斯托克《计量经济学》Ch7
计量经济学 第七章答案
练习题7.1参考解答（1）先用第一个模型回归，结果如下：22216.4269 1.008106 t=(-6.619723) (67.0592)R 0.996455 R 0.996233 DW=1.366654 F=4496.936PCE PDI =-+==利用第二个模型进行回归，结果如下：122233.27360.9823820.037158 t=(-5.120436) (6.970817) (0.257997)R 0.996542 R 0.996048 DW=1.570195 F=2017.064t t t PCE PDI PCE -=-++==（2)从模型一得到MPC=1.；从模型二得到，短期MPC=0.，长期MPC= 0.+(0.)=1.01954练习题7.2参考答案（1）在局部调整假定下，先估计如下形式的一阶自回归模型：*1*1*0*tt ttu Y X Y +++=-ββα估计结果如下：122ˆ15.104030.6292730.271676 se=(4.72945) (0.097819) (0.114858)t= (-3.193613) (6.433031) (2.365315)R =0.987125 R =0.985695 F=690.0561 DW=1.518595t t t Y X Y -=-++根据局部调整模型的参数关系，有****11 ttu u αδαβδββδδ===-=将上述估计结果代入得到： *1110.2716760.728324δβ=-=-=*20.738064ααδ==-*0.864001ββδ==故局部调整模型估计结果为： *ˆ20.7380640.864001ttYX =-+ 经济意义解释：该地区销售额每增加1亿元，未来预期最佳新增固定资产投资为0.亿元。
运用德宾h 检验一阶自相关：(121(1 1.34022d h =-=-⨯=在显著性水平05.0=α上，查标准正态分布表得临界值21.96h α=，由于21.3402 1.96h h α=<=，则接收原假设0=ρ，说明自回归模型不存在一阶自相关。
斯托克《计量经济学》Ch6
检验模型：（以残差代替误差） 检验假设： H 0 : 1 2 r 0,
ˆ i2 0 1 z1i r zri vi
H1 : 存在 i 使得 i 0, i 1,2,, r
检验步骤：S1：OLS回归原模型，得到残差序列； S2：将残差平方对影响变量回归，得出拟合优度R2；
Ch6：异方差、自相关和多重共线性
自变量包含因变量滞后项—— 德宾检验（DurbinTest）： 检验假设：
计量经济学PPT
H 0 : 1 2 r 0; H1 : 1 , 2 ,, r 至少一个不为0
检验统计量及分布：辅助回归的拟合优度为R2，则n×R2渐进服从自 由度为r的χ2（r）分布。Eviews操作。 自相关的修正：广义差分法 回归模型：
ˆ ˆ Var ( 1 ) ˆ ( xi x ) 2 i2 i 1
n
计量经济学PPT
n ( xi x ) 2 i 1
2
以此计算的t-统计量
ˆ 1 1 ˆ t ( 1 ) * ˆ s ( 1 )
*
在大样本下渐进有效（参见本章附录）。 Eviews模型设定选项可进行选择
yt 0 1 x1t k xkt yt 1 t , t 1,2,, n
检验统计量及其分布：
n DW h 1 ~ a） N (0,1)ቤተ መጻሕፍቲ ባይዱ （ ˆ 2 1 nVar (ˆ )
自相关检验（二）——布劳殊-戈弗雷（Breusch-Godfrey）
Ch6：异方差、自相关和多重共线性
对古典线性回归模型基本假设不满足的处理：广义OLS. 包括（i）基本假设不满足时仍采用OLS带来的后果； （ii）对基本假设是否满足进行检验； （iii）对OLS方法的改进——GLS 一、异方差 定义：存在i,j，使得
计量经济学斯托克沃森第三版答案
计量经济学斯托克沃森第三版答案1、盈余公积是企业从（）中提取的公积金。
[单选题] *A.税后净利润(正确答案)B.营业利润C.利润总额D.税前利润2、企业在转销已经确认无法支付的应付账款时，应贷记的会计科目是（）。
[单选题] *A.其他业务收入B.营业外收入(正确答案)C.盈余公积D.资本公积3、企业因解除与职工的劳动关系给予职工补偿而发生的职工薪酬，应借记的会计科目是（）。
[单选题] *A.管理费用(正确答案)B.计入存货成本或劳务成本C.营业外支出D.计入销售费用4、由投资者投资转入的无形资产，应按合同或协议约定的价值，借记“无形资产”科目，按其在注册资本所占的份额，贷记“实收资本”科目，按其差额记入（）科目。
[单选题] *A.“资本公积—资本溢价”(正确答案)B.“营业外收入”C.“资本公积—其它资本公积”D.“营业外支出”5、下列各项，不影响企业营业利润的项目是（）。
[单选题] *A.主营业务收入B.其他收益C.资产处置损益D.营业外收入(正确答案)6、2018年12月31日，甲公司某项固定资产计提减值准备前的账面价值为1 000万元，公允价值为980万元，预计处置费用为80万元，预计未来现金流量的现值为1 050万元。
2018年12月31日，甲公司应对该项固定资产计提的减值准备为（）万元。
[单选题] *A.0(正确答案)B.20C.50D.1007、．（年浙江省高职考）下列各项中，属于会计对经济活动进行事中核算的主要形式的是（）[单选题] *A预测B决策C计划D控制(正确答案)8、专利权有法定有效期限，一般发明专利的有效期限为（）。
[单选题] *A.5年B.10年C.15年D.20年(正确答案)9、．（年预测）下列属于货币资金转换为生产资金的经济活动的是（）[单选题] *A购买原材料B生产领用原材料C支付工资费用(正确答案)D销售产品10、．（年浙江省第一次联考）下列各项中，不属于会计核算的前提条件的是（）[单选题] *A持续经营B货币计量C权责发生制(正确答案)D会计主体11、下列各项税金中不影响企业损益的是（）。
斯托克、沃森着《计量经济学》第二章
Chapter 2. Review of Probability2.1 Random Variables and Probability Distributions概率Probability：在大量重复实验下，事件发生的频率趋向的某个稳定值。
例如，记事件“下雨”为A，其发生的概率为P()A。
条件概率Conditional Probability ：例：已知明天会出太阳，下雨的概率有多大？记事件“出太阳”为B 。
则在出太阳的前提条件下降雨的“条件概率”（conditional probability ）为，P()P()P()A B A B B ∩≡其中，“∩”表示事件的交集（intersection ），故P()A B ∩为“太阳雨”的概率，参见图2.1。
条件概率是计量经济学的重要概念之一。
图2.1、条件概率示意图独立事件Independence ：如果条件概率等于无条件概率，即P()P()A B A =，即B 是否发生不影响A 的发生，则称,A B 为相互独立的随机事件。
此时，P()P()P()P()A B A B A B ∩≡=，故P()P()P()A B A B ∩=也可以将此式作为独立事件的定义。
全概公式如果事件组{}12,,,(2)n B B B n ≥ 两两互不相容，()0(1,,)i P B i n >∀= ，且12n B B B ∪∪∪ 为必然事件（即在12,,,n B B B 中必然有某个i B 发生，“∪”表示事件的并集，union ），则对任何事件A 都有（无论A 与{}12,,,n B B B 是否有任何关系），1P()P()P()ni i i A B A B ==∑全概公式把世界分成了n 个可能的情形，再把每种情况下的条件概率“加权平均”而汇总成无条件概率（权重为每种情形发生的概率）。
该公式有助于理解后面的迭代期望定律。
离散型随机变量Discrete Random Variable ：假设随机变量X 的可能取值为{}12,,,,k x x x ，其对应的概率为{}12,,,,k p p p ，即(P )k k p X x ≡=，则称X 为离散型随机变量，其分布律可以表示为，1212k k X x x x pp p p其中，0k p ≥，1kkp=∑。
斯托克《计量经济学》Ch8
ˆ LR 2[l ( x, y,: β) l ( x, y,: 0)] ~ 2 (k )
ˆ l ( x, y : β) ：对数似然函数在参数极大似然估计处的取值
l ( x, y,0) ：对数似然函数在原假设下的取值
MacFadden R2：
ˆ l ( x, y : ) 1 l ( x, y : 0)
n
因此：
ˆ ˆ ~ N β, V β (a) n
检验假设： 检验统计量：
H0 : i 0,
H1 : i 0
ˆ i zi ~ N 0, 1 ˆ ) (a) ˆ s(i
©上海财经大学经济学院
Ch8：分类选择模型
计量经济学PPT
Probit 模型的检验：整体检验-似然比检验 检验假设： H0 : 1 k 0 ，H1 : 存在i 0, i 1,2,, k 检验统计量：
?????n构造z检验统计量21111xxxxxeexxeeexxf?iiixiixxiiepypeepyp?111011112??1??ii??????????i?????inixxaxxeenvv?上海财经大学经济学院ch8
Ch8：分类选择模型
计量经济学PPT
定义：又称离散选择模型，是指因变量取离散值，用以描述分类、状态等 的模型。 二元选择模型 因变量只取两个值0，1。 传统线性回归模型对二元选择建模的缺陷： （i）人为增加约束条件： P( yi 1) pi , P( yi 0) 1 pi
E( yi ) 1 P( yi 1) 0 P( yi 0) pi
0 pi 0 1x1i k xki 1
（ii）人为导致异方差：
1 0 1 x1i k xki 1 pi , yi 1 i ( 0 1 x1i k xki ) pi , yi 0
斯托克《计量经济学》Ch4
ˆ i ~ N i , ci 2 , i Байду номын сангаас,1,2,, k
©上海财经大学经济学院
Ch4：多元线性回归模型
当k=2时，参数OLS估计可以写为：
ˆ ˆ ˆ ˆ 0 y 1 x1 2 x2 k xk n ( o ) ( o ) n ( o ) 2 n ( o ) ( o ) n ( o ) ( o ) x1i yi x2i x2i yi x1i x2i i 1 i 1 i 1 ˆ 1 i 1 2 n ( o ) 2 n ( o ) 2 n ( o ) ( o ) x1i x2i x1i x2i i 1 i 1 i 1 n ( o ) ( o ) n ( o ) 2 n ( o ) ( o ) n ( o ) ( o ) x2i yi x1i x1i yi x1i x2i i 1 i 1 i 1 ˆ 2 i 1 2 n ( o ) 2 n ( o ) 2 n ( o ) ( o ) x1i x2i x1i x2i i 1 i 1 i 1
Ch4：多元线性回归模型
模型设定： 总体模型：
计量经济学PPT
y 0 1 x1 2 x2 k xk xβ
其中
x (1, x1 , x2 , xk )
β (0 , 1 , 2 ,, k )
样本模型：
yi 0 1 x1i 2 x2i k xki i , i 1,2,, n
ˆ ˆ ˆ ˆ ˆ ˆ y 0 1x1 2 x2 k xk xβ
斯托克,沃森计量经济学第七章实证练习stata
