Final sample exam. Choose the one alternative that best completes the statement or answers the question.

Transcription

1 Final sample exam Muliple-Choice Quesions Choose he one alernaive ha bes complees he saemen or answers he quesion. 1) A possible soluion o errors-in-variables bias is o A) miigae he problem hrough insrumenal variables regression. B) use log-log specificaions. C) use he square roo of ha variable since he error becomes smaller. D) choose differen funcional forms. 2) The following equaions belong o he class of linear regression model excep: A) Y = β + β X + β X + u. 2 i 0 1 i 2 i i B) lny i β0 β1x1 i u i = + +. C) Y ln ( β β X u ) = + +. i 0 1 i i D) ln ( β β ) Y = + X + u. i 0 1 i i 3) The inerpreaion of he slope coefficien in he model β β ( ) Y = + X + u is: a ln i 0 1 i i A) 1% change in X is associaed wih a β 1 % change in Y. B) change in X by one uni is associaed wih a 100 β 1 % change in Y. C) 1% change in X is associaed wih a change in Y of 0.01β 1. D) change in X by one uni is associaed wih a β 1 change in Y. 4) To es he populaion regression funcion is linear raher han a polynomial of order r, A) look a he paern of he coefficiens: if hey change from posiive o negaive o posiive, ec., hen he polynomial regression should be used. B) use he es of (r-1) resricions using he F-saisic. C) compare he TSS from boh regressions. 1

2 D) check wheher he regression R 2 for he polynomial regression is higher han ha of he linear regression. 5) Including an ineracion erm beween wo independen variables, X 1 and X 2,allows for he following, excep ha: he ineracion erm A) les he effec on Y of a change in X 2 depend on he value of X 1. B) les he effec on Y of a change in X 1 depend on he value of X 2. C) coefficien is he effec of a uni increase in ( X X ). 1 2 D) coefficien is he effec of a uni increase in X 1 and X 2 above and beyond he sum of he individual effecs of a uni increase in he wo variables alone. 6) The ADL(p, q) model is represened by he following equaion Y = β + βy + β Y + + β Y + δ + δ X + u. A) p p q Y = β + βy + β Y + + β Y + δ X + δ X + + δ X + u. B) p p q q Y = β + βy + β Y + + β Y + δ u. C) p p q q D) Y = β0 + βpy p + δqx q + u. 7) In he log-log model, he slope coefficien indicaes Δ Y Y A) he elasiciy of Y wih respec o X. B). ΔX X C) ΔY Δ X. D) he effec ha a uni change in X has on Y. 8) Simulaneous causaliy A) means ha a hird variable affecs boh Y and X. B) leads o correlaion beween he repressor and he error erm. C) canno be esablished since regression analysis only deecs correlaion beween variables. 2

3 D) means you mus run a second repression of X on Y. 9) Sample selecion bias A) resuls in he OLS esimaor being biased, alhough i is sill consisen. B) is more imporan for nonlinear leas squares esimaion han for OLS. C) is only imporan for finie sample resuls. D) occurs when a selecion process influences he availabiliy of daa and ha process is relaed o he dependen variable. 10) Possible soluions o omied variable bias, when he omied variable is no observed, include he following wih he excepion of A) use of insrumenal variables regressions. B) panel daa esimaion. C) use of randomized conrolled experimens. D) nonlinear leas squares esimaion. 11) The Granger causaliy es A) uses he F-saisic o es he hypohesis ha cerain repressors have no predicive conen for he dependen variable beyond ha conained in he oher repressors. B) is a special case of he augmened Dickey-Fuller es. C) esablishes he direcion of causaliy (as used in common parlance) beween X and Y in addiion o correlaion. D) is a raher complicaed es for saisical independence. 12) The roo mean squared forecas error (RMSFE) is defined as ˆ. B) ( Y ˆ ) 2 Y 1. A) E Y Y 1 C) E ( Y ˆ ) 2 Y 1. D) E ( Y ˆ Y 1). 3

4 13) In order o make reliable forecass wih ime series daa, all of he following condiions are needed wih he excepion of A) he presence of omied variable bias. B) he regression having high explanaory power. C) coefficiens having been esimaed precisely. D) he regression being sable. 14) The firs difference of he logarihm of Y equals A) he difference beween he lead and he lag of Y. B) he growh rae of Y exacly. C) approximaely he growh rae of Y when he growh rae is small. D) he firs difference of Y. 15) Saionariy means ha he A) error erms are no correlaed. B) forecass remain wihin 1.96 sandard deviaion ouside he sample period. C) ime series has a uni roo. D) probabiliy disribuion of he ime series variable does no change over ime. 16) Negaive auocorrelaion in he change of a variable implies ha A) he daa are negaively rended. B) he variable conains only negaive values. C) he series is no sable. D) an increase in he variable in one period is, on average, associaed wih a decrease in he nex. 4

