOR HEIGHT-FOR-AGE, WEIGHT-FOR-AGE AND BMI-FOR-AGE

COMPUTATION OF CENTILES AND Z-SCORES FOR HEIGHT-FOR-AGE, WEIGHT-FOR-AGE AND BMI-FOR-AGE The mehod used o consruc he 2007 WHO references relied on GAMLSS wih he Box-Cox power exponenial disribuion (Rigby

WHAT ARE OPTION CONTRACTS?

WHAT ARE OTION CONTRACTS? By rof. Ashok anekar An oion conrac is a derivaive which gives he righ o he holder of he conrac o do 'Somehing' bu wihou he obligaion o do ha 'Somehing'. The 'Somehing' can be

Differential Equations and Linear Superposition

Differenial Equaions and Linear Superposiion Basic Idea: Provide soluion in closed form Like Inegraion, no general soluions in closed form Order of equaion: highes derivaive in equaion e.g. dy d dy 2 y

AP Calculus BC 2010 Scoring Guidelines

AP Calculus BC Scoring Guidelines The College Board The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in, he College Board

MTH6121 Introduction to Mathematical Finance Lesson 5

26 MTH6121 Inroducion o Mahemaical Finance Lesson 5 Conens 2.3 Brownian moion wih drif........................... 27 2.4 Geomeric Brownian moion........................... 28 2.5 Convergence of random

THE PRESSURE DERIVATIVE

Tom Aage Jelmer NTNU Dearmen of Peroleum Engineering and Alied Geohysics THE PRESSURE DERIVATIVE The ressure derivaive has imoran diagnosic roeries. I is also imoran for making ye curve analysis more reliable.

TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS

TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS RICHARD J. POVINELLI AND XIN FENG Deparmen of Elecrical and Compuer Engineering Marquee Universiy, P.O.

RC, RL and RLC circuits

Name Dae Time o Complee h m Parner Course/ Secion / Grade RC, RL and RLC circuis Inroducion In his experimen we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors.

Chapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m

Chaper 2 Problems 2.1 During a hard sneeze, your eyes migh shu for 0.5s. If you are driving a car a 90km/h during such a sneeze, how far does he car move during ha ime s = 90km 1000m h 1km 1h 3600s = 25m

CHARGE AND DISCHARGE OF A CAPACITOR

REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:

Density Dependence. births are a decreasing function of density b(n) and deaths are an increasing function of density d(n).

FW 662 Densiy-dependen populaion models In he previous lecure we considered densiy independen populaion models ha assumed ha birh and deah raes were consan and no a funcion of populaion size. Long-erm

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE

Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees

Random Walk in 1-D. 3 possible paths x vs n. -5 For our random walk, we assume the probabilities p,q do not depend on time (n) - stationary

Random Walk in -D Random walks appear in many cones: diffusion is a random walk process undersanding buffering, waiing imes, queuing more generally he heory of sochasic processes gambling choosing he bes

AP Calculus AB 2007 Scoring Guidelines

AP Calculus AB 7 Scoring Guidelines The College Board: Connecing Sudens o College Success The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and

Price elasticity of demand for crude oil: estimates for 23 countries

Price elasiciy of demand for crude oil: esimaes for 23 counries John C.B. Cooper Absrac This paper uses a muliple regression model derived from an adapaion of Nerlove s parial adjusmen model o esimae boh

House Price Index (HPI)

House Price Index (HPI) The price index of second hand houses in Colombia (HPI), regisers annually and quarerly he evoluion of prices of his ype of dwelling. The calculaion is based on he repeaed sales

Capacitors and inductors

Capaciors and inducors We coninue wih our analysis of linear circuis by inroducing wo new passive and linear elemens: he capacior and he inducor. All he mehods developed so far for he analysis of linear

Full-wave rectification, bulk capacitor calculations Chris Basso January 2009

ull-wave recificaion, bulk capacior calculaions Chris Basso January 9 This shor paper shows how o calculae he bulk capacior value based on ripple specificaions and evaluae he rms curren ha crosses i. oal

Time Series Analysis Using SAS R Part I The Augmented Dickey-Fuller (ADF) Test

ABSTRACT Time Series Analysis Using SAS R Par I The Augmened Dickey-Fuller (ADF) Tes By Ismail E. Mohamed The purpose of his series of aricles is o discuss SAS programming echniques specifically designed

Answer, Key Homework 2 David McIntyre 45123 Mar 25, 2004 1

Answer, Key Homework 2 Daid McInyre 4123 Mar 2, 2004 1 This prin-ou should hae 1 quesions. Muliple-choice quesions may coninue on he ne column or page find all choices before making your selecion. The

