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Econometrics I,Fall2012Assignment4The due date for this assignment is Dec.10.1.Generate a sample of size25from the modely t= 1+ 2y t 1+u t,u t i:i:d:(0;1)with 1=1and 2=0:8.For simplicity,assume that y0=0and that the u t are normally e this sample to compute the OLS estimates b 1and b 2. Repeat at least100times,and…nd the averages of the b 1and the b e these averages to estimate the bias of the OLS estimators of 1and 2.Repeat this exercise for sample sizes of50,100,and200.What happens to the bias ofb 1and the b 2as the sample size is increased?2.Consider the modely= 1+ 21t+u t;u t i:i:d:N(0; 2):Let 0i be the true value of the parameter i;and b i denote the OLS estimator of i (i=1;2).Show that(a)b 1is consistent(b)b 2is inconsistent,by proving that the probability limit of b 2 02is a normalrandom variable with mean0and variance6 2= 2.You may use the following results in order to construct your demonstration:1X t=11t2= 26;lim n!11n[s(n)]k=0;where s(n)=n X t=11t;k=1;2:3.Assume that the DGP was generated by the following model with the true values( 0; 20)of parameters,y=X +"," IID(0; 2I),but E[X0"]=0: Since the error terms are correlated with the regressors,we use the(generalized)IV estimator,b IV (X0P Z X) 1X0P Z y;where Z is an n l instrument matrix(l>k)and P Z Z(Z0Z) 1Z0.Suppose thatZ0Z n p! zz,X0Znp! xz,and Z0"pnd!N 0; 20 zzwhere zz is positive de…nite and xz is a k l matrix with rank( xz)=k.(a)Show that b IV is consistent and asymptotically normally distributed,and that the asymptotic covariance matrix of p n b GIV 0 is 20p lim X0P Z X n 1.(b)Show thats2IV 1n y X b IV 0 y X b IV p! 20:4.Gaver and Geisel(1974)propose two forms of a consumption function:M1:C t= 1+ 2Y t+ 3Y t 1+"t;M2:C t= 1+ 2Y t+ 3C t 1+u t;where C t and Y t are real consumption and disposable income in period t.The…rst model states that consumption responds to changes in income over two periods,whereas the second states that the e¤ects of changes in income on consumption persist for many periods.For the data set of consumption.txt used in Assignment2,test both the speci…cations of a consumption function by using the following procedures:(a)the encompassing approach discussed in the class.(b)the comprehensive approach-the J and J A Tests.(c)Compare your testing results.5.Consider a model with two explanatory variables x and zy= + x+ z+e;and suppose that y and x are measured with errors but z is not,i.e.we observeY=y+u;X=x+v,Z=z;where e,u,v are mean zero,variances 2e; 2u; 2v respectively,and mutually uncorre-lated.Also e,u and v are uncorrelated with y;x;and z.(a)Write the regression on Y;X and Z,Y= + X+ Z+":What is the error term"?Compute Cov(X;").(b)Let Cov(x;z)= , 2x V ar(x)and 2z V ar(z).Compute V ar(Y),Cov(Y;X),and Cov(Y;Z):(c)Compute the probability limits of the OLS estimators b and b .。
Econometrics I,Fall2012Assignment2The due date for this assignment is Monday Nov.5.1.The…le consumption.txt contains data on real personal disposable income and con-sumption expenditures in Canada,seasonally adjusted in1986dollars,from the…rst quarter of1947until the last quarter of1996.The layout of the data is explained at the end of the…le.(a)The simplest imaginable model of the Canadian consumption function would haveconsumption expenditures as the dependent variable,and a constant and personaldisposable income as explanatory variables.Run this regression for the period1953:1to1996:4.What is your estimate of the marginal propensity to consumeout of disposable income?