5 17) The AR(p) model A) is defined asy = β0 + β py p + u. B) can be wrien as Y = β0 + β1y 1+ u p. C) represens Y as a linear funcion of p of is lagged values. D) can be represened as follows: Y = β0 + β1x + βpy p + u. 18) To choose he number of lags in eiher an auoregression or a ime series regression model wih muliple predicors, you can use any of he following es saisics wih he excepion of A) Bayes informaion crierion. B) augmened Dickey-Fuller es. C) Akaike informaion crierion. D) F-saisic. 19) A possible soluion o errors-in-variables bias is o A) miigae he problem hrough insrumenal variables regression. B) use log-log specificaions. C) use he square roo of ha variable since he error becomes smaller. D) choose differen funcional forms. 20) Pseudo ou-of-sample forecasing can be used for he following reasons wih he excepion of A) analyzing wheher or no a ime series conains a uni roo. B) esimaing he RMSFE. C) evaluaing he relaive forecasing performance of wo or more forecasing models. D) giving he forecaser a sense of how well he model forecass a he end of he sample. 5

6 Essay Quesions. The size of es is 5% if no specified in quesion. 1. Discuss he five hreas o he inernal validiy of regression sudies. (20) To regress Beef Demand (B) on he Consan (C), he price of Beef (P) and Per Capia Disposable Income (YD), obain Dependen Variable: B Mehod: Leas Squares Dae: 12/12/07 Time: 15:54 Sample: Included observaions: 28 Variable Coefficien Sd. Error -Saisic Prob. C P YD R-squared Mean dependen var Adjused R-squared S.D. dependen var S.E. of regression Akaike info crierion Sum squared resid Schwarz crierion Log likelihood F-saisic Durbin-Wason sa Prob(F-saisic) a) Omied Variable Bias b) Wrong Funcional Form c) Errors-in-Variables Bias d) Sample Selecion Bias e) Simulaneous Causaliy Bias Answers: a) We know if he regressor(he price of Beef) is correlaed wih a variable ha has been omied from he analysis bu ha deermines, in par, he dependen variable(beef Demand), hen he OLS esimaor will have omied variable bias. And omied variable bias means ha he firs leas square assumpion ha Eu ( X ) = 0, is incorrec. Then β 1 will be he inconsisen esimaor of β 1. i i 6

7 And we know he pork or muon or oher mea is he subsiues for beef. The change of heir prices will influence he demand of beef. So if we exclude he price of pork or muon as regressor, here will be omied variable bias in he model. b) The regressor is he price of Beef (P) and Per Capia Disposable Income (YD).I assumes ha he relaion beween he demand of beef and Per Capia Disposable Income is linear. Bu in 2 fac, he relaion may be no linear. Perhaps YD will influence he demand of beef significanly. Thus he funcion form will be wrong. c) Errors in variables bias in he OLS esimaor arises when an independen variable is measured imprecisely. Then β 1 will be biased owards zero, even in large sample. We know he price of beef,yd and he demand of beef is dynamic. The daa we ge may be imprecise. There will be measuremen bias for hese variables. d) Sample selecion bias arises when a selecion process influences he availabiliy of daa and ha process is relaed o he dependen variable. Sample selecion induces correlaion beween one or more regressors and he error erm, leading o bias and inconsisency of he OLS esimaor. For he above model, ha how do we choose he sample is very imporan. For example if we ge he daa from differen areas, and if he people in one area didn like beef for some reasons, and in anoher area he people never ea pork, he coefficien will be very differen. e) Simulaneous causaliy bias arises in a regression of Y on X when, in addiion o he causal link of ineres from X o Y, here is a causal link from Y on X. This reverse causaliy makes X correlaed wih he error erm in he populaion regression of ineres. For his quesion, we know he price of beef will influence he demand of beef. Bu if he demand of beef increase, according o he supply and demand heory, he price of beef will increase oo. Thus here will be Simulaneous causaliy bias. 2. Time Series Analysis of US Inflaion Raes (20) Define DINF = INF INF(-1), which is he firs difference of inflaion rae. Before you run auoregressive models, you did a ADF ess on inflaion rae. ADF Tes Saisic % Criical Value* % Criical Value % Criical Value *MacKinnon criical values for rejecion of hypohesis of a uni roo. 7

8 Augmened Dickey-Fuller Tes Equaion Dependen Variable: D(INF) Mehod: Leas Squares Dae: 12/15/07 Time: 18:50 Sample(adjused): 1960:2 1999:4 Included observaions: 159 afer adjusing endpoins Variable Coefficien Sd. Error -Saisic Prob. INF(-1) D(INF(-1)) D(INF(-2)) D(INF(-3)) C R-squared Mean dependen var Adjused R-squared S.D. dependen var S.E. of regression Akaike info crierion Sum squared resid Schwarz crierion Log likelihood F-saisic Durbin-Wason sa Prob(F-saisic) Regress inflaion rae on is firs lag erm and ge he resul as follows: Dependen Variable: INF Mehod: Leas Squares Dae: 12/15/07 Time: 18:26 Sample: 1960:1 1999:4 Included observaions: 160 Variable Coefficien Sd. Error -Saisic Prob. C INF(-1) R-squared Mean dependen var Adjused R-squared S.D. dependen var S.E. of regression Akaike info crierion Sum squared resid Schwarz crierion Log likelihood F-saisic Durbin-Wason sa Prob(F-saisic)

