Econometrics Problem Set 1 11210690112 张婷
英语数学词汇E
数学专业词汇对照以字母 E 开头eccentric angle 离心角eccentric angle of an ellipse 椭圆的离心角eccentric anomaly 离心角eccentricity 离心率eccentricity of a hyperbola 双曲线的离心率echelon matrix 梯阵econometrics 计量经济学eddy 涡流旋涡edge 边edge connectivity 边连通度edge homomorphism 边缘同态edge of a solid 立体棱edge of regression 回归边缘edge of the wedge theorem 楔的边定理editcyclic markov chain 循环马尔可夫链effective area 有效面积effective convergence 有效收敛effective cross section 有效截面effective differential cross section 有效微分截面effective divisor 非负除数effective interest rate 有效利率effective number of replications 有效重复数effective variance of error 有效误差方差effectively computable function 能行可计算函数efficiency 效率efficiency factor 效率因子efficient estimator 有效估计量efficient point 有效点egyptian numerals 埃及数字eigenelement 特摘素eigenfunction 特寨数eigenspace 本照间eigenvalue 矩阵的特盏eigenvalue problem 特盏问题eigenvector 特镇量eigenvector of linear operator 线性算子的特镇量einstein equation 爱因斯坦方程einstein metric 爱因斯坦度量elastic coefficient 弹性常数elastic constant 弹性常数elastic deformation 弹性变形elastic limit 弹性限度elastic modulus 弹性模数elastic scattering 弹性散射elasticity 弹性elastodynamics 弹性动力学electrodynamics 电动力学electromagnetism 电磁electronic computer 电子计算机electronic data processing machine 电子数据处理机electronics 电子学electrostatics 静电学element 元件element of area 面积元素element of best approximation 最佳逼近元素element of finite order 有限阶元素element of surface 面元素elementary 基本的elementary chain 初等链elementary circuit 基本回路elementary conjunction 基本合取式elementary divisor 初等因子elementary divisor theorem 初等因子定理elementary event 简单事件elementary formula 原始公式elementary function 初等函数elementary geometry 初等几何elementary matrix 初等阵elementary number theory 初等数论elementary operation 初等运算elementary path 有向通路elementary set 初等集elementary subdivision 初等重分elementary symmetric function 初等对称函数elementary theory of numbers 初等数沦elevation 正视图eliminant 结式eliminate 消去elimination 消去elimination by substitution 代入消元法elimination method 消元法elimination of unknowns 未知数消去elimination theorem 消去定理ellipse 椭圆ellipse of deformation 变形椭圆ellipsograph 椭圆规ellipsoid 椭面ellipsoid of inertia 惯性椭球ellipsoid of revolution 回转椭面ellipsoid of rotation 回转椭面ellipsoidal 椭面的ellipsoidal coordinates 椭球面]坐标ellipsoidal harmonics 椭球低函数elliptic catenary 椭圆悬链线elliptic coordinates 椭圆坐标elliptic curve 椭圆曲线elliptic cylinder 椭圆柱elliptic cylinder function 椭圆柱函数elliptic differential operator 椭圆型微分算子elliptic equation 椭圆型微分方程elliptic function 椭圆函数elliptic function of the second kind 第二类椭圆函数elliptic function of the third kind 第三类椭圆函数elliptic geometry 椭圆几何elliptic integral 椭圆积分elliptic irrational function 椭圆无理函数elliptic modular function 椭圆模函数elliptic modular group 椭圆模群elliptic motion 椭圆运动elliptic orbit 椭圆轨道elliptic paraboloid 椭圆抛物面elliptic point 椭圆点elliptic quartic curve 椭圆四次曲线elliptic space 椭圆空间elliptic surface 椭圆曲面elliptic system 椭圆型方程组elliptic type 椭圆型ellipticity 椭圆率elongation 伸长embedding 嵌入embedding operator 嵌入算子embedding theorem 嵌入定理empirical curve 经验曲线empirical distribution curve 经验分布曲线empirical distribution function 经验分布函数empirical formula 经验公式empty mapping 空映射empty relation 零关系empty set 空集end 端end around carry 循环进位end device 输出设备endless 无穷的endomorphism 自同态endomorphism group 自同态群endomorphism ring 自同态环endpoint 端点energetic inequality 能量不等式energy 能量energy barrier 能量障碍energy distribution 能量分布energy integral 能量积分energy level 能级energy method 能量法energy momentum tensor 能量动量张量energy norm 能量范数energy operator 能量算子energy principle 能量原理energy space 能量空间energy surface 能面enlarge 扩大enneagon 九边形enriques surface 讹凯斯面ensemble 总体entire 整个的entire function 整函数entire modular form 整模形式entire rational function 整有理函数entire series 整级数entire transcendental function 整超越函数entrance angle 入射角entropy 熵enumerability 可数性enumerable 可数的enumerable set 可数集enumerate 列举enumeration 列举enumeration data 计数数据enumeration problem 列举问题enumerative geometry 枚举几何envelope 包络线envelope of holomorphy 正则包enveloping algebra 包络代数enveloping ring 包络环enveloping surface 包络面epicycle 周转圆epicycloid 外摆线epicycloidal 圆外旋轮线的epimorphic 满射的epimorphic image 满射像epimorphism 满射epitrochoid 长短辐圆外旋轮线epitrochoidal curve 圆外旋轮曲线epsilon chain 链epsilon function 函数epsilon map 映射epsilon neighborhood 邻域epsilon net 网epsilonnumber 数equal 相等的equal set 相等集equal sign 等号equality 等式equality constraint 等式约束equalization 平衡化;同等化equally possible event 相等可能事件equate 使...相等equation 方程equation of a circle 圆方程equation of a curve 曲线方程equation of continuity 连续方程equation of heat conduction 热传导方程equation of higher order 高阶方程式equation of jacobi 雅可比方程equation of mixed type 混合型方程equation of motion 运动方程equation of state 状态方程equation of the straight line 直线方程equation root 方程的根equation with integral coefficients 整系数方程equatorial coordinates 赤道座标equatorial radius 赤道半径equi asymptotic stability 等度渐近稳定性equi luminosity curve 均匀光度曲线equiangular 等角的equiangular spiral 对数螺线equiareal 保积的equiconjugate diameter 等共轭直径equicontinuity 同等连续性equicontinuous 等度连续的equicontinuous functions 等度连续函数equicontinuous set 等度连续集equiconvergence 同等收敛性equidimensional ideal 纯理想equidistant 等距的equidistant curve 等距曲线equilateral 等边的equilateral cone 等边锥面equilateral hyperbola 等轴双曲线equilateral triangle 等边三角形equilibrium 平衡equilibrium concentration 平衡浓度equilibrium conditions 平衡条件equilibrium constant 平衡常数equilibrium diagram 平衡图equilibrium point 平衡点equilibrium principle 平衡原理equilibrium state 平衡状态equipartition 匀分equipotent 等势的;对等的equipotent set 等势集equipotential 等势的equipotential line 等位线equipotential surface 等位面equivalence 等价equivalence class 等价类equivalence problem 等价问题equivalence relation 等价关系equivalent 等价的equivalent equation 等价方程equivalent fiber bundle in g g 等价纤维丛equivalent form 等价形式equivalent functions 等价函数equivalent knot 等价纽结equivalent mapping 保面积映射equivalent matrix 等价阵equivalent metric 等价度量equivalent neighborhood system 等价邻域系equivalent norm 等价范数equivalent point 等价点equivalent proposition 等值命题equivalent states 等价状态equivalent stochastic process 等价随机过程equivalent terms 等价项equivalent transformation 初等运算equivariant map 等变化映射erasing 擦除ergodic chain 遍历马尔可夫链ergodic hypothesis 遍历假说ergodic markov chain 遍历马尔可夫链ergodic property 遍历性ergodic state 遍历态ergodic theorem 遍历定理ergodic theorem in the mean 平均遍历定理ergodic theory 遍历理论ergodic transformation 遍历变换ergodicity 遍历性error 误差error analysis 误差分析error band 