(b)Plot a graph of the OLS residuals for the consumption function regression againsttime.All modern regression packages will generate these residuals for you onrequest.Does the appearance of the residuals suggest that this model of theconsumption function is well speci…ed?(c)Simulate the consumption function model you have just estimated in(a)for thesame sample period,using the actual data on disposable income.For the para-meters,use the OLS estimates obtained in(a).For the error terms,use drawingsfrom the N(0;s2)distribution,where s2is the estimate of the error variance pro-duced by the regression package.(d)Run a regression using the simulated consumption data as the dependent vari-able and the constant and disposable income as explanatory variables.Are theparameter estimates the same as those obtained using the real data?Why or whynot?(e)Plot the residuals from the regression with simulated data.Does the plot looksubstantially di¤erent from the one obtained using the real data?It should!2.The…le tbrate.txt contains data for1950:1to1996:4for three series:r t,the interestrate on90-day treasury bills, t,the rate of in‡ation,and y t,the logarithm of real GDP.For the period1950:4to1996:4,run the regression4r t= 1+ 2 t 1+ 34y t 1+ 44r t 1+ 5r t 2+u t;(1) where4is the…rst-di¤erence operator,de…ned so that4r t=r t r t 1.(a)Plot the residuals and…tted values against time.Then regress the residuals on the…tted values and on a constant.What do you learn from this second regression?Now regress the…tted values on the residuals and on a constant.What do youlearn from this third regression?(b)For the same sample period,regress4r t on a constant,4y t 1,4r t 1and4r t 2.Save the residuals from this regression,and call them b e t.Then regress t 1on aconstant,4y t 1,4r t 1and4r t 2.Save the residuals from this regression,andcall them b v t .Now regress b e t on b v t .How are the estimated coe¢cient and the residuals from this last regression related to anything that you obtained when you estimated regression (1)?(c)Calculate the diagonal elements of the hat matrix P X for regression (1)anduse them to calculate a measure of leverage,h t X 0t [X 0X ] 1X t ,where X i =(x t;1;:::;x t;k )0.We say that observations for which h t is large have high leverage or are leverage points.A leverage point is not necessarily in‡uential,but it has the potential to be in‡uential.Plot this measure against time.On the basis of this plot,which observations seem to have unusually high leverage?3.Consider the following linear regression:y =X +"=X 1 1+X 2 2+",where y is n 1,X 1is n k 1,X 2is n k 2,X =[X 1;X 2]is n k (k 1+k 2=k <n ),and 0=[ 01; 02].Suppose that X ,X 1and X 2are of full column rank.The OLS estimator b = b 01;b 020are expressed as b = b 1b 2 =(X 0X ) 1X 0y = X 01X 02 [X 1;X 2] 1 X 01X 02 y = X 01X 1X 01X 2X 02X 1X 02X 2 1 X 01y X 02y:(a)Use the formula of partitioned inverse (see A-74,page824)to show thatb 1=[X 01M 2X 1] 1X 01M 2y =[X 01X 1] 1X 01y b 2=[X 02M 1X 2] 1X 02M 1y =[X 02X 2] 1X 02y whereP i X i (X 0i X i ) 1X 0i ,M i I P i ,i =1;2X 1=M 2X 1;y =M 2y ;X 2=M 1X 2;y =M 1y :(b)Note that a square matrix is an orthogonal projection if and only if it is symmetricand e this result to show that P X P 1is an orthogonal projection matrix.What is the trace of P X P 1?(c)Show that any n 1vector z of the form M 1X 2 ,for an arbitrary k 2 1vec-tor ,is left unchanged when premultiplied by P X P 1;that is,show that(P X P 1)M 1X 2 =M 1X 2 .