斯托克,沃森计量经济学第七章实证练习stataE7.2E7.3E7.4-------------------------------------------- (1) (2) ahe ahe -------------------------------------------- age 0.605*** 0.585*** (15.02) (16.02) female -3.664*** (-17.65)bachelor 8.083*** (38.00)_cons 1.082 -0.636 (0.93) (-0.59)（表2）Robust ci in parentheses*** p<0.01, ** p<0.05, * p<0.1-------------------------------------------- N 7711 7711 -------------------------------------------- t statistics in parentheses* p<0.10, ** p<0.05, *** p<0.01 (表1)（1）建⽴ahe 对age 的回归。
截距估计值是1.082，斜率估计值是0.605。
（2）①建⽴ahe 对age ，female 和bachelor 的回归。
Age 对收⼊的效应的估计值是0.585。
② age 回归系数的95%置信区间： (0.514，0.657)（3）设H 0:βa,（2）-βa,（1）=0 H1:βa,（2）-βa （1）≠0由表3，得SE ，SE(βa,（2）-βa,（1）)=√（0.0403）2+(0.0365)2=0.054t=（0.605-0.585）/0.054=0.37<1.96所以不拒绝原假设，即在5%显著⽔平下age 对ahe 的效应估计没有显著差异，所以（1）中的回归没有遭遇遗漏变量偏差。
斯托克,沃森计量经济学第七章实证练习stata
E7.2E7.3E7.4-------------------------------------------- (1) (2) ahe ahe -------------------------------------------- age 0.605*** 0.585*** (15.02) (16.02)female -3.664*** (-17.65)bachelor 8.083*** (38.00)_cons 1.082 -0.636 (0.93) (-0.59)（表2）Robust ci in parentheses*** p<0.01, ** p<0.05, * p<0.1-------------------------------------------- N 7711 7711 -------------------------------------------- t statistics in parentheses* p<0.10, ** p<0.05, *** p<0.01 (表1)（1） 建立ahe 对age 的回归。
截距估计值是1.082，斜率估计值是0.605。
（2） ①建立ahe 对age ，female 和bachelor 的回归。
Age 对收入的效应的估计值是0.585。
② age 回归系数的95%置信区间： (0.514，0.657)（3） 设H 0:βa,（2）-βa,（1）=0 H1:βa,（2）-βa （1）≠0由表3，得SE ，SE(βa,（2）-βa,（1）)=√（0.0403）²+(0.0365)²=0.054t=（0.605-0.585）/0.054=0.37<1.96所以不拒绝原假设，即在5%显著水平下age 对ahe 的效应估计没有显著差异，所以（1）中的回归没有遭遇遗漏变量偏差。
计量经济学斯托克答案
计量经济学斯托克答案【篇一：计量经济学教材推荐】txt>【计量经济学的内容体系】古扎拉蒂《计量经济学基础》白砂堤津耶《通过例题学习计量经济学》伍德里奇《计量经济学导论：现代观点》斯托克、沃森《计量经济学导论》林文夫（fumio hayashi）《计量经济学》雨宫健（takeshi amemiya ）《高级计量经济学》李子奈、潘文卿编著《计量经济学》【计量经济学的内容体系】狭义的计量经济学以揭示经济现象中的因果关系为目的，主要应用回归分析方法。
广义的计量经济学是利用经济理论、统计学和数学定量研究经济现象的经济计量方法，除了回归分析方法，还包括投入产出分析法、时间序列分析方法等。
把计量经济学分为初级、中级、高级三个层次，初级计量经济学一般包括计量经济学所必须的基础数理统计只是和矩阵代数只是、经典的线性计量经济学模型理论与方法（以单一方程模型为主）、单方程模型的应用等内容；中级计量经济学以经典的线性计量经济学模型理论与方法及其应用为主要内容，包括单一方程模型和联立方程模型。
在应用方面，主要讨论计量经济学模型在生产、需求、消费、投资、货币需求和宏观经济系统等传统领域的应用，注重于应用过程中实际问题的处理。
在描述方法上普遍运用矩阵描述；高级计量经济学以扩展的线性模型理论与方法、非线性模型理论与方法和动态模型理论与方法，以及它们的应用为主要内容。
从研究对象和侧重点的角度讲，理论计量经济学侧重于理论与方法的数学证明与推导，与数理统计联系极为密切；应用计量经济学则以建立与应用计量经济学模型为主要内容，强调应用模型的经济学和统计学基础，侧重于建立与应用模型过程中实际问题的处理。
纵观计量经济学发展史，20世纪70年代之前发展并广泛应用的计量经济学称为经典计量经济学，其理论特征是：以经济理论为导向建立因果分析的随机模型，模型具有明确的形式和参数，模型变量之间的关系多表现为线性关系，或者可以化为线性关系，以时间序列数据或者截面数据为样本，采用最小二乘方法或者极大似然方法估计模型。
斯托克 计量经济学教材
斯托克计量经济学教材全文共四篇示例，供读者参考第一篇示例：斯托克计量经济学教材是一本经典的经济学教材，被广泛应用于大学本科和研究生阶段的经济学专业课程中。
该教材由文字严谨，内容深入浅出，涵盖了计量经济学的各个方面，为学生提供了全面的理论知识和实践技能。
一、教材内容《斯托克计量经济学》是由詹姆斯·斯托克（James Stock）和马克·沃森（Mark Watson）合著的一本经典教材，在经济学界享有盛誉。
该教材涵盖了计量经济学的基本理论、方法和实证研究，内容涉及回归分析、时间序列分析、面板数据分析、因果推断等多个方面，旨在帮助学生建立起对经济现象的客观量化分析能力。
二、教材特点1. 理论与实践相结合：《斯托克计量经济学》教材注重理论与实践相结合，既强调了基本的计量经济学理论框架，又通过大量实证案例展示了如何将理论运用到实际数据分析中。
2. 清晰易懂的讲解方式：该教材在文字表达上十分严谨清晰，避免了学术术语的过度使用，让学生更容易理解和掌握复杂的计量经济学理论。
3. 大量练习题和案例分析：为了帮助学生更好地掌握知识点，教材中设置了大量的练习题和案例分析，让学生通过实际操作来巩固所学知识。
4. 近年最新研究成果：《斯托克计量经济学》不仅汇总了经典的计量经济学研究成果，还尽可能地涵盖了最新的研究进展和方法，使学生对计量经济学领域的发展趋势有所了解。
三、教材在教学中的应用斯托克计量经济学教材以其深入浅出的讲解方式、丰富实例和案例、以及严谨的理论基础，成为了经济学领域不可或缺的经典教材，为学生们打开了通往计量经济学世界的大门，引导他们更好地理解和应用计量经济学知识，为未来的学习和研究提供了坚实的基础。
希望更多的学生能通过学习《斯托克计量经济学》，在经济学领域取得更为出色的成就。
第二篇示例：斯托克（Stock）是计量经济学领域内享有盛誉的学者，他的著作《计量经济学》（Introduction to Econometrics）广泛应用于全球各大高校的计量经济学课程中。
ch7参数估计
不随意更换样本单位
3、搜集样本数据
按规定的项目、表式、时间和方式进行，不遗漏
4、整理样本数据
审查、输入、分组汇总、计算样本指标（估计量）
5、推断总体指标并计算抽样误差
§7.1.4抽样误差
1.误差：调查结果与实际值之间的差异
抽样调查中的误差
登记性误差(非抽样误差) 误差 系统误差（非抽样误差） 代表性误差随机误差（抽样误差）
有若干个方差可选择时，选方差最大者 对于成数，方差最大即指成数最接近0.5，最 保守的估计是取P＝0.5来计算
例7-1，随机抽取100名学生，测得他们的平均体重为 58公斤，标准差为50公斤，抽样误差为多少？。
解：
n=100
s sx n
S=50
50 5(公斤） 100
例 7-2 ，随机从 60000 桶罐头中抽取 300 桶调查，
总体指标－－用来反映总体数量特征的指标。
总体指标的数值是客观存在的、确定的，但 又是未知的
在抽样估计中也称之为待估计的总体参数。
通常，所要估计的总体指标有总体平均数、 总体成数Ｐ、总体标准差或方差以及总体标 志总量（ＮX）或总体中具有某一属性的单位 总数（ＮＰ）等。
5
成数又称为是非比率,指总体中具有两种属性中的
ˆ X,
n n 1 1 ˆ 2 X i2 X 2 ( X i X ) 2 . n i 1 n i 1
29
【例7－2】设X1,X2，…Xn是来下列自均匀分布的样本， 试求θ 的矩估计量。
1 f ( x, ) 0
0 x 其它
发现有6桶不合格。问合格率的抽样误差为多大？
斯托克、沃森着《计量经济学》第一章
计量经济学EconometricsChapter 1. Economic Questions and Data计量经济学的定义：Econometrics is the science and art of using economic theory and statistical techniques to analyze economic data.其他定义：（1） The science of testing economic theory.（2） The set of tools used for forecasting future values of economic variables.（3） The process of fitting mathematical economic models to real-world data.（4） The science and art of using historical data to make quantitative policy recommendations in government and business.计量经济学的用途：经济学的各个领域；政治学；社会学等Why econometrics?Economics suggests interesting relations, often with policy implications, but virtually never suggests quantitative magnitudes of causal effects.•What is the price elasticity of cigarettes?•What is the effect of reducing class size on studentachievement?