误差范围error coefficient 误差系数error component 误差分量error curve 误差曲线error equation 误差方程error estimation 误差估计error function 误差函数error in the input data 输入数据误差error law 误差律error limit 误差界限error mean square 误差方差error model 误差模型error of estimation 估计误差error of first kind 第一类误差error of measurement 测量误差error of observation 观测误差error of reading 读数误差error of second kind 第二类误差error of the third kind 第三类误差error of truncation 舍位误差error originated from input 输入误差error probability 误差概率error sum of squares 误差平方和error variance 误差方差escribe 旁切escribed 旁切的escribed circle 旁切圆essential 本性的essential boundary condition 本质边界条件essential convergence 本质收敛essential epimorphism 本质满射essential extension 本质开拓essential homomorphism 本质同态essential inferior limit 本质下极限essential infimum 本性下确界essential parameter 本质参数essential point 本质点essential singular kernel 本性奇核essential singularity 本性奇点essential spectrum 本质谱essential strategy 本质策略essential superior limit 本质上极限essential supremum 本性上确界essential undecidability 本质不可判定性essentially bounded 本质有界的essentially convergent sequence 本质收敛序列essentially self adjoint operator 本质自伴算子estimable function 可估计函数estimable hypothesis 可估计假设estimate 估计estimation 估计estimation of error 误差估计estimation of parameter 参数的估计estimation region 估计区域estimation theory 估计论estimator 估计量etale neighborhood 层邻域etale space 层空间etale topology 层拓扑etalon 标准euclid factorization theorem for rational integers 因子分解定理euclid lemma 欧几里得引理euclid parallel postulate 欧几里得平行公设euclidean algorithm 欧几里得算法euclidean domain 欧几里得整环euclidean geometry 欧几里得几何euclidean metric 欧几里得度量euclidean norm 欧几里得范数euclidean plane 欧几里得平面euclidean ring 欧几里得整环euclidean space 欧几里得空间euclidean vector space 欧几里得向量空间euler characteristic 欧拉示性数euler class 欧拉类euler constant 欧拉常数euler criterion 欧拉判别准则euler differential equation 欧拉微分方程euler formula 欧拉公式euler identity 欧拉恒等式euler number 欧拉数euler poincare formula 欧拉庞加莱公式euler poincare relation 欧拉庞加莱公式euler polyhedron theorem 欧拉多面体定理euler polynomial 欧拉多项式euler summation formula 欧拉总和公式eulerian angle 欧拉角evaluate 求...的值evaluation 计算evaluation of functions 函数值计算evaluation of integrals 积分计算even 偶数的even function 偶函数even number 偶数even parity 偶数同位even permutation 偶置换evenness 偶数性event 事件everywhere convergent sequence 处处收敛序列evidence 迷evident 迷的evolute 缩闭线evolute surface 渐屈面evolution 开方evolution equation 发展方程evolvent 渐伸线exact cohomology sequence 正合上同凋列exact differential equation 全微分方程exact division 正合除法exact homotopy sequence 正合同伦序列exact solution 精确解exact square 正合平方exactitude 精确度exactness axiom 正合性公理example 例exceed 超过excenter 外心exceptional curve 例外曲线exceptional jordan algebra 例外约当代数exceptional point 例外点exceptional value 例外值excess 超过excess function 超过函数excess of nine 舍九法exchange 交换exchange integral 交换积分exchange lattice 交换格exchange theorem 交换定理excircle 旁切圆excision 切除excision isomorphism 切除同构exclude 排除exclusion 排除exclusive disjunction 不可兼析取exclusive events 互斥事件exclusive or 不可兼的或executive program 执行程序exist 存在existence 存在existence conditions 存在条件existence of extremum 极值的存在existence theorem 存在定理existence theorem for roots 根的存在性定理existence theorem of implicit function 隐函数的存在性定理existential quantifier 存在量词exogenous variable 局外变量exotic space 异种空间expactation vector 期望值向量expand 展开expansion 展开expansion coefficient 展开系数expansion in series 级数展开expansion in terms of eigenfunction 本寨数展开expansion of a determinant 行列式的展开expansion theorem 展开定理expectation 期望值expected gain 期望增益expected payoff 期望增益expected value 期望值expected value vector 期望值向量experiment 实验experimental 实验的experimental error 实验误差explicit difference scheme 显式差分格式explicit differential equation 显式微分方程explicit function 显函数exponent 指数exponent notation 指数记法exponent of convergence 收敛指数exponential 指数函数exponential curve 指数曲线exponential distribution 指数分布exponential equation 指数方程exponential family 指数族exponential form of complex number 复数的指数形式exponential fourier transformation 指数型傅里叶变换exponential function 指数函数exponential integral 积分指数exponential law 指数定律exponential map 指数映射exponential p adic valuation 指数p 进赋值exponential process 指数过程exponential series 指数级数exponential sum 指数和exponential type 指数型exponential valuation 指数赋值exponentially asymptotic stability 指数式渐近稳定exportation 输出express 表示expression 式exradius 外圆半径extend 扩大extended commutator 广义换位子extended complex plane 扩张平面extended ideal 广义理想extended mean value theorem 广义均值定理extended plane 扩张平面extended point transformation 开拓的点变换extended predicate calculus 广义谓词演算extended riemann hypothesis 广义黎曼假设extended unitary group 广义酉群extension 扩张extension module 扩张模extension of a field 域的扩张extension of the residue field 剩余域的扩张extension principle of propositional logic 命题逻辑的外延性原理extension theorem 扩张定理extensionality 外延extensive quantity 外延量extent 范围exterior 外exterior algebra 外代数exterior angle 外角exterior approximation 外逼近exterior boundary problem 外边界问题exterior derivative 外导数exterior differential 外微分exterior differential form 外微分形式exterior differentiation 外微分法exterior domain 外域exterior interior angles 同位角exterior multiplication 外乘exterior normal 外法线exterior point 外点exterior power 外幂exterior problem 外边界问题exterior product 外积exterior product of tensors 张量的外积external 外部的external composition 外部合成external composition law 外部合成律external direct sum 外直和external division 外分external law of composition 外部合成律external memory 外存储器external program 外部程序external ratio 外分比external store 外存储器externally stable set 控制集externally tangent 外切的extract 开方extraction of a root 开方extraneous root 额外根extrapolate 外推extrapolation 外插extremal 极值曲线;极值的extremal element 极值元素extremal function 极值函数extremal length 极值长度extremal point 极值点extremal property 极值性质extremal surface 极值曲面extreme 外项extreme form 极型extreme point 极值点extreme term 外项extreme value 极值extreme value distribution 极值分布extreme value problem 极值问题extremity 端extremum 极值extremum conditions 极值条件extremum problem with subsidiary condition 附加条件极值问题extremum with a condition 条件极值extremum with a constraint 条件极值。
计量经济学 伍德里奇 第一章
The main challenge of an impact evaluation is the construction of a suitable counterfactual situation.
An ideal experiment can be conducted to obtain the causal effect of fertilizer amount on yield when the levels of fertilizer are assigned to plots independently of other plot features that affect yield.