9 Furhermore, you run he AR(3) model and ge Dependen Variable: INF Mehod: Leas Squares Dae: 12/15/07 Time: 18:30 Sample: 1960:1 1999:4 Included observaions: 160 Variable Coefficien Sd. Error -Saisic Prob. C INF(-1) INF(-2) INF(-3) R-squared Mean dependen var Adjused R-squared S.D. dependen var S.E. of regression Akaike info crierion Sum squared resid Schwarz crierion Log likelihood F-saisic Durbin-Wason sa Prob(F-saisic) Then, you run AR(1) and AR(3) model abou DINF, respecively. Dependen Variable: DINF Mehod: Leas Squares Dae: 12/15/07 Time: 18:35 Sample: 1960:1 1999:4 Included observaions: 160 Variable Coefficien Sd. Error -Saisic Prob. C DINF(-1) R-squared Mean dependen var Adjused R-squared S.D. dependen var S.E. of regression Akaike info crierion Sum squared resid Schwarz crierion Log likelihood F-saisic Durbin-Wason sa Prob(F-saisic)

10 Dependen Variable: DINF Mehod: Leas Squares Dae: 12/15/07 Time: 18:38 Sample(adjused): 1960:2 1999:4 Included observaions: 159 afer adjusing endpoins Variable Coefficien Sd. Error -Saisic Prob. C DINF(-1) DINF(-2) DINF(-3) R-squared Mean dependen var Adjused R-squared S.D. dependen var S.E. of regression Akaike info crierion Sum squared resid Schwarz crierion Log likelihood F-saisic Durbin-Wason sa Prob(F-saisic) a) Explain he meaning and purpose of ADF es in ime series analysis. b) Inerpre resul of he ADF es. Why he dependen variable is DINF in regression? c) Afer you ge he above regression resuls, you decide o use one of he four models o forecas he nex-period inflaion rae. Explain your decision. d) Given he quarerly inflaion raes in 1999, wha is your forecas of 2000:I. Answers: 1999:I 1999:II 1999:III 1999:IV a) The ADF es for a uni auoregressive roo ess he null hypohesis H : δ = 0 0 agains he one-sided alernaive H : 0 1 δ < in he regression Δ Y = + Y + Δ Y + Δ Y + + Δ Y + u β0 δ 1 γ1 1 γ γ p p Under he null hypohesis, Y has a sochasic rend; under he alernaive hypohesis, Y is saionary. The ADF saisic is he OLS -saisic esing δ = 0 in las equaion. 10

11 b) DINF ( ) = INF( 1) DINF ( ( 1)) DINF ( ( 2)) DINF ( ( 3)) The ADF -saisic esing is he -saisic esing he hypohesis ha he coefficien on INF( 1) is zero; ha is = And he 5% criical value is Because he ADF saisic is less negaive han , we can rejec he null hypohesis a he 5% significance level. So we can rejec he hypohesis a he 5% significance level ha he inflaion has a uni auoregressive roo, ha inflaion conains a sochasic rend, agains ha alernaive ha i is saionary. c) The fourh model is he bes. Because according o he ADF es a he 5% significance level, we can rejec he null hypohesis ha inflaion conains a sochasic rend agains ha alernaive ha i is saionary. So we should use he lags of D(INF) as regressors. For he AR(1) and AR(3) model, he R-squared is and respecively, so AR(3) is beer han AR(1); And Akaike info crierion is and , so AR(3) is beer han AR(1); And Schwarz crierion is and , so AR(3) is beer han AR(1). According he above saemens, we should choose he fourh model. d) According o he fourh model, we ge DINF = DINF 0.29DINF DINF, Then we can ge DINF 1999: II = = 1.2, DINF 1999: III = = 0.02 DINF 1999: IV = = 0.38, Thus, DINF 2000: I = DINF1999: IV 0.29DINF1999: III DINF1999: II = = Then, INF 2000: = INF 1999: + DINF 2000: = = I IV I 11

12 3. Measuremen Errors in Variables (20) Assume here exiss an exac linear relaionship beween rue weighs and rue heighs: W i = β 0 + β 1 H i. However, weighs and heighs are measured wih errors as follows: Y i = W i + w i and X i = H i + v i, where w i and v i are uncorrelaed wih W i and H i respecively. To figure ou he relaionship beween weighs and heighs, suppose you run he following regression: Y i = β 0 + β 1 X i + u i for i = 1, 2,, n. a) Show ha OLS esimaor of β 1 is biased oward zero. b) Under which condiions, he OLS esimaor of β 1 is unbiased? Answers: a) 12

13 σ β β σ σ 2 p H b) Since H v Then if here is no measuremen error, 2 σ v = 0 p so β 1 β1. 一 单选题答案 A D C B C B A B D D A C A C D D C B A A 13