•What is the effect on earnings of a year of education? •What is the effect on output growth of a 1 percentage point increase in interest rates by the Fed?The focus of this course is the use of statistical and econometric methods to quantify causal effects.1.1 Economic Questions We ExamineQuestion #1: Does Reducing Class Size Improve Elementary School EducationThe marginal benefit and cost of reducing class sizeData: 420 California school districts in 1998Evidence: Students in districts with small class sizes tend to perform better on standardized tests than in districts with larger classes.Complications: While this fact is consistent with the idea that smaller classes produce better test scores, it might simply reflect many other advantages that students in districts with small classes have (e.g. wealthier residents, better teachers, more extra learning outside classroom).Solution: We use multiple regression（多元回归）analysis to isolate the effect of changes in class size from changes in other factors, such as the economic background of the students（引入足够多的控制变量）.Question #2: Is There Racial Discrimination in the Market for Home Loans?By law, U.S. lending institutions cannot take race intoaccount when deciding to grant or deny a request for a mortgage.美国的种族歧视VS 中国的户籍歧视Evidence: Federal Reserve Bank of Boston found (using data from the early 1990s) that 28% of black applicants are denied mortgages, while only 9% of white applicants are denied.Complication: Black and white applicants differ in many ways other than their races.Need to know: Is there a difference in the probability of being denied for otherwise identical applicants（除种族以外，其他方面都完全相同的贷款申请者）? How large is this difference?Solution: Hold constant other application characteristics, suchas their ability to repay the loan.Question #3: How Much Do Cigarette Taxes Reduce Smoking?由于吸烟的外部性（externality），故政府希望对香烟征税，以降低香烟消费。
斯托克、沃森着《计量经济学》第八章
Chapter 8. Nonlinear Regression Functions8.1 A General Strategy for Modeling Nonlinear Regression Functions•Everything so far has been linear in the X’s•The approximation that the regression function is linearmight be good for some variables, but not for others.•The multiple regression framework can be extended to handle regression functions that are nonlinear in one or more X.The TestScore – STR relation looks approximately linear…But the TestScore – average district income relation looks like it is nonlinear.If a relation between Y and X is nonlinear:•The effect on Y of a change in X depends on the value of X – that is, the marginal effect of X is not constant•A linear regression is mis-specified – the functional form is wrong•The estimator of the effect on Y of X is biased – it needn’t even be right on average. 遗漏高次项会带来遗漏变量偏差。
计量经济学导论第四版第七章
当我们把（7.1）和（7.6）结合起来时，
便发现 实际上服从一个二阶自回归模型，
或AR(2)模型。为说明这一点，我们把它
写成 ut -1 yt 1 0 1yt 2，并代入 ut ut 1 et
于是（7.6）就可以写成：
12
出现滞后因变量时的序列相关
中的t统计量忽略了 和 −1 之间可能
的相关，所以在回归元不是严格外生的
情况下它不是有效的。
27
例2检验最低工资方程中的AR(1)序列
相关
在第5章，我们考察了最低工资对波多黎
各就业率的影响 ，我们现在来检验误差
中是否包含了序列相关，所用的检验并
不假定最低工资和GNP有严格外生性。
我们假定潜在的随机过程是弱相关的，
7
效率和推断
单个假设的t统计量也不再确当。因为较
小的标准误意味着较大的t统计量，所以
当 > 时，通常t统计量常常过大。用
于检验多重假设的通常F统计量和LM统
计量也不再可靠。
8
拟合优度
有时我们有这样一种观点：时间序列回
归模型中的误差若存在序列相关，我们
通常的拟合优度指标2 和调整 2 便失效
如同检验异方差性那样，虚拟假设就是
相应的高斯-马尔科夫假定正确。在
AR(1)模型中，误差序列无关的这个虚
拟假设是：H 0 : 0 (7.12)
这里我们把定理（6.2）的渐进正态结论
直接应用于动态回归模型：
ut ut 1 et , t 2,3..., n (7.13)
15
严格外生时对AR(1)的t检验
值。
17
例1菲利普斯曲线AR(1)序列相关
斯托克《计量经济学》Ch2
©上海财经大学经济学院
Ch2：概率统计复习
概率论复习
计量经济学PPT
连续随机变量：在连续的实数区间取值，用概率密度函数描述概率分布。 连续随机变量的取值均假设为一切实数，只取部分实数时，将不取值部分 对应的概率密度设为0。 重要特例：正态分布（Normal distribution） 取值：（-∞，+∞） 概率密度：
（5）一个非参数检验的例子：正态分布检验（J-B检验）
ˆ n ˆ2 ( 3) 2 JB 6 4
©上海财经大学经济学院
Ch2：概率统计复习
概率论复习 随机变量：取值和概率分布为其决定因素，分为离散和连续
计量经济学PPT
离散随机变量：取有限或者可列无限多值，用分布函数描述概率分布 重要特例：二项分布（binomial distribution） 取值：0，1，2，……n， 概率：
n=1时为两点分布（0-1分布） 取值：0，1 概率：
计量经济学PPT
©上海财经大学经济学院
Ch2：概率统计复习
概率论复习 随机向量： 协方差和相关系数：
计量经济学PPT
相关系数等于0意味着什么？相关系数等于1呢？
（3）条件分布 条件概率分布函数： 条件概率密度函数： 乘法公式：
©上海财经大学经济学院
Ch2：概率统计复习
概率论复习 随机向量： （3）条件分布 条件矩： 条件数学期望：
ˆ p limn
ˆ E ( )
ˆ ˆ Var(1 ) Var(2 )
（2）无偏估计：
ˆ ˆ （3）有效估计： 1 , 2 都是 的无偏估计
一致性是估计量的最低要求，也是最为重要的性质。一致性是在样本量无 限大时对估计量的评价，有效性则是在样本量有限时对估计量的比较。
斯托克、沃森着《计量经济学》第六章
斯托克、沃森着《计量经济学》第六章Chapter 6. Linear Regression with Multiple Regressors 6.1 Omitted Variable Bias（遗漏变量偏差）OLS estimate of the Test Score/STR relation:nTestScore= 698.9 –2.28×STR, R2 = .05, SER = 18.6(10.4) (0.52)Is this a credible estimate of the causal effect on test scores of a change in the student-teacher ratio?1No: there are omitted confounding factors (family income; whether the students are native English speakers) that bias the OLS estimator: STR could be “picking up” the effect of these confounding factors.2Omitted Variable BiasThe bias in the OLS estimator that occurs as a result of an omitted factor is called omitted variable bias. For omitted variable bias to occur, the omitted factor “Z” must be:1.a determinant of Y; and2.correlated with the regressor X.3Both conditions must hold for the omission of Z to result in omitted variable bias.Example #1: In the test score example:1.English language ability (whether the student hasEnglish as a second language) plausibly affectsstandardized test scores: Z is a determinant of Y.42.Immigrant communities tend to be less affluent and thushave smaller school budgets – and higher STR: Z iscorrelated with X.