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2010
Dandan Zhang (NSD)
Sep.-Dec. 2014 1 / 37
1. Introduction
Course Structure
1. Introduction (We4 Chapter 1) 2. Mathematical Foundations,Probability Theory (We4 Appendix B & C) 3. The Bivariate Linear Regression Model (We4 Chapter 2) 4. The Multivariate Linear Regression Model (We4 Chapter 3) 5. Inference (We4 Chapter 4) 6. Further Issues (We4 Chapter 6) 7. Multiple Regression Analysis with Qualitative Information (We4 Chapter 7) 8. Heteroscedasticity (We4 Chapter 8) 9. Specification and Data Issues (We4 Chapter 9) 10. Instrument variables (We4 Chapter 15) 11. Panel Data (We4 Chapter 14)
计量经济学试题（Econometricsquestions）
计量经济学试题（Econometrics questions）A glossary (a total of 20 points, 4 points for each item)1 Econometrics2 least square method3 dummy variables4 instrumental variable methodIdentification of 5 simultaneous equationsTwo short answer questions (30 points, 6 points for each item)1 the classical assumption that the least square method should be satisfied2 steps to solve problems in EconometricsThe reason for the existence of 3 sequence correlation Steps of economic structure test in 4 regression analysis Characteristics of 5 stochastic perturbationsThree calculation analysis (30 points)1., according to the following information, study the income and consumption of farmers in Hebei province.Requirements: (1) to establish regression model (list and calculation formula, test only for economic significance and goodness of fit test);(2) if the per capita net income of farmers in Hebei in 2008 is 3200 yuan, 2008 of the per capita living expenses of farmers in Hebei should be predicted.Particular yearItem 1994199519961997 1998199920002001 20022003Per capita net income of farmers (100 yuan) 111721232424252627 29Living expenses (100 yuan) 811141413131414151Four discussion questions (20 points)1 briefly describe the meaning, sources and consequences of heteroscedasticity, and write the test steps combined with the G-Q test method.Econometrics entry final exam questions B answerFirst, noun interpretation1 econometrics is the integration of mathematics, statistics and economic theory, combined with the theory and practice of economic behavior and phenomenon.2 least square method: the least square method for minimizing the sum of residuals of all observations is the least square method.3 dummy variables: there are some temporary factors in the study of economic life. Such as war, natural disasters, man-made disasters, these factors do not occur frequently in the economy, but with the same characteristics, these economists do not occur frequently, and temporary effect called virtual variables.4 instrumental variable method: instrumental variable method takes the predetermined variable as instrumental variable instead of the endogenous variable in structural equation as explanatory variable, in order to reduce the correlation between random item and explanatory variable.Identification of 5 simultaneous equations: a single equation that constitutes a simultaneous equation has only a statistical form in its simultaneous equations, and this equation is known to be identifiable, otherwise it is called non recognizable. If every equation in the simultaneous equation can be identified, this simultaneous equation is called identity, otherwise it is called non recognizable.Two, simple answer1 the classical assumption that the least square method should be satisfiedAnswer: (1) the mean of random items is zero;(2) random sequence non correlation and heteroscedasticity;(3) explanatory variables are non random, and if random, they are not related to random items;(4) there is no multicollinearity between explanatory variables.2 the steps of applying econometrics to solve economic problemsAnswer: 1) building models;2) estimation parameters;3) verification theory;4) use modelThe reason for the existence of 3 sequence correlationSequence correlation: that is, the random term U is related to other previous terms. It is called sequence correlation or autocorrelation.The cause of existence:First of all, with the continuous problem in economic life and time, namely the repetition time repeated, therefore, the explanatory variables associated with.Secondly, the error of model selection is established, which makes the explanatory variables relevant.Finally, when the model is established, the random term has autocorrelation, and the sequence has autocorrelation.The method of economic structure test in 4 regression analysisChow puts forward the following test method:Firstly, two samples were merged to form the sample of the number of observation value +, and the model (4.25) was regressed, and the regression equation was obtained:(4.28)The sum of squares of residuals is obtained, and the degree of freedom is + -k-1,Here K is the number of variables explained.Secondly, the use of two small sample given above, respectively (4.25) of the regression analysis, the regression equation respectively (4.26) and (4.27), calculated the sum of squared residuals, respectively, the degree of freedom for -k-1 and -k-1 respectively.Then, according to the sum of squares of residuals, the following statistic is constructed:~ F (k+1, + -2k-2) (4.29)Using statistical (4.29) test (4.26), (4.27) the significant similarities and differences, that is, test hypothesis: (j=0, 1,2,... K).Given the significant level (such as =0.05, =0.01), the F distribution table with the first degree of freedom as k+1 and the second degree of freedom as the + -2k-2 is obtained, and the critical value is obtained.If rejected, that (4.26), (4.27) there is a significant difference, the economic relations of the two or two samples reflect different, we say that the changes in the economic structure; on the contrary, we believe that the economic structure is relatively stable.Some properties of the 5 random perturbation term:1. the complex represented by many factors on the explanatory variable Y;2., the influence direction of Y should be different, there are positive and negative;3. as a secondary factor, the total average impact on Y may be zero;The effect of 4. on Y is non trending and stochastic.Three computational analysis1., according to the following information, study the income and consumption of farmers in Hebei province.Particular yearItem 1994199519961997 1998199920002001 20022003Per capita net income of farmers (100 yuan) 111721232424252627 29Living expenses (100 yuan) 811141413131414151According to economic theory, there is a correlation between farmers' living expenditure and their net income. The basic source of farmers' consumption expenditure lies in their net income, so the increase of per capita net income of farmers is the reason for the increase of their living expenses. In addition, farmers' living expenses are also affected by savings, psychological preferences and other factors, so the model is regression model.If Ct is the farmer's consumption expenditure, and Y is the net income per capita of farmers, the following regression model can be establishedCt=c+aYtDependent Variable: CTMethod: Least SquaresDate: 12/15/97 Time: 16:44Sample: 19942003Included observations: 10Variable Coefficient