(d)Why do the above results prove that P X P 1=P M 1X 2,where this last matrix denotes the orthogonal projection on to S (M 1X 2)?(e)Consider the following regressions,all to be estimated by OLS:(a)y =X 2 2+u ;(b)P 1y =X 2 2+u ;(c)P 1y =P 1X 2 2+u ;(d)P X y =X 1 1+X 2 2+u ;(e)P X y =X 2 2+u ;(f)M 1y =X 2 2+u ;(g)M 1y =M 1X 2 2+u ;(h)M 1y =X 1 1+M 1X 2 2+u ;(i)M 1y =M 1X 1 1+M 1X 2 2+u ;(j)P X y =M 1X 2 2+u :For which of these regressions are the estimates of 2the same as for the original regression?Why?For which are the residuals the same?Why?。
2022-2022上海财经大学金融硕士(金融分析师)考研详情介绍与经验指上海财经大学金融分析师原标题：2022-2022上海财经大学金融硕士（金融分析师）考研详情介绍与经验指学院简介历史悠久上海财经大学金融学院的前身为建立于1921年的国立东南大学银行系，是我国高等院校中最早创设的金融学科之一，学科创始人杨荫薄、朱斯煌等教授为近代中国金融学的奠基人。
建国后，彭信威、刘絜敖、朱元、吴国隽、王宏儒、龚浩成、谢树森、王学青、俞文青等资深教授均对新中国金融高等教育的发展有重要贡献。
1998年，为了适应我国金融事业发展的需要，进一步促进金融学科发展，上海财经大学成立了金融学院，这也是我国大陆高校中设立的第一个金融学院。
体系完整金融学院设有银行系、保险系、国际金融系、证券期货系以及公司金融系共5个系，现有本科四个专业、四个学术型硕士点、两个专业学位硕士点和四个博士点。
凭借学院优良的基础设施、资深的师资团队以及现代化的管理方式和国际化视野，成就了一批批活跃于金融界的学术和实践人才。
师资雄厚学院拥有一流的师资队伍，现有专职教师74人，其中教授26人，副教授25人。
获得博士学位的教师人数超过全体教师比例的89%，其中30位教师获得海外博士学位。
近年来学院注重从国外引进高层次科研与教学人才，现有常任轨教师24人，均具有海外博士学位。
学院还聘请多名海外著名高校的知名学者担任特聘教授，聘请海内外大型金融企业负责人担任兼职教授。
近三年来，学院共有十多名教师参加"国家留基委"项目、学校双语师资培训项目以及美国富布莱特基金资助项目，均提高了教师的研究和教学能力。
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上海财经大学《 Financial Econometrics 》课程考试卷一课程代码 课程序号姓名 学号 班级Part 1 Term Explanation （20 marks ）1．White Noise 2．RandomWalk3．Akaike Information Criterion 4．Jarque-Bera Statistic 5．Chow TestImportant Point ：1．White Noise ：White Noise is the special case of stationary stochastic process. We call a stochastic process purely random or white noise if it has zero mean, constant variance and is serially uncorrelated. 2．RandomWalk: Random walk means that the stochastic process is nonstationary and value of this period is highly related to the past values. For example, the stock price today may equal the yesterday ’s price plus a random shock. Random walk without drift can be expressed as t t t u y y +=-13．Akaike Information Criterion: AIC provide a way to select the better regression model among several models by comparing their forecast performance. The lower the AIC, the better the forecast performance will be. AIC will also be used to determine the lag length in ARDL approach.4．Jarque-Bera Statistic: The Jarque-Bera test is the test of normality. We first calculate the skewness and the kurtosis, and it is also based on the residual of the regression.The Jarque-Bera Statistic=)24)3(6(22-+K S n , where S is the skewness and K is the kurtosis,n is sample size, and for normal distribution, S=0, K=3, if JB statistic is not significantly different from zero, p value is quite low, we reject the null hypothesis that the residual is normally distributed.5．Chow Test: The test of structural change of the regression. The estimate of the parameter of the regression may not retain the same through the entire time period; we use the Chow test to test whether the relationship is stable and find the break point. It develop the F statistics=)/(/)(k N RSS mRSS RSS ur ur r --, the null hypothesis is the regression is stable.Part 2 Explain main purpose(s) of constructing following two models and making comments on the empirical results. (25marks)1.Gregory Chow (1966)where M = natural logarithm of total money stock Yp = natural logarithm of permanent income Y = natural logarithm of current income R = natural logarithm of rate of interest2.Taylor and Newhouse (1969)本题答题要点：1。