β is biasedAccordingly,1What is the direction of this bias?What does common sense suggest?If common sense fails you, there is a formula…5Example #2: Time of day of the test.Time of day of the test could affect test scores, but is uncorrelated with the student-teacher ratio (STR).Example #3: Parking lot space per pupil.Schools with more teachers per pupil probably have more teacher parking space, but parking lot space has no direct 6effect on learning (learning takes place in the classroom, not parking lot).Example #4: The Mozart EffectA study published in Nature in 1993 suggested that listening to Mozart for 10-15 minutes could temporarily raise your IQ by8 or 9 points.A review of dozens of studies found that students who take7optional music or arts courses in high school do in fact have higher English or math test scores than those who don’t.Problem: The academically better students might have more time to take optional music courses or more interest in doing so, or those schools with a deeper music curriculum might just bebetter schools across the board.Evidence from randomized controlled experiments: Many89controlled experiments on the Mozart effect fail to show that listening to Mozart improves IQ or general test performance.A formula for omitted variable bias : Recall the equation,1?β –β1 = 121()()ni i i n i i X X u X X ==??∑∑ = 1211ni i Xv n n s n =∑where v i = (X i –X )u i ? (X i –μX )u i .10Under Least Squares Assumption #1,E[(X i –μX )u i ] = cov(X i , u i ) = 0.But what if E[(X i –μX )u i ] = cov(X i , u i ) = σXu ≠ 0? Then 1?β =β1 + 121()()n i i i n i i X X u X X ==??∑∑ = β1 + 121()1ni i i XX X u n n s n =∑11其中，22pXXs σ??→，11n n→，[]11()E ()(0)cov(,)n pi i i X i i i Xu X u i X X u X u X u n μρσσ=→??==∑，where ρXu = corr(X , u ) （X 与u 的相关系数）因此，有如下Omitted variable bias formula:1βp→ β1 + u Xu XσρσIf an omitted factor Z is both :(1) a determinant of Y (that is, it is contained in u); and(2) correlated with X,β is biased.the n ρXu≠ 0 and the OLS estimator1The math makes precise the idea that districts with few ESL students (1) do better on standardized tests and (2) have smaller classes (bigger budgets), so ignoring the ESL factor results in overstating the class size effect.12Is this actually going on in the CA data?13Districts with fewer English Learners have higher test scores Districts with lower percent EL (PctEL) have smaller classes Among districts with comparable PctEL, the effect of class size is small (recall overall “test score gap” = 7.4)14Three ways to overcome omitted variable bias：1.Run a randomized controlled experiment in whichtreatment (STR) is randomly assigned: then PctEL is stilla determinant of T estScore, but PctEL is uncorrelated withSTR. (But this is unrealistic in practice.)2.Adopt the “cross tabulation” approach, with finergradations of STR and PctEL (But soon we will run out of15data, and what about other determinants like familyincome and parental education?)e a method in which the omitted variable (PctEL) is nolonger omitted: include PctEL as an additional regressor ina multiple regression.166.2 The Multiple Regression Model（多元回归模型）Considerthe case of two regressors:Y i = β0 + β1X1i + β2X2i + u i, i = 1,…,nX1, X2 are the two independent variables (regressors) ?(Y i, X1i, X2i) denote the i th observation on Y, X1, and X2. ?β0 = unknown population intercept17β1 = effect on Y of a change in X1, holding X2 constantβ2 = effect on Y of a change in X2, holding X1 constantu i = “error term” (omitted factors)Interpretation of multiple regression coefficientsY i = β0 + β1X1i + β2X2i + u i, i = 1,…,n Consider changing X1 by ΔX1 while holding X2 constant:18Population regression line before the change:Y = β0 + β1X1 + β2X2Population regression line, after the change:Y + ΔY = β0 + β1(X1 + ΔX1) + β2X219。
斯托克计量经济学课后习题实证答案
斯托克计量经济学课后习题实证答案P ART T WO Solutions to EmpiricalExercisesChapter 3Review of StatisticsSolutions to Empirical Exercises1. (a)Average Hourly Earnings, Nominal $’sMean SE(Mean) 95% Confidence Interval AHE199211.63 0.064 11.50 11.75AHE200416.77 0.098 16.58 16.96Difference SE(Difference) 95% Confidence Interval AHE2004 AHE1992 5.14 0.117 4.91 5.37(b)Average Hourly Earnings, Real $2004Mean SE(Mean) 95% Confidence Interval AHE199215.66 0.086 15.49 15.82AHE200416.77 0.098 16.58 16.96Difference SE(Difference) 95% Confidence Interval AHE2004 AHE1992 1.11 0.130 0.85 1.37(c) The results from part (b) adjust for changes in purchasing power. These results should be used.(d)Average Hourly Earnings in 2004Mean SE(Mean) 95% Confidence Interval High School13.81 0.102 13.61 14.01College20.31 0.158 20.00 20.62Difference SE(Difference) 95% Confidence Interval College High School 6.50 0.188 6.13 6.87Solutions to Empirical Exercises in Chapter 3 109(e)Average Hourly Earnings in 1992 (in $2004)Mean SE(Mean) 95% Confidence Interval High School13.48 0.091 13.30 13.65 College19.07 0.148 18.78 19.36Difference SE(Difference) 95% Confidence Interval College High School5.59 0.173 5.25 5.93(f) Average Hourly Earnings in 2004Mean SE(Mean) 95% Confidence Interval AHE HS ,2004AHE HS ,19920.33 0.137 0.06 0.60 AHE Col ,2004AHE Col ,19921.24 0.217 0.82 1.66Col–HS Gap (1992)5.59 0.173 5.25 5.93 Col–HS Gap (2004)6.50 0.188 6.13 6.87Difference SE(Difference) 95% Confidence Interval Gap 2004 Gap 1992 0.91 0.256 0.41 1.41Wages of high school graduates increased by an estimated 0.33 dollars per hour (with a 95%confidence interval of 0.06 0.60); Wages of college graduates increased by an estimated 1.24dollars per hour (with a 95% confidence interval of 0.82 1.66). The College High School gap increased by an estimated 0.91 dollars per hour.