Std. Error t-Statistic Prob.YT 0.406238 0.046500 8.736250 0C 3.978409 1.080867 3.680755 0.0062R-squared 0.905126 Mean dependent var 13.20000Adjusted R-squared 0.893266 S.D. dependent var 2.250926 S.E. of regression 0.735380 Akaike info criterion 2.399998 Sum squared resid 4.326269 Schwarz criterion 2.460515Log likelihood -9.999988 F-statistic 76.32207Durbin-Watson stat 1.329130 Prob (F-statistic) 0.000023 The regression equation was Ct=3.9784+0.4062Yt(3.6801) (8.7363)Because T (a) =8.7363>T0.025 (8) =2.306F=76.3221>F0.05 (1,8) =5.32So the regression equation and its coefficients are significantR2=0.9051, which shows that the regression equation and the sample observation value have good goodness of fitFour topics1. answers:Meaning: for the random perturbation of the UI regression model, if the other assumption, the second assumption is not established, that is to say in the variance of random UI different observation value is not equal to a constant, Var (UI) = constant (i=1, 2,... (n), or Var (U) Var (U) (I J), then we call the random perturbation term UI has heteroscedasticity.Source: 1. model omitted economic variables, the measurement error of 2.The consequence of heteroscedasticity: the 1. parameter estimator is still linear unbiased, but not valid. 2. test failure based on t distribution and F distribution. The variance of 3. estimator increases, and the prediction accuracy decreases.Inspection: Inspection (Goldfeld - Quart Goldfield - Quandt G - Q test) test in 1965 by S.M.Goldfeld and R.E.Quandt proposed. This test method is applicable to large samples, usually require the capacity of n should be 30 or the number of observations is to estimate the parameters of more than 2 times(i.e., sample size is much larger than the N model included explanatory variables two times large numbers above). To test heteroscedasticity should meet the following conditions: first, using the method of random perturbation UI obey the normal distribution, and the variance of UI increased with a certain explanatory variables; second, random perturbation UI no serial correlation, namely E (uiuj) =0 (I J). The test method is mainly F test.The test hypothesis H0: UI is equal variance, and the alternative assumption is that H1: UI is heteroscedastic, and the specific steps of G - Q test are as follows:1. will explain the observed value of the variable Xi in absolute ascending order, be interpreted correspond to the variables of Xi Yi.2. the Xi are arranged in C values by deleting the centre of the remaining N-C observations is divided into two sub samples of the same capacity, the capacity of each sub sample respectively, a sub sample which is the larger part of the corresponding observation value, the other is a relatively small part of the observed value. It should be noted that the determination of the C value is not arbitrary, and it is determined by experiments by Goldfeld and Quandt. For the sample size when n is greater than 30, the number of C for the entire sample number 1/4 by deleting observations (e.g., sample size is 48, c=, n=12, removal of the observation value is 12, then the two sub sample volume respectively =18).3. the least squares method is used to calculate the regressionequation of the two sub samples, and then the corresponding residual sum of squares is calculated respectively. The sum of squares of residuals is the sum of the residuals of the sub samples with larger sample value, and their degree of freedom is -k, where k is the number of explanatory variables in the econometric model.4. establish statistics:F= can prove that F=RSS2/RSS1 ~ F (), that is, it follows the F distribution of degrees of freedom respectively. Obviously, if the two sub sample variance is equal, the value of F is close to 1, show that UI has equal variance; if the variance is not equal, according to the pre condition of RSS2 is greater than RSS1, F-measure should be greater than 1, then UI has heteroscedasticity, so we can use the F test to verify whether UI has heteroscedasticity of. That is, for the given significance level, the F distribution table is obtained corresponding critical value, if F>, reject H0, accept H1, that is, UI has heteroscedasticity; if F<, then accept H0, UI has equal variance.。
北大计量经济学讲义-工具变量与两阶段最小二乘法
large numbers. 当假定(15.4) 和(15.5) 成立时，可以应用大
数定律证明IV估计是b1的一致估计。
Intermediate Econometrics,
That is, Cov(z,u) = 0 (15.4) 即Cov(z,u) = 0
Intermediate Econometrics,
Yan Shen
8
Instrumental Variable: Who qualifies? 什么样的变量可以作为IV？
The instrument must be correlated with the endogenous variable x 工具变量应与内生变量 x 相关
Intermediate Econometrics,
Yan Shen
5
Why Use Instrumental Variables? 为何使用工具变量？
Instrumental Variables (IV) estimation is used when your model has endogenous x’s 当模型解释变量具有内生性时，使用工具 变量估计
Suppose the true model regresses log(wage) on education (educ) and ability (abil). 假定真实模型将对数工资对教育和能力回归
Now ability is unobserved, and the proxy, IQ, is not available. 现在能力不可观测，而且没有代理变量IQ
b1 . 当z=x时，我们得到b1的OLS估计
计量经济学(2010)(第五章 自相关)
年份
xi
3.3 3.3
y
i
i
0.0543 0.2543
1990 1991
6.2 7.8
1998 1999
2.5 2.7
1992
1993 1994 1995 1996
5.8
5.7 5.0 4.0 3.2
1.4
1.4 1.5 1.9 2.6
-0.3423
-0.3704 -0.4674 -0.3488 0.1262
残 差 图 1
.2 .0 -.2 -.4 -.6 1990 1992 1994 1996
1998 2000 2002 2004
( t 1 , t ) 图形
.6 .4
残 差 图 2
.2
RESID
.0 -.2 -.4 -.6 -.5 -.4 -.3 -.2 -.1 .0 .1 .2 .3 .4 .5 RESID(-1)
思考题与练习题
书上 P109 : 1，2，3 ，同时完成以下补充题：
补充题：在研究劳动力在价值增值中所占份额（即劳动力份额 Y ） 的时间 t 趋势变化中，根据1949~1964年间美国的数据， 得到如下回归结果： 模型A: t=
t21
ˆ ) 2(1 )
（4）根据DW检验临界值 (a) 当
dL , dU ，进行推断：
，则
0 d dL
u
t
存在正自相关；
(b) 当
(c) 当
dU d 4 dU
，则
，则
ut
不存在自相关。
存在负自相关。
4 dL d 4
u
t
DW检验应用说明
1、D-W检验仅适用于一阶线性自相关，对高阶自相关或 非线性自相关均不适用；也不适用于自回归模型。
计量经济学草稿(1)
计量经济学什么是计量经济学或商业计量经济学?Traditional Perception1.Econometrics is the branch of economics concerned with the use ofmathematical methods (especially statistics) in describing economic systems. 2.Econometrics is a set of quantitative techniques that are useful for making"economic decisions".3.Econometrics is a set of statistical tools that allows economists to testhypotheses using really world data. "Is the value of the US Dollar correlated to Oil Prices?" , “ls Fiscal policy really effective?" ,"Does growth in developedcountries stimulate growth in the developing countries?"4.The Economist's Dictionary of Economics defines Econometrics as "The settingup of mathematical models describing mathematical models describingeconomic relationships (such as that the quantity demanded of a good isdependent positively on income and negatively on price), testing the validity of such hypotheses and estimating the parameters in order to obtain a measure of the strengths of the influences of the different independentvariables."5.Econometrics is the intersection of economics, mathematics, and statistics.Econometrics adds empirical content to economic theory allowing theories to be tested and used for forecasting and policy evaluation.6.Econometrics is the branch of economics concerned with the use ofmathematical and statistical methods in describing, analyzing, estimating and forecasting economic relationships. Examples of Economic relationships orBusiness relations and interactions are:7.Estimation of the market model (demand and supply) o Are oil