SURVEYING THE RELATIONSHIP BETWEEN STOCK MARKET MAKER AND LIQUIDITY IN TEHRAN STOCK EXCHANGE COMPANIES

Inernaional Journal of Accouning Research Vol., No. 7, 4 SURVEYING THE RELATIONSHIP BETWEEN STOCK MARKET MAKER AND LIQUIDITY IN TEHRAN STOCK EXCHANGE COMPANIES Mohammad Ebrahimi Erdi, Dr. Azim Aslani,

The Real Business Cycle paradigm. The RBC model emphasizes supply (technology) disturbances as the main source of

Prof. Harris Dellas Advanced Macroeconomics Winer 2001/01 The Real Business Cycle paradigm The RBC model emphasizes supply (echnology) disurbances as he main source of macroeconomic flucuaions in a world

A Further Examination of Insurance Pricing and Underwriting Cycles

A Furher Examinaion of Insurance ricing and Underwriing Cycles AFIR Conference, Sepember 2005, Zurich, Swizerland Chris K. Madsen, GE Insurance Soluions, Copenhagen, Denmark Svend Haasrup, GE Insurance

A Re-examination of the Joint Mortality Functions

Norh merican cuarial Journal Volume 6, Number 1, p.166-170 (2002) Re-eaminaion of he Join Morali Funcions bsrac. Heekung Youn, rkad Shemakin, Edwin Herman Universi of S. Thomas, Sain Paul, MN, US Morali

Name: Algebra II Review for Quiz #13 Exponential and Logarithmic Functions including Modeling

Name: Algebra II Review for Quiz #13 Exponenial and Logarihmic Funcions including Modeling TOPICS: -Solving Exponenial Equaions (The Mehod of Common Bases) -Solving Exponenial Equaions (Using Logarihms)

Aggregate Output. Aggregate Output. Topics. Aggregate Output. Aggregate Output. Aggregate Output

Topics (Sandard Measure) GDP vs GPI discussion Macroeconomic Variables (Unemploymen and Inflaion Rae) (naional income and produc accouns, or NIPA) Gross Domesic Produc (GDP) The value of he final goods

When Is Growth Pro-Poor? Evidence from a Panel of Countries

Forhcoming, Journal of Developmen Economics When Is Growh Pro-Poor? Evidence from a Panel of Counries Aar Kraay The World Bank Firs Draf: December 2003 Revised: December 2004 Absrac: Growh is pro-poor

RC (Resistor-Capacitor) Circuits. AP Physics C

(Resisor-Capacior Circuis AP Physics C Circui Iniial Condiions An circui is one where you have a capacior and resisor in he same circui. Suppose we have he following circui: Iniially, he capacior is UNCHARGED

BALANCE OF PAYMENTS. First quarter 2008. Balance of payments

BALANCE OF PAYMENTS DATE: 2008-05-30 PUBLISHER: Balance of Paymens and Financial Markes (BFM) Lena Finn + 46 8 506 944 09, lena.finn@scb.se Camilla Bergeling +46 8 506 942 06, camilla.bergeling@scb.se

Acceleration Lab Teacher s Guide

Acceleraion Lab Teacher s Guide Objecives:. Use graphs of disance vs. ime and velociy vs. ime o find acceleraion of a oy car.. Observe he relaionship beween he angle of an inclined plane and he acceleraion

Morningstar Investor Return

Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion

Two Compartment Body Model and V d Terms by Jeff Stark

Two Comparmen Body Model and V d Terms by Jeff Sark In a one-comparmen model, we make wo imporan assumpions: (1) Linear pharmacokineics - By his, we mean ha eliminaion is firs order and ha pharmacokineic

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements

Inroducion Chaper 14: Dynamic D-S dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuing-edge

Factors Affecting Initial Enrollment Intensity: Part-Time versus Full-Time Enrollment

acors Affecing Iniial Enrollmen Inensiy: ar-time versus ull-time Enrollmen By Leslie S. Sraon Associae rofessor Dennis M. O Toole Associae rofessor James N. Wezel rofessor Deparmen of Economics Virginia

Imagine a Source (S) of sound waves that emits waves having frequency f and therefore

heoreical Noes: he oppler Eec wih ound Imagine a ource () o sound waes ha emis waes haing requency and hereore period as measured in he res rame o he ource (). his means ha any eecor () ha is no moing

5.8 Resonance 231. The study of vibrating mechanical systems ends here with the theory of pure and practical resonance.

5.8 Resonance 231 5.8 Resonance The sudy of vibraing mechanical sysems ends here wih he heory of pure and pracical resonance. Pure Resonance The noion of pure resonance in he differenial equaion (1) ()

Chapter 2: Principles of steady-state converter analysis

Chaper 2 Principles of Seady-Sae Converer Analysis 2.1. Inroducion 2.2. Inducor vol-second balance, capacior charge balance, and he small ripple approximaion 2.3. Boos converer example 2.4. Cuk converer

9. Capacitor and Resistor Circuits

ElecronicsLab9.nb 1 9. Capacior and Resisor Circuis Inroducion hus far we have consider resisors in various combinaions wih a power supply or baery which provide a consan volage source or direc curren

Why Did the Demand for Cash Decrease Recently in Korea?