(g) Gender Gap in Earnings for High School Graduates Yearm Y s m n m w Y s w n w m Y w Y SE (m Y w Y )95% CI 199214.57 6.55 2770 11.86 5.21 1870 2.71 0.173 2.37 3.05 200414.88 7.16 2772 11.92 5.39 1574 2.96 0.192 2.59 3.34There is a large and statistically significant gender gap in earnings for high school graduates.In 2004 the estimated gap was $2.96 per hour; in 1992 the estimated gap was $2.71 per hour(in $2004). The increase in the gender gap is somewhat smaller for high school graduates thanit is for college graduates.Chapter 4Linear Regression with One RegressorSolutions to Empirical Exercises1. (a) ·AHE 3.32 0.45 u AgeEarnings increase, on average, by 0.45 dollars per hour when workers age by 1 year.(b) Bob’s predicted earnings 3.32 0.45 u 26 $11.70Alexis’s predicted earnings 3.32 0.45 u 30 $13.70(c) The R2 is 0.02.This mean that age explains a small fraction of the variability in earnings acrossindividuals.2. (a)There appears to be a weak positive relationship between course evaluation and the beauty index.Course Eval 4.00 0.133 u Beauty. The variable Beauty has a mean that is equal to 0; the(b) ·_estimated intercept is the mean of the dependent variable (Course_Eval) minus the estimatedslope (0.133) times the mean of the regressor (Beauty). Thus, the estimated intercept is equalto the mean of Course_Eval.(c) The standard deviation of Beauty is 0.789. ThusProfessor Watson’s predicted course evaluations 4.00 0.133 u 0 u 0.789 4.00Professor Stock’s predicted course evaluations 4.00 0.133 u 1 u 0.789 4.105Solutions to Empirical Exercises in Chapter 4 111(d) The standard deviation of course evaluations is 0.55 and the standard deviation of beauty is0.789. A one standard deviation increase in beauty is expected to increase course evaluation by0.133 u 0.789 0.105, or 1/5 of a standard deviation of course evaluations. The effect is small.(e) The regression R2 is 0.036, so that Beauty explains only3.6% of the variance in courseevaluations.3. (a) ?Ed 13.96 0.073 u Dist. The regression predicts that if colleges are built 10 miles closerto where students go to high school, average years of college will increase by 0.073 years.(b) Bob’s predicted years of completed education 13.960.073 u 2 13.81Bob’s predicted years of completed education if he was 10 miles from college 13.96 0.073 u1 13.89(c) The regression R2 is 0.0074, so that distance explains only a very small fraction of years ofcompleted education.(d) SER 1.8074 years.4. (a)Yes, there appears to be a weak positive relationship.(b) Malta is the “outlying” observation with a trade share of 2.(c) ·Growth 0.64 2.31 u TradesharePredicted growth 0.64 2.31 u 1 2.95(d) ·Growth 0.96 1.68 u TradesharePredicted growth 0.96 1.68 u 1 2.74(e) Malta is an island nation in the Mediterranean Sea, south of Sicily. Malta is a freight transportsite, which explains its larg e “trade share”. Many goods coming into Malta (imports into Malta)and immediately transported to other countries (as exports from Malta). Thus, Malta’s importsand exports and unlike the imports and exports of most other countries. Malta should not beincluded in the analysis.Chapter 5Regression with a Single Regressor:Hypothesis Tests and Confidence IntervalsSolutions to Empirical Exercises1. (a) ·AHE 3.32 0.45 u Age(0.97) (0.03)The t -statistic is 0.45/0.03 13.71, which has a p -value of 0.000, so the null hypothesis can berejected at the 1% level (and thus, also at the 10% and 5% levels).(b) 0.45 r 1.96 u 0.03 0.387 to 0.517(c) ·AHE 6.20 0.26 u Age(1.02) (0.03)The t -statistic is 0.26/0.03 7.43, which has a p -value of 0.000, so the null hypothesis can berejected at the 1% level (and thus, also at the 10% and 5% levels).(d) ·AHE 0.23 0.69 u Age(1.54) (0.05)The t -statistic is 0.69/0.05 13.06, which has a p -value of 0.000, so the null hypothesis can berejected at the 1% level (and thus, also at the 10% and 5% levels).(e) The difference in the estimated E 1 coefficients is 1,1,??College HighScool E E 0.69 0.26 0.43. Thestandard error of for the estimated difference is SE 1,1,??()College HighScoolE E (0.032 0.052)1/2 0.06, so that a 95% confidence interval for the difference is 0.43 r 1.96 u 0.06 0.32 to 0.54(dollars per hour).2. ·_ 4.000.13CourseEval Beauty u (0.03) (0.03)The t -statistic is 0.13/0.03 4.12, which has a p -value of 0.000, so the null hypothesis can be rejectedat the 1% level (and thus, also at the 10% and 5% levels).3. (a) ?Ed13.96 0.073 u Dist (0.04) (0.013)The t -statistic is 0.073/0.013 5.46, which has a p -value of 0.000, so the null hypothesis can be rejected at the 1% level (and thus, also at the 10% and 5% levels).(b) The 95% confidence interval is 0.073 r 1.96 u 0.013 or0.100 to 0.047.(c) ?Ed13.94 0.064 u Dist (0.05) (0.018)Solutions to Empirical Exercises in Chapter 5 113(d) ?Ed13.98 0.084 u Dist (0.06) (0.013)(e) The difference in the estimated E 1 coefficients is 1,1,??Female Male E E 0.064 ( 0.084) 0.020.The standard error of for the estimated difference is SE 1,1,??