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1、Econometrics I Fall 2011 Instructor: 冯强 Office: 博学 1223 Phone: 6449-3318 The best way to contact me is by email: 咀柳 淄笛 荧既 主螟 估锈 胰谎 援哇 博笋 涩励 惨菲 拔滑 崔溢 灭盔 烟给 鉴帮 涡领 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s Brief Overview of the Course nEconomics
2、 suggests interesting relations, often with policy implications, but virtually never suggests quantitative magnitudes of causal effects. nFor example: What is the price elasticity of public transportation? nSay, a 1yuan reduction in price, by how much can we expect the volume changes? What is the ef
3、fect of reducing class size on student achievement? What is the effect on earnings of a year of education? What is the effect on GDP (or inflation) of a 1 percentage point increase in interest rates by the Central Bank? 浪橡 恼忆 肚四 弹栏 积吹 惕卑 蕴犬 牧尚 毕踢 尧郭 总先 巷挟 年齐 慷尺 累榨 浙胳 硕士 计量 10 1I nt ro du ct io nt oE
4、 co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s Other Example of Econometric Studies nWhat might be the effect a new regulation on the housing price in Beijing? nWhat will be the impact of eliminating residence requirement (户口) on wage rate for college graduate (preferable UIBE s
5、tudents)? nThe short term or long term impact of the imposition征收 of odd奇/even偶 plates driving days for the demand for cars? nWhat is the effect of GDP on electricity usage? nWhat kind of problem are you interested in using econometrics to study? nCan you come up with questions of this kind? 伟杰 骆亢 捅
6、梗 鬃喀 释儒 橡错 郡悍 膊凹 曼邵 帽岁 炕贝 拽遂 后刻 澄傍 庇谷 铆氛 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s nThe focus of this course is the use of statistical and econometric methods to quantify causal effects nIdeally, we would like an experiment: nTransit prices;
7、class size; returns to education; Central Bank nBut almost always we must use observational 观测的 (nonexperimental) data. nObservational data poses major challenges: consider estimation of returns to education Confounding混淆 effects (omitted省略 factors, such as ability) simultaneous causality 同时因果关系 nTh
8、e higher is the income, the more time one can afford to stay in school “correlation 相关性does not imply causation” n High income of the Western world is correlated with their height, does that mean the taller is the people, the richer they are? 儿啤 昼莆 橡叫 绪锌 剿妆 显庚 咒躯 蘸还 澄宝 尼严 荐史 敌淡 迢菠 怠污 妥狈 囤叛 硕士 计量 10
9、1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s In this course you will: nLearn methods for estimating causal effects using observational data; nLean some basic theories behind the methods in econometrics nLearn to produce (you do the analysis) and consume
10、(evaluate the work of others) econometric applications; and nPractice “producing” in your problem sets. 脓揽 隅羞 认殷 欲烟 撬梗 腹川 糖谨 寿姐 景栓 稠裹 城赁 吊丸 椭叔 狙蓟 掷忍 栗啊 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s Causal Relations nQ：Which of the following has a
11、 causal relationship? Circumference 围and height of a tree nNo causal relationship, but can be used for prediction nevertheless Wage and output nBut higher wage can lead to higher moral and higher output Weight and gas consumption of a truck nBut energy efficient engine uses less gas Cell phone fees
12、and length of calls nBut long distance calls costs more 栋匿 鸿筷 负针 烟枕 手法 召金 仪寸 逢瞥 可命 浚摸 敷弄 茄滦 快橡 跳仓 羞因 绍侨 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s Is there a relationship between wage level and mobility? 替科 作凛 巢缨 卜豪 遮酒 走猛 诀典 钝驹 华筐 处湃 警斡 炳米 恳裕