Why Did he Demand for Cash Decrease Recenly in Korea? Byoung Hark Yoo Bank of Korea 26. 5 Absrac We explores why cash demand have decreased recenly in Korea. The raio of cash o consumpion fell o 4.7% in

Does Option Trading Have a Pervasive Impact on Underlying Stock Prices? *

Does Opion Trading Have a Pervasive Impac on Underlying Soc Prices? * Neil D. Pearson Universiy of Illinois a Urbana-Champaign Allen M. Poeshman Universiy of Illinois a Urbana-Champaign Joshua Whie Universiy

17 Laplace transform. Solving linear ODE with piecewise continuous right hand sides

7 Laplace ransform. Solving linear ODE wih piecewise coninuous righ hand sides In his lecure I will show how o apply he Laplace ransform o he ODE Ly = f wih piecewise coninuous f. Definiion. A funcion

Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya.

Principal componens of sock marke dynamics Mehodology and applicaions in brief o be updaed Andrei Bouzaev, bouzaev@ya.ru Why principal componens are needed Objecives undersand he evidence of more han one

4 Convolution. Recommended Problems. x2[n] 1 2[n]

4 Convoluion Recommended Problems P4.1 This problem is a simple example of he use of superposiion. Suppose ha a discree-ime linear sysem has oupus y[n] for he given inpus x[n] as shown in Figure P4.1-1.

INTRODUCTION TO FORECASTING

INTRODUCTION TO FORECASTING INTRODUCTION: Wha is a forecas? Why do managers need o forecas? A forecas is an esimae of uncerain fuure evens (lierally, o "cas forward" by exrapolaing from pas and curren

Working Paper No. 482. Net Intergenerational Transfers from an Increase in Social Security Benefits

Working Paper No. 482 Ne Inergeneraional Transfers from an Increase in Social Securiy Benefis By Li Gan Texas A&M and NBER Guan Gong Shanghai Universiy of Finance and Economics Michael Hurd RAND Corporaion

Consumer sentiment is arguably the

Does Consumer Senimen Predic Regional Consumpion? Thomas A. Garre, Rubén Hernández-Murillo, and Michael T. Owyang This paper ess he abiliy of consumer senimen o predic reail spending a he sae level. The

Lecture 13 Auto/cross-correlation

Lecure 13 Auo/cross-correlaion 1 Generalized Regression Model The generalized regression model's assumpions: (A1) DGP: y = X + is correcly specified. (A) E[ X] = 0 (A3 ) Var[ X] = Σ =. (A4) X has full

Terms of Trade and Present Value Tests of Intertemporal Current Account Models: Evidence from the United Kingdom and Canada

Terms of Trade and Presen Value Tess of Ineremporal Curren Accoun Models: Evidence from he Unied Kingdom and Canada Timohy H. Goodger Universiy of Norh Carolina a Chapel Hill November 200 Absrac This paper

Section 7.1 Angles and Their Measure

Secion 7.1 Angles and Their Measure Greek Leers Commonly Used in Trigonomery Quadran II Quadran III Quadran I Quadran IV α = alpha β = bea θ = hea δ = dela ω = omega γ = gamma DEGREES The angle formed

Determinants of Capital Structure: Comparison of Empirical Evidence from the Use of Different Estimators

Serrasqueiro and Nunes, Inernaional Journal of Applied Economics, 5(1), 14-29 14 Deerminans of Capial Srucure: Comparison of Empirical Evidence from he Use of Differen Esimaors Zélia Serrasqueiro * and

CHAPTER FIVE. Solutions for Section 5.1

CHAPTER FIVE 5. SOLUTIONS 87 Soluions for Secion 5.. (a) The velociy is 3 miles/hour for he firs hours, 4 miles/hour for he ne / hour, and miles/hour for he las 4 hours. The enire rip lass + / + 4 = 6.5

Niche Market or Mass Market?

Niche Marke or Mass Marke? Maxim Ivanov y McMaser Universiy July 2009 Absrac The de niion of a niche or a mass marke is based on he ranking of wo variables: he monopoly price and he produc mean value.