()Female Male E E (0.0182 0.0132)1/20.022, so that a 95% confidence interval for the difference is 0.020 r 1.96 u 0.022 or 0.022 to0.064. The difference is not statistically different.Chapter 6Linear Regression with Multiple RegressorsSolutions to Empirical Exercises1. Regressions used in (a) and (b)Regressor a bBeauty 0.133 0.166Intro 0.011OneCredit 0.634Female 0.173Minority 0.167NNEnglish 0.244Intercept 4.00 4.07SER 0.545 0.513R2 0.036 0.155(a) The estimated slope is 0.133(b) The estimated slope is 0.166. The coefficient does not change by an large amount. Thus, theredoes not appear to be large omitted variable bias.(c) Professor Smith’s predicted course evaluation (0.166 u 0)0.011 u 0) (0.634 u 0) (0.173 u0) (0.167 u 1) (0.244 u 0) 4.068 3.9012. Estimated regressions used in questionModelRegressor a bdist 0.073 0.032bytest 0.093female 0.145black 0.367hispanic 0.398incomehi 0.395ownhome 0.152dadcoll 0.696cue80 0.023stwmfg80 0.051intercept 13.956 8.827SER 1.81 1.84R2 0.007 0.279R0.007 0.277Solutions to Empirical Exercises in Chapter 6 115(a) 0.073(b) 0.032(c) The coefficient has fallen by more than 50%. Thus, it seems that result in (a) did suffer fromomitted variable bias.(d) The regression in (b) fits the data much better as indicated by the R2, 2,R and SER. The R2 and R are similar because the number of observations is large (n 3796).(e) Students with a “dadcoll 1” (so that the student’s father went to college) complete 0.696 moreyears of education, on average, than students with “dadcoll 0” (so that the student’s father didnot go to college).(f) These terms capture the opportunity cost of attending college. As STWMFG increases, forgonewages increase, so that, on average, college attendance declines. The negative sign on thecoefficient is consistent with this. As CUE80 increases, it is more difficult to find a job, whichlowers the opportunity cost of attending college, so that college attendance increases. Thepositive sign on the coefficient is consistent with this.(g) Bob’s predicted years of education 0.0315 u 2 0.093 u58 0.145 u 0 0.367 u 1 0.398 u0 0.395 u 1 0.152 u 1 0.696 u 0 0.023 u 7.5 0.051 u 9.75 8.82714.75(h) Jim’s expected years of education is 2 u 0.0315 0.0630 less than Bob’s. Thus, Jim’s expectedyears of education is 14.75 0.063 14.69.3.Variable Mean StandardDeviation Unitsgrowth 1.86 1.82 Percentage Pointsrgdp60 3131 2523 $1960tradeshare 0.542 0.229 unit freeyearsschool 3.95 2.55 yearsrev_coups 0.170 0.225 coups per yearassasinations 0.281 0.494 assasinations per yearoil 0 0 0–1 indicator variable (b) Estimated Regression (in table format):Regressor Coefficienttradeshare 1.34(0.88)yearsschool 0.56**(0.13)rev_coups 2.15*(0.87)assasinations 0.32(0.38)rgdp60 0.00046**(0.00012)intercept 0.626(0.869)SER 1.59R2 0.29R0.23116 Stock/Watson - Introduction to Econometrics - Second EditionThe coefficient on Rev_Coups is í2.15. An additional coup in a five year period, reduces theaverage year growth rate by (2.15/5) = 0.43% over this 25 year period. This means the GPD in 1995 is expected to be approximately .43×25 = 10.75% lower. This is a larg e effect.(c) The 95% confidence interval is 1.34 r 1.96 u 0.88 or 0.42 to 3.10. The coefficient is notstatistically significant at the 5% level.(d) The F-statistic is 8.18 which is larger than 1% critical value of 3.32.Chapter 7Hypothesis Tests and Confidence Intervals in Multiple RegressionSolutions to Empirical Exercises1. Estimated RegressionsModelRegressor a bAge 0.45(0.03)0.44 (0.03)Female 3.17(0.18)Bachelor 6.87(0.19)Intercept 3.32(0.97)SER 8.66 7.88R20.023 0.1902R0.022 0.190(a) The estimated slope is 0.45(b) The estimated marginal effect of Age on AHE is 0.44 dollars per year. The 95% confidenceinterval is 0.44 r 1.96 u 0.03 or 0.38 to 0.50.(c) The results are quite similar. Evidently the regression in (a) does not suffer from importantomitted variable bias.(d) Bob’s predicted average hourly earnings 0.44 u 26 3.17 u 0 6.87 u 0 3.32 $11.44Alexis’s predicted average hourly earnings 0.44 u 30 3.17 u 1 6.87 u 1 3.32 $20.22 (e) The regression in (b) fits the data much better. Gender and education are important predictors of earnings. The R2 and R are similar because the sample size is large (n 7986).(f) Gender and education are important. The F-statistic is 752, which is (much) larger than the 1%critical value of 4.61.(g) The omitted variables must have non-zero coefficients and must correlated with the includedregressor. From (f) Female and Bachelor have non-zero coefficients; yet there does not seem to be important omittedvariable bias, suggesting that the correlation of Age and Female and Age and Bachelor is small. (The sample correlations are ·Cor(Age, Female) 0.03 and·Cor(Age,Bachelor) 0.00).118 Stock/Watson - Introduction to Econometrics - Second Edition2.ModelRegressor a b cBeauty 0.13**(0.03) 0.17**(0.03)0.17(0.03)Intro 0.01(0.06)OneCredit 0.63**(0.11) 0.64** (0.10)Female 0.17**(0.05) 0.17** (0.05)Minority 0.17**(0.07) 0.16** (0.07)NNEnglish 0.24**(0.09) 0.25** (0.09)Intercept 4.00**(0.03) 4.07**(0.04)4.07**(0.04)SER 0.545 0.513 0.513R2 0.036 0.155 0.1552R0.034 0.144 0.145(a) 0.13 r 0.03 