prices and thevalue of US dollar correlated?What are the determinants of growth?How are liquidity and profitability related?Modern View1.Econometrics is no more limited to testing, analyzing and estimating economictheory. Econometrics is used now in many subjects and disciplines like Finance, Marketing, Management, Sociology etc.2.Also, the advent of modern day computers and development of modernsoftware has helped in estimation and analysis of more complex models. Socomputer programing is now an essential component of modern dayeconometrics.3.Econometrics is the application of mathematics, statistical methods, and, morerecently, computer science, to economic data and is described as the branch of economics that aims to give empirical content to economic relations.4.It is no more limited to quantitative research but encompasses qualitativeresearch. So we can finally arrive at a simple but modern and comprehensive definition as:ing the tools of mathematics, statistics and computer sciences, Econometricsanalyses quantitative or qualitative phenomena (from Economics or otherdisciplines), based on evolution and development of theory, by recordingobservations based on sampling, related by appropriate methods of inference.计量经济学的方法(The Methodology of Business Econometrics)The methodology of Business Econometrics may be described by the following steps:(一)Creation of a statement of theory or hypothesis(二)Collection of Data(三)Model Specification(四)Model Estimation(五)Performing Diagnostic Tests(六)Testing the Hypothesis(七)Prediction or ForecastingThe creation of a statement of problem may be based on the existing theory of business and economics. We already know something about the interaction and relationship of variables. For example, we know that the quantity demanded may depend on price, income, prices of substitutes and complementary goods and someother variables. We collect data on these variables and specify our model based on demand theory. We can estimate the model with the help of some technique provided by Econometrics. The estimation may not be free form problems. Here some additional steps may be performed where we can check the validity of the model that we have specified by the use of various diagnostic tests to diagnose any possible problems in the estimation. For that, we test various hypothesis regardingthe effectiveness and validity of the estimators. The ultimate result may be predicting or forecasting outcomes like economic and financial events of outcomes. If the technique and model applied is appropriate, the forecasts would be better.一、模型设定所谓经济模型是指对经济现象或过程的一种数学模拟。
伍德里奇计量经济学名词解释
伍德里奇计量经济学名词解释伍德里奇计量经济学（WoodridgeEconometrics）：伍德里奇计量经济学是一种应用数学和统计学方法来分析经济现象和经济数据的学科。
它结合了经济学理论和数学统计学的工具，旨在提供经验性经济分析的定量解释和预测。
一阶自相关（First-orderAutocorrelation）：一阶自相关是指一个时间序列中当前观测值与前一个观测值之间的相关性。
在计量经济学中，一阶自相关是对时间序列数据的经济模型进行估计和推断时的一个重要考虑因素。
误差项（ErrorTerm）：误差项是指在经济模型中无法被观测到或测量到的影响因素，它代表了模型中未被考虑的其他影响因素对观测结果的影响。
误差项通常假设为随机变量，其期望值为零。
多重共线性（Multicollinearity）：多重共线性指的是经济模型中自变量之间存在高度相关性或线性相关性的情况。
多重共线性可能导致模型估计的不稳定性，使得对自变量系数的解释变得困难。
假设检验（HypothesisTesting）：假设检验是用于验证经济模型中假设是否成立的统计方法。
通过收集样本数据并进行统计推断，假设检验可以帮助我们判断经济模型中的假设是否支持或拒绝。
平稳性（Stationarity）：平稳性是指时间序列数据的统计性质在时间上保持不变的特性。
对于经济数据的分析，平稳性假设是许多计量经济模型的基础之一，它要求数据的均值、方差和协方差不随时间发生显著变化。
识别（Identification）：识别是指在经济模型中确定模型参数的唯一性和可估计性。
在伍德里奇计量经济学中，识别是一个重要的问题，它要求我们通过模型设定和数据的限制来确保模型参数能够被准确估计。
异方差性（Heteroscedasticity）：异方差性指的是在经济数据中，随着自变量的变化，误差项的方差也发生变化的现象。
CCER 计量经济学 第三次作业和答案
Intermediate Econometrics Class 1Problem Set 3 with AnswersHandout Date: Dec. 4th, 2011Due Date: Dec. 9th, 2011 (Hand in BEFORE class)1.An estimated equation iswith, and SSR = 1.5Use F-statistic to test the following(1).(2).(3).(Hint: The tests involve only the sub-matrix in the lower-right corner of .Refer to TA materials for the formula of inverses of partitioned matrices.)(1).equals the single element at the lower right-hand corner of,which is 2.5.Then the F-statistic is calculated asIt falls well short of any usually critical value for . So we cannot reject .(2).only involves the elements in the sub-matrix in the lowerright-hand corner ofThe F-statistic equalsFrom the tables of F distribution, , so we cannot reject the null at5% significance level.(3).Thus the test statistic becomesAgain, the test statistic falls well short of any usually critical value for . So wecannot reject .2. A four-variable regression using quarter data from 1958 to 1976 inclusive gave an estimatedequationThe explained sum of squares was 109.6, and the residual sum of squares, 18.48.(1).When the equation was re-estimated with three seasonal dummies added to thespecification, the explained sum of squares rose to 114.8. Test for the presence of seasonality.To test for the presence of seasonality we test the joint significance of the three seasonal dummy variables. The restricted is 18.48, while the unrestricted isThe rule-of-thumb F-statistic is calculated asThe 5% critical value is (is usually not given in statistic tables,so here we use the instead). We can reject the hypothesis of no seasonality at 5%significance level.(2).Two further regressions based on the original specification were run for the sub-periods1958.1 to 1968.4 and 1969.1 to 1976.4, yielding residual sums of squares of 9.32 and 7.46, respectively. Test for the constancy of the relationship over the two sub-periods.To test the parameter consistency over the two sub-samples, consider the Chow test,The 5% critical value is . Hence we cannot reject the hypothesis ofparameter constancy at 5% significance level.3.Survey records for a large sample of families show the following weekly consumptionexpenditure (Y) and weekly income (X):Y 70 76 91 …… 120 146 135 X 80 95 105 …… 155 165 175* * *Families with an asterisk (*) reported that their income is higher than in the previous year.(1).To examine the impact of weekly income on weekly consumptions, one sets up thefollowing modelHe is concerned that the error terms may have heterogeneous variance. Derive the robust standard error of .Under HSK, the large sample distribution of isThe sample estimate of iswhereThe robust standard error of is the 2nd diagonal element of the estimated covariancematrix of(2).If he wants to estimate directly the elasticity of consumption with respect of income, howshould he modify the model in (1).(3).If he wants to test whether the event of an increase in income, holding the level of incomeunchanged, helps to explain the consumption behavior, how should he extend the model in (1)?(4).If he wants to test whether the marginal propensity to consume (the slope coefficient) offamilies experiencing an increase in income is different from that of families who did not experience an increase, how should he extend the model in (3)?4.Consider the equationwhere is the cumulative college grade point average, is size of high schoolgraduating class, in hundreds, is academic percentile in graduating class, iscombined SAT score, is a dummy gender variable, and is a dummy variablewhich is one for student-athletes.