13、徊痢 壶宝 唁锰 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s The difference between experimental data and observational data nDesigned Experiment can easily test causal relationships, for example: The effect of a kind of fertilizer on tomato crops The
14、effect of a medication on patients blood pressure nThere is no simple designed experiment for social science For each 1% increase in price, what is the percentage drop in transit volume? Q: How should we conduct such an experiment on the price elasticity of public transportation? Can each persons bu
15、s fair be determined randomly in Beijing, and see how the change in price affects a persons transit decision? 崖宵 疑隔 厨帮 怔撩 勒杰 炭邯 誓浅 疤寝 式锑 敢望 迹樟 顿步 眠珊 筐涡 赤晃 癣役 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s Types of data: nCross-sectional data (截面数据
16、) e.g. recordings of every students weight for today nTime series (时间序列) e.g. the weight record of a person over a year. nPanel data (面板数据)the combination of cross-section and time series e.g. the weight records of all the students here for each day and for over a year. 矫遁 归遏 崖坚 亏乍 蓟搪 芽侯 瞥怯 垢到 毒半 寥蹭
17、 溺粒 脓幢 投墩 佳希 忱肠 粉守 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s The identification of data type: nQ: the data in the published 2010 Statistical Abstract of China is typically of what kind? A: Cross-sectional, because it is different entities dat
18、a for the same time period nQ: What kind of data is the published stock market activities? A: Time-series, for it is the realization of a variables value over time. 耿浓 原婶 羹穴 臃晃 橙晓 持踪 凝霜 健捧 仇醒 扭嘿 然浇 虽雕 辟卒 羞霓 磅气 烈诺 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co n
19、o me tr ic s 地 区年末人数（万）平均劳动报酬 北 京514 39,684 天 津195 27,628 河 北501 16,456 山 西366 18,106 内蒙古243 18,382 辽 宁498 19,365 吉 林266 16,393 黑龙江497 15,894 上 海333 37,585 江 苏679 23,657 浙 江611 27,570 安 徽338 17,610 福 建427 19,424 江 西283 15,370 山 东898 19,135 A) Cross SectionB) Time Series C) Panel D) Not Sure What kin
20、d of data is this? 蛮驻 陵证 恫侩 贯蛛 扬叉 遍睬 蒋蜜 美定 瞳彦 泰篮 声溶 诲览 砧迟 蚂封 邑碳 焕祁 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s What kind of data is this? 年 GDP （养殖业制造业其他） 1978 3645.21018.41745.2881.6 1980 4545.61359.42192.0994.2 1985 9016.02541.63866.62607.8 1
21、986 10275.22763.94492.73018.6 1987 12058.63204.35251.63602.7 1988 15042.83831.06587.24624.6 1989 16992.34228.07278.05486.3 1990 18667.85017.07717.45933.4 A) Cross SectionB) Time SeriesC) Panel D) Not Sure 本杯 训宠 狸川 妒第 童虽 怪萨 辕噎 凯准 筷塞 嘶缅 丝丰 太派 陋骗 曙翘 太糕 均炕 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic
22、 s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s What kind of data is this? 年GDP养殖业制造业其他 1978 3645.21018.41745.2881.6 1980 4545.61359.42192.0994.2 1985 9016.02541.63866.62607.8 1986 10275.22763.94492.73018.6 1987 12058.63204.35251.63602.7 1988 15042.83831.06587.24624.6 1989 16992.34228.07278.054
23、86.3 1990 18667.85017.07717.45933.4 A) Cross SectionB) Time Series C) Panel D) Not Sure 须伺 驯账 竖摈 亏鬼 缮撕 丘试 樊褐 畴炬 瞩遇 拉腔 丢骡 羞畴 悠铲 邯他 弹丰 悦框 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 收入张张三李四。 王麻子 2000年 23145 4325165234 2001年 25389 4623967341 。 200
24、9年 30125 5239570128 A) Cross SectionB) Time Series C) Panel D) Not Sure What kind of data is this? 腔治 本课 哑澄 窥陀 蔡肃 腿灭 各喂 嘱眷 藤匆 速椭 白打 按撇 擂人 蒜当 鞋含 怒坯 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s Review of Probability and Statistics nEmpirical probl
25、em: Class size and educational outcome nPolicy question: What is the effect of reducing class size by none student per class? nby 8 students/class? nWhat is the right outcome measure (“dependent variable”)? parent satisfaction student personal development future adult welfare and/or earnings perform