Market Efficiency or Not? The Behaviour of China s Stock Prices in Response to the Announcement of Bonus Issues

Discussion Paper No. 0120 Marke Efficiency or No? The Behaviour of China s Sock Prices in Response o he Announcemen of Bonus Issues Michelle L. Barnes and Shiguang Ma May 2001 Adelaide Universiy SA 5005,

Employee Stock Option Accounting in a Residual Income Valuation Framework

Employee Sock Opion Accouning in a Residual Income Valuaion Framework Wayne R. Landsman Kenan-Flagler Business School Universiy of Norh Carolina a Chapel Hill Chapel Hill, NC 7599 Ken Peasnell Managemen

SPEC model selection algorithm for ARCH models: an options pricing evaluation framework

Applied Financial Economics Leers, 2008, 4, 419 423 SEC model selecion algorihm for ARCH models: an opions pricing evaluaion framework Savros Degiannakis a, * and Evdokia Xekalaki a,b a Deparmen of Saisics,

Does Option Trading Have a Pervasive Impact on Underlying Stock Prices? *

Does Opion Trading Have a Pervasive Impac on Underlying Sock Prices? * Neil D. Pearson Universiy of Illinois a Urbana-Champaign Allen M. Poeshman Universiy of Illinois a Urbana-Champaign Joshua Whie Universiy

Trade Costs, Asset Market Frictions and Risk Sharing

Trade Coss, Asse Marke Fricions and Risk Sharing Doireann Fizgerald July 2010 Absrac I use bilaeral impor daa o es for he role of rade coss and asse marke fricions in impeding inernaional consumpion risk

DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS

DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS Hong Mao, Shanghai Second Polyechnic Universiy Krzyszof M. Osaszewski, Illinois Sae Universiy Youyu Zhang, Fudan Universiy ABSTRACT Liigaion, exper

A Curriculum Module for AP Calculus BC Curriculum Module

Vecors: A Curriculum Module for AP Calculus BC 00 Curriculum Module The College Board The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy.

The Relationship between Stock Return Volatility and. Trading Volume: The case of The Philippines*

The Relaionship beween Sock Reurn Volailiy and Trading Volume: The case of The Philippines* Manabu Asai Faculy of Economics Soka Universiy Angelo Unie Economics Deparmen De La Salle Universiy Manila May

A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation

A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion

The Kinetics of the Stock Markets

Asia Pacific Managemen Review (00) 7(1), 1-4 The Kineics of he Sock Markes Hsinan Hsu * and Bin-Juin Lin ** (received July 001; revision received Ocober 001;acceped November 001) This paper applies he

Recovering Market Expectations of FOMC Rate Changes with Options on Federal Funds Futures

w o r k i n g p a p e r 5 7 Recovering Marke Expecaions of FOMC Rae Changes wih Opions on Federal Funds Fuures by John B. Carlson, Ben R. Craig, and William R. Melick FEDERAL RESERVE BANK OF CLEVELAND

Making a Faster Cryptanalytic Time-Memory Trade-Off

Making a Faser Crypanalyic Time-Memory Trade-Off Philippe Oechslin Laboraoire de Securié e de Crypographie (LASEC) Ecole Polyechnique Fédérale de Lausanne Faculé I&C, 1015 Lausanne, Swizerland philippe.oechslin@epfl.ch

ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS

ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS R. Caballero, E. Cerdá, M. M. Muñoz and L. Rey () Deparmen of Applied Economics (Mahemaics), Universiy of Málaga,

1. y 5y + 6y = 2e t Solution: Characteristic equation is r 2 5r +6 = 0, therefore r 1 = 2, r 2 = 3, and y 1 (t) = e 2t,

Homework6 Soluions.7 In Problem hrough 4 use he mehod of variaion of parameers o find a paricular soluion of he given differenial equaion. Then check your answer by using he mehod of undeermined coeffiens..

Section 5.1 The Unit Circle

Secion 5.1 The Uni Circle The Uni Circle EXAMPLE: Show ha he poin, ) is on he uni circle. Soluion: We need o show ha his poin saisfies he equaion of he uni circle, ha is, x +y 1. Since ) ) + 9 + 9 1 P

Signal Rectification

9/3/25 Signal Recificaion.doc / Signal Recificaion n imporan applicaion of juncion diodes is signal recificaion. here are wo ypes of signal recifiers, half-wae and fullwae. Le s firs consider he ideal

3.1. The F distribution [ST&D p. 99]

Topic 3: Fundamenals of analysis of variance "The analysis of variance is more han a echnique for saisical analysis. Once i is undersood, ANOVA is a ool ha can provide an insigh ino he naure of variaion