(1).What are your expected signs for the coefficients in this equation? Explain.Holding all other variables constant, the expected sign for high school size should be negative, but at a diminishing rate, because larger high schools tend to have lower teacher-to-student ratios, and the effect becomes less important as the size increase. The higher sat should be positively related to GPA. So should hsperc and female (why should this be the case might be controversial; either because female students tend to study harder to overcome gender discrimination in society, or they tend to take classes where they excel more). I suppose the coefficient for athlete might be negative. However, this might just be my own prejudice.(This answer is provided by the solution manual of Introductory Econometrics: A Modern Approach. It is only for your reference. You’ll receive full credit so long your arguments make sense.)(2).To allow the effect of being an athlete to differ by gender, how should you extend themodel? Write out the null hypothesis if you want to test whether there is no ceteris paribus difference between women athletes and women nonalthletes.Adding to the model we have:In this setup, the intercepts for 4 different categories are:Male non-athleteMale athleteFemale non-athleteFemale athleteSo the test between female athletes and female non-athletes is the test of5.One application of ADL models is the Adaptive Expectation Model:⁄(5.1)⁄(5.2)wheredemand for moneyinterest rate (observables)equilibrium, optimum, or expected long-run interest rate (unobservable)the coefficient of expectation (,)Rewrite Eq.(5.2)⁄(5.3)Substitute Eq. (5.3) into Eq. (5.2)⁄(5.4)(1).Lag Eq. (5.1) one period, then substitute it into Eq. (5.4). You should be able to show thatthe short-run demand is in essence an ADL process of the observables. Write outthe model, and calculate the long-run impact multiplier of .The ADL model isUse lag operator to rewrite the modelThe long-run impact multiplier of isNote the long-run impact multiplier of in the short-rum model is essentially the coefficientof in Eq. (5.1), the equilibrium/long-run model.(2).Now consider another application that incorporates the partial adjustment of into theAdoptive Expectations Model:where are defined as in (1), and:actual capital stock (observable)desired level of capital (unobservable)the coefficient of adjustmentShow that the observed short-run demand is in essence an ADL process. (Hint: Ifyou derive the model correctly, you will find the error terms are serially correlated.)The ADL model is。
计量作业
Econometrics Problem Set1 Let m be the logarithm of M1, p be the log of price level, R denote the opportunity cost of holding money. The following regressions were estimated: (1) (1.69)(0.038)(0.245)3.9580.749 3.44t t t t m p R e =−+−+20.987,0.0919,0.25R s DW ===(2) 11234(0.063)(0.109)(0.105)(0.106)(0.105)0.1180.0850.0220.0730.032t t t t t t e e e e e e residual −−−−−Δ=−+Δ+Δ−Δ+Δ+,20.057,0.041R s ==(3) 21(0.051)0.108,0.043,0.045t t e e residual R s −Δ=−+==(a) Is equation (1) a spurious regression? Either yes or no, you need to conduct a formal test.(b) Why equation (3) was estimated?2 Some first order autoregressive models with normal iid errors are estimated: Model 1: 25022110.50.96, 3.16,0.92t t t t t y y e e R −==++==∑Model 2: 25022110.10.050.98, 2.03,0.95t t t t t y t y e e R −==+++==∑Conduct the unit root test for both models. Be sure state the underlying data generating hypothesis for t y .3 The following regressions about the production function are estimated based on 60 time series observations:2(0.25)(0.18)ln 0.565ln 0.525ln , .85t t t t Q K L e R =++=24(0.15)(0.08)(0.06)0.085ln 0.05ln 0.25, 0.08t t t t e K L e R −=++=; In addition, the first order correlation coefficient of residuals is 0.2. (a) Is there a strong evidence of the first order serial correlation?(b) Write down the null hypothesis for which the auxiliary regression tests (be sure todefine your notations clearly). Explain why the null hypothesis is of interest. (c) Calculate the test statistic for the null hypothesis specified in (a). Do you accept orreject the null hypothesis?(d) Disregard your test result in (c), suppose that you reject the null hypothesis, howwould you estimate the production function more efficiently?4 Consider a simple model for investment:*1t t t Y αβπε+=++, (1)where t Y is the investment expenditure for time period t, and *1t π+ is the expected profit in the period of t+1, t ε satisfies the Gauss Markov assumption. Since *1t π+ is not observed, a model for *1t π+ is proposed.***1()t t t t ππδππ+=+−, where t π is the actual profit for time period t, and δ<1. (a) Interpret the profit expectation model.(b) Express *1t π+ in terms of the observable profit t π, 1t π−,…(c) Transform model (1), so that it can be estimated. Is there always a serial correlated error after transformation?(d) Comment on the OLS applied to your transformed model5 (a) Implement the LM test for serial correlation when the regression error term follows AR(1): 1t t t u u ρε−=+, where t εis a white noise.(b) If the error term follows MA(1): 1t t t u εθε−=+, is the LM test for MA(1) any different than the LM test in part(a)?(c) Is LM test for ARMA(1,1) error equivalent to the LM test for AR(2)? MA(2)?。
上海财经大学《高级计量经济学II》习题四及答案
2
(c) We would apply the delta method. Thus, we would require the full variance matrix of the probit estimates as well as the gradient of the expression of interest.
Solution 2 (a) If P (y = 1jz1; z2) = z1 1 + 1z2 + 2z22 , then
@P (y = 1jz1; z2) = ( @z2
1+2
2z2)
z1 1 + 1z2 + 2z22
for given z, this is estimated as
(^ consistently estimated by maximizing
X N
X N
li ( ) = fyi ln (Ui
i=1
i=1
x0i ) + (1
yi) ln [1
(Ui x0i )]g
1
(c) The partial e¤ ect of x3 on P (yi = 1jxi) is
and P (yi1 = 1jxi; ci; ni = 1) = 1 [(xi2 xi1) ]
2
Advanced Econometrics II Answer 4
Yahong Zhou March 2, 2014
1. Consider a latent variable modeled by
y = x0i + "i
上海财经大学《高级计量经济学II》习题四及答案
Advanced Econometrics II Problem Set 4
基本无害的计量经济学 英文版
基本无害的计量经济学英文版以下为您生成 20 个关于“写基本无害的计量经济学”（Writing Essentially harmless econometrics）的相关英语释义、短语、单词、用法和双语例句：1. **单词**：econometrics （英语释义：The branch of economics that uses statistical methods to analyze economic data. ）- 用法：“Econometrics is a complex subject.”（计量经济学是一门复杂的学科。
）2. **单词**：harmless （英语释义：Not causing harm or damage. ）- 用法：“The snake is harmless.”（这条蛇无害。
）3. **单词**：essentially （英语释义：In the most important or fundamental way. ）- 用法：“Essentially, this is a difficult problem.”（从根本上说，这是个难题。
）4. **单词**：writing （英语释义：The activity of putting words on paper or a computer screen. ）- 用法：“I enjoy writing stories.”（我喜欢写故事。
）5. **短语**：statistical method （英语释义：A way of dealing with and analyzing data using statistics. ）- 用法：“We used statistical methods to analyze the data.”（我们使用统计方法来分析数据。
）6. **短语**：economic data （英语释义：Information related to the economy. ）- 用法：“The research is based on extensive economic data.”（这项研究基于大量的经济数据。
沃森计量经济学课后