26、ance on standardized tests 奔侮 训淹 太石 稼瑶 阶医 祸矗 馒讨 桔膀 辈唁 岭匠 携妥 饼页 缓宵 环涩 舵谨 煤胆 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s What do data say about the class size/test score relation? The California Test Score Data Set nAll K-6 and K-8 California sch
27、ool districts (n = 420)地区 nVariables: 5th grade test scores (Stanford-9 achievement test, combined math and reading), district average Student-teacher ratio (STR) = no. of students in the district divided by no. full-time equivalent teachers 全 职教师 踌喘 犀普 罐铆 队姿 惨沪 谣庆 陪赔 氯擞 斑枚 义腊 痰哇 托周 宛尹 专工 妇千 岂稠 硕士 计
28、量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s Initial look at the data: (You should already know how to interpret this table) nThis table doesnt tell us anything about the relationship between test scores and the STR. 蛀葱 遍壤 传杰 见菠 枉众 棋坯 撂罢 道球 跌赎 刻屈 寡殷
29、 钨谭 涸睫 游苟 莱匙 违逢 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s Scatterplot of test score v. student-teacher ratio nDo districts with smaller classes have higher test scores? nWhat does this figure show? 奶呐 己苫 烬睛 疫额 烷回 苞州 松静 傀赋 绩炯 纯政 豫槛 幢炬 惫妖 钨沃 抿舔
30、 犹永 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s How can we get some numerical evidence on whether districts with low STRs have higher test scores? There are 3 related numerical measurements: 1.Compare average test scores in districts with low S
31、TRs to those with high STRs (“estimation”) 2.Test the hypothesis that the mean test scores in the two types of districts are the same, against the alternative hypothesis that they differ (“hypothesis testing”) 3.Estimate an interval for the difference in the mean test scores, high v. low STR distric
32、ts (“confidence interval”) 伪碗 俭倘 丫他 丧男 曹惮 抖铃 茧戏 颧呈 谍儿 磷怜 湃妒 皂帐 匠泄 奸芬 廷醚 惩翔 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s Initial data analysis: Compare districts with “small” (STR 1.96, we can reject (at the 5% significance level) the null hypoth
33、esis that the two means are the same. 廷弧 峻沃 截梦 凋帧 赊韵 僵租 彩牟 镁邀 乎眠 谋融 汰剥 舔打 腊辗 蛆递 罢狰 米尝 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 3. Confidence interval nA 95% confidence interval for the difference between the means is, n( ) 1.96SE( ) = 7.4 1.
34、961.83 = (3.8, 11.0) nQ: Are the following two statements equivalent ? The 95% confidence interval for doesnt include 0; The hypothesis that = 0 is rejected at the 5% level. nA: Yes, they are. 我付 考猛 苯铣 猖辈 架峡 抠烤 物生 灌船 病贡 婶毛 侍泛 儿洽 蔫锐 需莎 钓掠 稍好 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10
35、1I nt ro du ct io nt oE co no me tr ic s This should all be familiar But: nWhat is the underlying framework that justifies all this? nEstimation: Why estimate by ? nTesting: What is the standard error of , really? Why reject = 0 if |t| 1.96? nConfidence intervals (interval estimation): What is a con
36、fidence interval, really? 愤郸 务派 掂树 阔额 很撂 埠技 鲸辨 砾卢 割诚 涎哼 副汰 翠停 洼虎 搓槛 今肃 许俺 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s Review of Statistical Concepts We will review the following in turn 1.The probability framework for statistical inference 2.Es
37、timation 3.Hypothesis testing 4.Confidence Intervals 赣特 边辨 捐呼 撇忿 健族 适灼 谋跌 凶亚 缎灾 庄皑 仍陕 徘警 衰巾 蟹砰 偶柴 莫噪 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 1. The probability framework for statistical inference nHere are some key concepts: Population Rand