u 1.96 or 0.07 to 0.20(b) See the table above. Intro is not significant in (b), but the other variables are significant.A reasonable 95% confidence interval is 0.17 r 1.96 u 0.03 or0.11 to 0.23.Solutions to Empirical Exercises in Chapter 7 119 3.ModelRegressor (a) (b) (c)dist 0.073**(0.013) 0.031**(0.012)0.033**(0.013)bytest 0.092**(0.003) 0.093** (.003)female 0.143**(0.050) 0.144** (0.050)black 0.354**(0.067) 0.338** (0.069)hispanic 0.402**(0.074) 0.349** (0.077)incomehi 0.367**(0.062) 0.374** (0.062)ownhome 0.146*(0.065) 0.143* (0.065)dadcoll 0.570**(0.076) 0.574** (0.076)momcoll 0.379**(0.084) 0.379** (0.084)cue80 0.024**(0.009) 0.028** (0.010)stwmfg80 0.050*(0.020) 0.043* (0.020)urban 0.0652(0.063) tuition 0.184(0.099)intercept 13.956**(0.038) 8.861**(0.241)8.893**(0.243)F-statitisticfor urban and tuitionSER 1.81 1.54 1.54R2 0.007 0.282 0.284R0.007 0.281 0.281(a) The group’s claim is that the coefficien t on Dist is 0.075 ( 0.15/2). The 95% confidence forE Dist from column (a) is 0.073 r 1.96 u 0.013 or 0.099 to 0.046. The group’s claim is includedin the 95% confidence interval so that it is consistent with the estimated regression.120 Stock/Watson - Introduction to Econometrics - Second Edition(b) Column (b) shows the base specification controlling for other important factors. Here thecoefficient on Dist is 0.031, much different than the resultsfrom the simple regression in (a);when additional variables are added (column (c)), the coefficient on Dist changes little from the result in (b). From the base specification (b), the 95% confidence interval for E Dist is0.031 r1.96 u 0.012 or 0.055 to 0.008. Similar results are obtained from the regression in (c).(c) Yes, the estimated coefficients E Black and E Hispanic are positive, large, and statistically significant.Chapter 8Nonlinear Regression FunctionsSolutions to Empirical Exercises1. This table contains the results from seven regressions that are referenced in these answers.Data from 2004(1) (2) (3) (4) (5) (6) (7) (8)Dependent VariableAHE ln(AHE) ln(AHE) ln(AHE) ln(AHE) ln(AHE) ln(AHE) ln(AHE) Age 0.439**(0.030) 0.024**(0.002)0.147**(0.042)0.146**(0.042)0.190**(0.056)0.117*(0.056)0.160Age2 0.0021**(0.0007) 0.0021** (0.0007)0.0027**(0.0009)0.0017(0.0009)0.0023(0.0011)ln(Age) 0.725**(0.052)Female u Age 0.097 (0.084) 0.123 (0.084) Female u Age2 0.0015 (0.0014)0.0019 (0.0014) Bachelor u Age 0.064 (0.083)0.091 (0.084) Bachelor u Age2 0.0009 (0.0014) 0.0013 (0.0014) Female 3.158**(0.176) 0.180**(0.010)0.180**(0.010)0.180**(0.010)(0.014)1.358*(1.230)0.210**(0.014)1.764(1.239)Bachelor 6.865**(0.185) 0.405**(0.010)0.405**(0.010)0.405**(0.010)0.378**(0.014)0.378**(0.014)0.769(1.228)1.186(1.239)Female u Bachelor 0.064** (0.021) 0.063**(0.021)0.066**(0.021)0.066**(0.021)Intercept 1.884(0.897) 1.856**(0.053)0.128(0.177)0.059(0.613)0.078(0.612)0.633(0.819)0.604(0.819)0.095(0.945)F-statistic and p-values on joint hypotheses(a) F-statistic on terms involving Age 98.54(0.00)100.30(0.00)51.42(0.00)53.04(0.00)36.72(0.00)(b) Interaction termswithAge24.12(0.02)7.15(0.00)6.43(0.00)SER 7.884 0.457 0.457 0.457 0.457 0.456 0.456 0.456 R0.1897 0.1921 0.1924 0.1929 0.1937 0.1943 0.1950 0.1959 Significant at the *5% and **1% significance level.122 Stock/Watson - Introduction to Econometrics - Second Edition(a) The regression results for this question are shown in column (1) of the table. If Age increasesfrom 25 to 26, earnings are predicted to increase by $0.439 per hour. If Age increases from33 to 34, earnings are predicted to increase by $0.439 per hour. These values are the samebecause the regression is a linear function relating AHE and Age .(b) The regression results for this question are shown in column (2) of the table. If Age increasesfrom 25 to 26, ln(AHE ) is predicted to increase by 0.024. This means that earnings are predicted to increase by 2.4%. If Age increases from 34 to 35, ln(AHE ) is predicted to increase by 0.024.This means that earnings are predicted to increase by 2.4%. These values, in percentage terms,are the same because the regression is a linear function relating ln(AHE ) and Age .(c) The regression results for this question are shown in column (3) of the table. If Age increasesfrom 25 to 26, then ln(Age ) has increased by ln(26) ln(25) 0.0392 (or 3.92%). The predictedincrease in ln(AHE ) is 0.725 u (.0392) 0.0284. This means that earnings are predicted toincrease by 2.8%. If Age increases from 34 to 35, then ln(Age ) has increased by ln(35) ln(34) .0290 (or 2.90%). The predicted increase in ln(AHE ) is 0.725 u (0.0290) 0.0210. This means that earnings are predicted to increase by 2.10%.(d) When Age increases from 25 to 26, the predicted change in ln(AHE ) is(0.147 u 26 0.0021 u 262) (0.147 u 25 0.0021 u 252) 0.0399.This means that earnings are predicted to increase by 3.99%.When Age increases from 34 to 35, the predicted change in ln(AHE ) is(0. 147 u 35 0.0021 u 352) (0. 147 u 34 0.0021 u 342) 0.0063.This means that earnings are predicted to increase by 0.63%.(e) The regressions differ in their choice of one of the regressors. They can be compared on the basis of the .R The regression in (3) has a (marginally) higher 2,R so it is preferred.