1Undergraduate Econometrics (Spring 2013) Due Date: School of Economics, SDU March 12, 2013本人学号_________________________批改人学号_______________________ 成绩____________Problem Set 1 (Part B)1. Let Y be a Bernoulli random variable with success probability (1)P Y p ==, and let1,,n Y Y …be i.i.d. draws from this distribution. Let ˆpbe the fraction of success (1s) in this sample. a . Show that ˆpY =. b . Show that ˆpis an unbiased estimator of p . c . Show that ˆvar()(1)/pp p n =−.2. The CNN/USA Today/Gallup poll conducted on September 3-5, 2004, surveyed 755 likely voters; 405 reported a preference for President George W. Bush, and 350 reported a preference for Senator John Kerry. The CNN/USA Today/Gallup poll conducted on October 1-3, 2004, surveyed 756 likely voters; 378 reported a preference for Bush, and 378 reported a preference for Kerry.a . Construct a 95% confidence interval for the fraction of likely voters in the population who favored Bush in early September 2004.b . Construct a 95% confidence interval for the fraction of likely voters in the population who favored Bush in early October 2004.c . Was there a statistically significant change in voters’ opinions across the two dates?3. a . Y is an unbiased estimator of Y μ. Is 2Y an unbiased estimator of 2Y μ? b . Y is a consistent estimator of Y μ. Is 2Y a consistent estimator of 2Y μ?特注：（1） 你可以与同学共同讨论，但最后必须亲自完成作业。
英汉对照计量经济学术语
英汉对照计量经济学术语A校正R2〔Adjusted R-Squared〕：多元回归剖析中拟合优度的量度，在估量误差的方差时对添加的解释变量用一个自在度来调整。
统一假定〔Alternative Hypothesis〕：检验虚拟假定时的相对假定。
AR〔1〕序列相关〔AR(1) Serial Correlation〕：时间序列回归模型中的误差遵照AR〔1〕模型。
渐近置信区间〔Asymptotic Confidence Interval〕：大样本容量下近似成立的置信区间。
渐近正态性〔Asymptotic Normality〕：适当正态化后样本散布收敛到规范正态散布的估量量。
渐近性质〔Asymptotic Properties〕：当样本容量有限增长时适用的估量量和检验统计量性质。
渐近规范误〔Asymptotic Standard Error〕：大样本下失效的规范误。
渐近t 统计量〔Asymptotic t Statistic〕：大样本下近似听从规范正态散布的t 统计量。
渐近方差〔Asymptotic Variance〕：为了取得渐近规范正态散布，我们必需用以除估量量的平方值。
渐近有效〔Asymptotically Efficient〕：关于听从渐近正态散布的分歧性估量量，有最小渐近方差的估计量。
渐近不相关〔Asymptotically Uncorrelated〕：时间序列进程中，随着两个时点上的随机变量的时间距离添加，它们之间的相关趋于零。
衰减偏误〔Attenuation Bias〕：总是朝向零的估量量偏误，因此有衰减偏误的估量量的希冀值小于参数的相对值。
自回归条件异方差性〔Autoregressive Conditional Heteroskedasticity, ARCH〕：静态异方差性模型，即给定过去信息，误差项的方差线性依赖于过去的误差的平方。
一阶自回归进程[AR〔1〕]〔Autoregressive Process of Order One [AR(1)]〕：一个时间序列模型，其以后值线性依赖于最近的值加上一个无法预测的扰动。
计量经济学第九章联立方程组模型
12
计量经济学 Econometrics
阅读课本P261-262
注意 ▪ 结构参数和简化参数之间关系
▪ 利用简化参数的最小二乘估计量和参数关系 所得到的结构参数估计量虽然仍是有偏的， 但具有一致性
2020/2/16
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计量经济学 Econometrics
联立方程组模型的识别及识别条件
计量经济学 Econometrics
Ct a0 a1Yt 1t It b0 b1Yt b2Yt1 2t
Yt Ct It Gt
前定变量 外生变量
Ct ——t期的消费额
It ——t期的投资额
Yt ——t期的国民收入
Gt ——t期的政府支出额
Y2020/2/16 t 1
——t-1期的国民收入
内生变量
联立方程模型定义
▪ 含有两个以上方程的模型 ▪ 每个方程描述变量间的一个因果关系
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计量经济学 Econometrics
变量类型
▪ 内生变量 ➢由模型系统决定其取值的变量 ▪ 外生变量 ➢由模型系统以外的因素决定其取值的变量 ▪ 前定变量 ➢内生变量的滞后值与外生变量
2020/2/16
8
例2 计量经济学
Econometrics
▪ 某种农产品的市场局部均衡模型
需求方程 Dt a0 a1Pt a2Yt 1t
供给方程 均衡方程
St b0 b1Pt1 b2Wt 2t
Dt St
这里内生变量为： 外生变量为： 前定变量为：
Dt , St , Pt
Yt ,Wt
计量经济学 Econometrics
第九章 联立方程组模型
伍德里奇计量经济学英文版各章总结(K12教育文档)
伍德里奇计量经济学英文版各章总结(word版可编辑修改)编辑整理：尊敬的读者朋友们：这里是精品文档编辑中心，本文档内容是由我和我的同事精心编辑整理后发布的，发布之前我们对文中内容进行仔细校对，但是难免会有疏漏的地方，但是任然希望（伍德里奇计量经济学英文版各章总结(word版可编辑修改)）的内容能够给您的工作和学习带来便利。
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CHAPTER 1TEACHING NOTESYou have substantial latitude about what to emphasize in Chapter 1。
I find it useful to talk about the economics of crime example （Example 1.1) and the wage example （Example 1.2） so that students see， at the outset，that econometrics is linked to economic reasoning, even if the economics is not complicated theory.I like to familiarize students with the important data structures that empirical economists use, focusing primarily on cross—sectional and time series data sets, as these are what I cover in a first—semester course. It is probably a good idea to mention the growing importance of data sets that have both a cross—sectional and time dimension。
计量经济学（英文）重点知识点考试必备汇编
计量经济学（英文）重点知识点考试必备汇编第一章1.Econometrics（计量经济学）：the social science in which the tools of economic theory, mathematics, and statistical inference are applied to the analysis of economic phenomena.the result of a certain outlook on the role of economics, consists of the application of mathematical statistics to economic data to lend empirical support to the models constructed by mathematical economics and to obtain numerical results.2.Econometric analysis proceeds along the following lines计量经济学分析步骤1)Creating a statement of theory or hypothesis.建立一个理论假说2)Collecting data.收集数据3)Specifying the mathematical model of theory.设定数学模型4)Specifying the statistical, or econometric, model of theory.设立统计或经济计量模型5)Estimating the parameters of the chosen econometric model.估计经济计量模型参数6)Checking for model adequacy : Model specification testing.核查模型的适用性：模型设定检验7)Testing the hypothesis derived from the model.检验自模型的假设8)Using the model for prediction or forecasting.利用模型进行预测●Step2：收集数据T hree types of data三类可用于分析的数据1)Time series(时间序列数据):Collected over a period of time,are collected at regular intervals.按时间跨度收集得到2)Cross-sectional截面数据:Collected over a period of time, are collected at regular intervals.按时间跨度收集得到3)Pooled data合并数据（上两种的结合）●Step3：设定数学模型1.plot scatter diagram or scattergram2.write the mathematical model●Step4：设立统计或经济计量模型C LFPR is dependent variable应变量C UNR is independent or explanatory variable独立或解释变量（自变量）W e give a catchall variable U to stand for all these neglected factorsI n linear regression analysis our primary objective is to explain the behavior of the dependent variable in relation to the behavior of one or more other variables, allowing for the data that the relationship between them is inexact.线性回归分析的主要目标就是解释一个变量（应变量）与其他一个或多个变量（自变量）只见的行为关系，当然这种关系并非完全正确●Step5：估计经济计量模型参数I n short, the estimated regression line gives the relationship between average CLFPR and CUNR 简言之，估计的回归直线给出了平均应变量和自变量之间的关系T hat is, on average, how the dependent variable responds to a unit change in theindependent variable.单位因变量的变化引起的自变量平均变化量的多少。
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Econometrics Problem Set 1 11210690112 张婷The code is simplified in the hard copy1 Compute the sample mean for average log of earnings (lnY) for both men and women. Compute 90% and 95% confidence intervals for the population mean of lnY. Formulate a statistical test of whether the mean of lnY are different for men and women. Calculate the p-value of the test. Do you reject H0 at the 1% level of significance?CODE：Library(foreign);F=read.dta("C:/earningsdata_females.dta");M=read.dta("C:/earningsdata_males.dta");MeanlnF=mean(F[0,1]);lnM=mean(M[0,1]);mean(lnF);[1] 7.68859mean(lnM);[1] 7.94615One sample t-test90% t.test(F[1],conf.level=0.90) t.test(M[1],conf.level=0.90)95% t.test(F[1],conf.level=0.95) t.test(M[1],conf.level=0.95)t.test(F[1],M[1],conf.level=0.99) we get that means of lnF and lnM is differentwelch two sample t-testdata: M[1] and F[1]t = 39.7296, df = 7272.124, p-value < 2.2e-16alternative hypothesis: true difference in means is not equal to 099 percent confidence interval:0.2408862 0.2742963sample estimates:mean of x mean of y7.946150 7.688559Final answer:Female malemean 7.94615 7.6885990% confidence level [7.939378, 7.952921] [7.938081,7.954219]95% confidence level [7.680317, 7.696801] [7.678737, 7.698380]Test the means of lnF and lnM are different, run a t-testH0: ln Ym=ln YfCalculate p value=(lnYm −lnYf)/√var (lnYm )Nm +var (ln Yf )Nf =2.2e-16<0.01We get the conclusion that the means of lnF and lnM are statistically different at 1% significance level2 Compute Now compute the sample mean for earnings (mean(Y)). Do you find that mean(Y)=exp(lnY)? ExplainCODE:lnF=F[0,1];lnM=M[0,1];lnY=c(lnF,lnM); lnY