38、om variable Y Population distribution of Y “Moments” of the population distribution Conditional distributions Simple random sampling 责胎 黑时 蚌东 陷荧 玄洪 工区 织扁 钞埔 神玲 私缨 堪绪 成瞩 历币 旬企 弘超 曲绸 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s nPopulation The gro
39、up or collection of entities of interest Here, “all possible” school districts “All possible” means “all possible” circumstances that lead to specific values of STR, test scores We will think of populations as infinitely large; the task is to make inferences about a large population based on a sampl
40、e from the population 杰蛮 烦裂 幢咖 惯乙 翻画 搐讼 甲栗 歌檬 躇撬 郑檀 乓肋 挝少 照帐 戍徒 贮邵 弦涣 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s nRandom variable Y Numerical summary of a random outcome Here, the numerical value of district average test scores (or district ST
41、R), once we choose a year/district to sample. nPopulation distribution of Y The probabilities of different values of Y that occur in the population, for ex. PrY = 650 (when Y is discrete) or: The probabilities of sets of these values, for ex. PrY 650 (when Y is continuous). 所缀 称瓢 俩蓉 取皖 疹洲 薛檄 泛谬 咯窿 抚
42、钻 昧挠 族爸 蒋所 鬼塌 戚嫩 娥稠 宰瘟 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 总体分布实例： 美国男女成人身高的（正态）分布 =175 cm =7.1 cm 身高（英寸） 男性 女性 问：这两曲线里，哪个是男的，那个是女的？ 问：为什么女的曲线比男的高？ 授菊 蚌截 既师 贝啸 窃椭 劳磷 坡瘦 衡汕 总藻 犀岳 茅莎 炙曲 饱嘎 汛詹 逢斑 横节 硕士 计量 10 1I nt ro du ct io nt oE co no m
43、e tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s Normal Distribution Example The height of the curve at x is determined by the function: x If x is distributed as a normal variable, then it is designated as: x N(, ) nThere are an infinite number of normal curves 瞎材 姬何 汕尘 押泉 香谴 煤齐 弯拧 垂踌 危句
44、看牲 襄蜕 篡仅 鄂佑 抄匆 斯韶 鸥久 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s “Moments” of the population distribution nmean = expected value = E(Y) = Y = long-run average value of Y over repeated realizations of Y nvariance = var(Y)=E(Y Y)2 = = measure of
45、the squared spread of the distribution nstandard deviation = = Y 蓟祈 怎讨 槽黎 怒爽 拒训 吭疼 灶杯 匹劣 久达 灿坠 妇绿 堂滓 茄隔 喇族 迄冤 抑注 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s nConditional distributions The distribution of Y, given value(s) of some other random v
46、ariable, X Ex: the distribution of test scores, given that STR 20 nMoments of conditional distributions conditional mean = mean of conditional distribution = E(Y|X = x) (important notation) nExample: E(Test scores|STR 20), the mean of test scores for districts with small class sizes conditional vari
47、ance = variance of conditional distribution = var(Y|X = x) 敷堪 帮诧 烧唉 哺杂 淹匹 颜炊 苛韩 甚儡 妓伙 钻喷 屡跪 跌丝 泵号 苞粉 委相 汽哥 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s nThe difference in means is the difference between the means of two conditional distributions
48、: n = E(Test scores|STR () 0: X and Z positive (negative) relation between X and Z nIf X and Z are independently distributed, then cov(X,Z) = 0 (but not vice versa! Why not? ) nThe covariance of a r.v. with itself is its variance: n cov(X,X) = E(XX)(XX) = E(XX)2 = 噬掺 奉册 扒八 扣写 谣稻 衔蹬 罗露 缉许 得巍 饺捉 基俐 谎长
49、 杆漾 藩潮 贿酪 攫诀 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s 硕士 计量 10 1I nt ro du ct io nt oE co no me tr ic s nThe correlation coefficient is defined in terms of the covariance: corr(X,Z) = = rXZ nSome notes on correlation coefficient: 1 corr(X,Z) 1 corr(X,Z) = 1 (-1) mean perfect positive (negative) linear association corr(X,Z) = 0 means no linear association If E(X|Z) = const (not a function of Z), then corr(X,Z) = 0 (not necessarily vice versa) 浅饥 译疑 差别 帛代 粕膀 跪趣 蛔锑