(f) The regression in (4) adds the variable Age 2 to regression(2). The coefficient on Age 2 isstatistically significant ( t 2.91), and this suggests that the addition of Age 2 is important. Thus,(4) is preferred to (2).(g) The regressions differ in their choice of one of the regressors. They can be compared on the basis of the .R The regression in (4) has a (marginally) higher 2,R so it is preferred.(h)Solutions to Empirical Exercises in Chapter 8 123 The regression functions using Age (2) and ln(Age) (3) are similar. The quadratic regression (4) is different. It shows a decreasing effect of Age on ln(AHE) as workers age.The regression functions for a female with a high school diploma will look just like these, but they will be shifted by the amount of the coefficient on the binary regressor Female. The regression functions for workers with a bachelor’s degree will also look just like these, but they would be shifted by the amount of the coefficient on the binary variable Bachelor.(i) This regression is shown in column (5). The coefficient on the interaction term Female uBachelor shows the “extra effect” of Bachelor on ln(AHE) for women relative the effect for men.Predicted values of ln(AHE):Alexis: 0.146 u 30 0.0021 u 302 0.180 u 1 0.405 u 1 0.064 u 1 0.078 4.504Jane: 0.146 u 30 0.0021 u 302 0.180 u 1 0.405 u 0 0.064 u 0 0.078 4.063Bob: 0.146 u 30 0.0021 u 302 0.180 u 0 0.405 u 1 0.064 u 0 0.078 4.651Jim: 0.146 u 30 0.0021 u 302 0.180 u 0 0.405 u 0 0.064 u 0 0.078 4.273Difference in ln(AHE): Alexis Jane 4.504 4.063 0.441Difference in ln(AHE): Bob Jim 4.651 4.273 0.378Notice that the difference in the difference predicted effects is 0.441 0.378 0.063, which is the value of the coefficient on the interaction term.(j) This regression is shown in (6), which includes two additional regressors: the interactions of Female and the age variables, Age and Age2. The F-statistic testing the restriction that the coefficients on these interaction terms is equal to zero is F 4.12 with a p-value of 0.02. This implies that there is statistically significant evidence (at the 5% level) that there is a different effect of Age on ln(AHE) for men and women.(k) This regression is shown in (7), which includes two additional regressors that are interactions of Bachelor and the age variables, Age and Age2. The F-statistic testing the restriction that the coefficients on these interaction terms is zero is 7.15 with a p-value of 0.00. This implies that there is statistically significant evidence (at the 1% level) that there is a different effect of Age on ln(AHE) for high school and college graduates.(l) Regression (8) includes Age and Age2 and interactions terms involving Female and Bachelor.The figure below shows the regressions predicted value of ln(AHE) for male and females with high school and college degrees.124 Stock/Watson - Introduction to Econometrics - Second EditionThe estimated regressions suggest that earnings increase as workers age from 25–35, the rangeof age studied in this sample. There is evidence that the quadratic term Age2 belongs in theregression. Curvature in the regression functions in particularly important for men.Gender and education are significant predictors of earnings, and there are statistically significant interaction effects between age and gender and age and education. The table below summarizes the regressions predictions for increases in earnings as a person ages from 25 to 32 and 32 to 35Gender, Education Predicted ln(AHE) at Age(Percent per year)25 32 35 25 to 32 32 to 35Males, High School 2.46 2.65 2.67 2.8% 0.5%Females, BA 2.68 2.89 2.93 3.0% 1.3%Males, BA 2.74 3.06 3.09 4.6% 1.0%Earnings for those with a college education are higher than those with a high school degree, andearnings of the college educated increase more rapidly early in their careers (age 25–32). Earnings for men are higher than those of women, and earnings of men increase more rapidly early in theircareers (age 25–32). For all categories of workers (men/women, high school/college) earningsincrease more rapidly from age 25–32 than from 32–35.。
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©上海财经大学经济学院
Ch7：内生性和工具变量估计
工具变量的作用（示意图）
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©上海财经大学经济学院
Ch7：内生性和工具变量估计
计量经济学PPT
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©上海财经大学经济学院
Ch7：内生性和工具变量估计
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计量经济学PPT
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©上海财经大学经济学院
©上海财经大学经济学院
Ch7：内生性和工具变量估计
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计量经济学PPT
内生性解释变量对因变量的影响路径：
©上海财经大学经济学院
Ch7：内生性和工具变量估计
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Ch7：内生性和工具变量估计
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计量经济学PPT
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Ch7：内生性和工具变量估计
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计量经济学PPT
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©上海财经大学经济学院
Ch7：内生性和工具变量估计
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计量经济学PPT
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