represent the total ln of F and MY=exp(lnY);mean(Y)[1] 2730.177mean(lnY);[1] 7.854298Y1=mean(lnY);exp(Y1);[1] 2576.787We can get that Y is not equal to Y1Final answer:Mean(Y) is not equal to mean(exp(lnY))Y=2730.177 Y2=2576.787Y is the arithmetic mean and Y1 is the geometric mean3 Use the data set for males and estimate the regression equation lnY i = α+ βi S i +u i Specify your assumptions about the error terms u i : What assumptions are needed for the OLS estimator to be i) unbiased, ii) consistent and iii) asymptotically normally distributed?CODE:s=M[ ,2];lm_M=lm(Male$ln_y_~1+s)Summary(lm_M)Call:lm(formula=Male$ln_y_ ~ 1+s)Residuals:Min 1Q Median 3Q Max-1.62232 -0.18988 -0.03525 0.15989 1.77426Coefficients:Estimate Std. Error t value Pr(>|t|)(Intercept) 7.703346 0.009361 822.88 <2e-16 ***s 0.047029 0.001652 28.47 <2e-16 ***Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1Residual standard error: 0.2953 on 5857 degrees of freedomMultiple R-squared: 0.1215, Adjusted R-squared: 0.1214F-statistic: 810.4 on 1 and 5857 DF, p-value: < 2.2e-16Final answer:LnY=7.703346+0.0470092SAssumptions:(1)Unbiased(mean value of residual is zero(2)Consistent(mean value of residual is zero and residual is uncorrelated with Yi)(3)Asymptotically normally(mean value of residual is zero and residual is uncorrelated with Xi)4 According to your estimates, what is the conditional expectation E(lnY i |S) for men and women, respectively? Calculate the expected log earnings for a man and woman, respectively, with 12 year schooling. Does schooling account for a large fraction of the variance in earnings across individuals? Explain.CODEs=F[ ,2];Lm_F=lm(Female$ln_y_~1+s)Summary(lm_F);Call:Lm(formula== Female$ln_y_ ~ 1 +s)Residuals:Min 1Q Median 3Q Max-1.28203 -0.14014 -0.00748 0.12850 1.99665Coefficients:Estimate Std. Error t value Pr(>|t|)(Intercept) 7.449845 0.011325 657.81 <2e-16 ***Female$s 0.043848 0.001897 23.11 <2e-16 ***Significance codes:0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1Residual standard error: 0.2646 on 3245 degrees of freedomMultiple R-squared: 0.1413, Adjusted R-squared: 0.1411F-statistic: 534 on 1 and 3245 DF, p-value: < 2.2e-16Final answer:As the answers from the code, we can get the regression function for lnYf:lnYf=7.449845+0.043848sif s=12 years CE of lnYm=7.703346+0.047029*(12-7)=7.935 (Males) (according to answer of Q3) CE of lnYf = 7.449845+0.043848*(12-7)=7.6695(Females)The power of s is not significant, so I think school years do not affect the var of earnings very much5 Give a 95% confidence interval for β1. What is your estimated expected marginal return to schooling, ∂E(lnYi|Si)/ ∂S i? What is the estimated percentage increase in income of one additional year of schooling? Do these calculations both for men and women.CODE:Alpha=0.05A=summary(lm_M)$coefficientsDf=lm_male$df.residualLeft=A[,1]-A[,2]*qt(1-alpha/2,df)Right=A[,1]+A[,2]*qt(1-alpha/2,df)Rowname=dimnames(A)[[1]]Colname=c("Estimates","Left","Right")matrix(c(A[,1], left, right), ncol=3,dimnames = list(rowname, colname))Estimates Left Right(Intercept) 7.70334617 7.68499439 7.72169794Male$s 0.04702921 0.04379056 0.05026786B=summary(lm_F)$coefficientsDf=lm_female$df.residualLeft=B[,1]-B[,2]*qt(1-alpha/2,df)Right=B[,1]+B[,2]*qt(1-alpha/2,df)Rownam=dimnames(B)[[1]]Colname=c("Estimates","Left","Right")matrix(c(B[,1], left, right), ncol=3,dimnames = list(rowname, colname))Estimates Left Right(Intercept) 7.44984480 7.42763963 7.47204996Female$s 0.04384815 0.04012787 0.04756843Final answer:When school years increase from 0-1, the income of male increases 0.61% and female increases 0.59% respectively.6 We want to test whether the returns to schooling is different for men and women. Set up an appropriate test statistic and carry out a formal statistical test. Discuss the results.CODE:New=rbind(data.frame(Male,dummy=1),data.frame(Female,dummy=0))summary(lm(New[[1]]~New[[2]]+New[[2]]*New[[34]]))Call:lm(formula = New[[1]] ~ New[[2]] + New[[2]] * New[[34]])Residuals:Min 1Q Median 3Q Max-1.62232 -0.17157 -0.02197 0.14736 1.99665Coefficients:Estimate Std. Error t value Pr(>|t|)(Intercept) 7.449845 0.012189 611.176 <2e-16 ***New[[2]] 0.043848 0.002042 21.471 <2e-16 ***New[[34]] 0.253501 0.015167 16.714 <2e-16 ***New[[2]]:New[[34]] 0.003181 0.002590 1.228 0.219---Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1Residual standard error: 0.2847 on 9102 degrees of freedomMultiple R-squared: 0.2505, Adjusted R-squared: 0.2503F-statistic: 1014 on 3 and 9102 DF, p-value: < 2.2e-16Final answer:First we set dummy variables to get the following function:LnY=α+β1*s+β2dummy+β3*dummy*s+μDummy=0, we get the male dataDummy=1, we get the female dataThe null assumption H0: β3=0 , H1: β3 is not equal to 0From R, we get P value of β3 is 0.219 which is bigger than the Sign.levelwe can ‘t reject HO, so the effect of s on earnings is not different.7 if the main interest parameter is β1, i.e. the marginal returns to schooling, do you see any problems with running a univariate regression? Discuss possible sources of bias of your estimates.Answer:From Q above, we know that we can’t explain all the changes in the earning relying on only single factors.If we want to run a unvariate regression, we must also consider the effect of other factors on the factor we are analyzing and that becomes quite complex8 Now try out for yourself some of the other possible explanatory variables in your data set. Choose one of the data sets. Compare different univariate regressions and compare their R squared. Comment on the results. What does R squared say? Which of the regresses you try appear to explain most of the variation in the earnings data.CODE:For e( experience)Malelm_male2=lm(Male$ln_y_~1+Male$e)summary(lm_male2)we getResidual standard error: 0.3148 on 5857 degrees of freedom Multiple R-squared: 0.002108, Adjusted R-squared: 0.001937F-statistic: 12.37 on 1 and 5857 DF, p-value: 0.0004395Femalelm_female2=lm(Female$ln_y_~1+Female$e)summary(lm_female2)we getResidual standard error: 0.2844 on 3245 degrees of freedom Multiple R-squared: 0.007875, Adjusted R-squared: 0.007569F-statistic: 25.76 on 1 and 3245 DF, p-value: 4.091e-07For e^2(experience squared)Malelm_male3=lm(Male$ln_y_~1+Male$e_2)summary(lm_male3)we getResidual standard error: 0.315 on 5857 degrees of freedom Multiple R-squared: 0.0007927, Adjusted R-squared: 0.0006221F-statistic: 4.646 on 1 and 5857 DF, p-value: 0.03116Femalelm_female3=lm(Female$ln_y_~1+Female$e_2)summary(lm_female3)we getResidual standard error: 0.2844 on 3245 degrees of freedom Multiple R-squared: 0.007814, Adjusted R-squared: 0.007508F-statistic: 25.56 on 1 and 3245 DF, p-value: 4.534e-07For public(occupation in public service)Malelm_male4=lm(Male$ln_y_~1+Male$public)summary(lm_male4)we getResidual standard error: 0.315 on 5857 degrees of freedom Multiple R-squared: 0.0007927, Adjusted R-squared: 0.0006221 F-statistic: 4.646 on 1 and 5857 DF, p-value: 0.03116Femalelm_female4=lm(Female$ln_y_~1+Female$public)summary(lm_female4)we getResidual standard error: 0.2844 on 3245 degrees of freedom Multiple R-squared: 0.007814, Adjusted R-squared: 0.007508F-statistic: 25.56 on 1 and 3245 DF, p-value: 4.534e-07。