2022年计量经济学重点知识点考试必备.docx

精选学习资料 - - - - - - - - - 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. Econometric analysis proceeds along the following lines计量经济学分析步骤 2.1Creating a statement of theory or hypothesis.建立一个理论假说 2Collecting data.收集数据 3Specifying the mathematical model of theory.设定数学模型 4Specifying the statistical, or econometric, model of theory.设立统计或经济计量 模型5Estimating the parameters of the chosen econometric model. 估量经济计量模型 参数6Checking for model adequacy : Model specification testing.核查模型的适用性：模型设定检验7Testing the hypothesis derived from the model.检验自模型的假设 8Using the model for prediction or forecasting.利用模型进行猜测 Step2：收集数据 . Three types of data三类可用于分析的数据 1Time 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 2Cross-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 3Pooled data合并数据（上两种的结合）Step3：设定数学模型1.plot scatter diagram or scattergram 2.write the mathematical model Step4：设立统计或经济计量模型 . CLFPR is dependent variable应变量 . CUNR is independent or explanatory variable独立或说明变量（自变量）. We give a catchall variable U to stand for all these neglected factors . In 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.线性回来分析的 主要目标就是说明一个变量（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：估量经济计量模型参数 . In short, the estimated regression line gives the relationship between average CLFPR and CUNR 简言之,估量的回来直线给出了平均应变量和自变量之间 的关系. That is, on average, how the dependent variable responds to a unit change in the 名师归纳总结 - - - - - - -第 1 页,共 26 页精选学习资料 - - - - - - - - - independent variable.单位因变量的变化引起的自变量平均变化量的多少；Step6：核查模型的适用性：模型设定检验 The purpose of developing an econometric model is not to capture total reality, but just its salient features. Step7：检验自模型的假设 Why do we perform hypothesis testing. We want to find our whether the estimated model makes economic sense and whether the results obtains conform with the underlying economic theory. 其次章1. The meaning of regression（回来）Regression analysis is concerned with the study of the relationship between one variable called the dependent or explained variable, and one or more other variables called independent or explanatory variables. 2. Objectives of regression 1Estimate the mean, or average, and the dependent values given the independent values 2Test hypotheses about the nature of the dependence -hypotheses suggested by the underlying economic theory 3Predict or forecast the mean value of the dependent variable given the values of the independents 4One or more of the preceding objectives combined 3. Population Regression Line（PRL）In short, the PRL tells us how the mean, or average, value of Y is related to each value of X in the whole population 4. The dependence of Y on X, technically called the regression of Y on X. 5. How do we explain it. A students S.A.T. score, say, the ith individual, corresponding to a specific family income can be expressed as the sum of two components 1The component can be called the systematic, or deterministic, component. 2May be called the nonsystematic or random component 6. What is the nature of Ustochastic error term？1The error term may represent the influence of those variables that are not explicitly included in the model. 误差项代表了未纳入模型变量的影响 2Some intrinsic randomness in the math score is bound to occur that can not be explained even we include all relevant variables.即使模型包括了打算性数学分数 的全部变量,内在随机性也不行防止,这是做任何努力都无法说明的；3U may also represent errors of measurement. U仍代表了度量误差 4The principle of Ockham s razor - the description be kept as simple as possible until proved inadequate - would suggest that we keep our regression model as simple as possible.“ 奥卡姆剃刀原就” ,描述应当尽可能简洁,只要不遗漏重要 信息；这说明回来模型应尽可能简洁；7. How do we estimate the PRF（population regression function）. Unfortunately, in practice, We rarely have the entire population in our disposal, 名师归纳总结 - - - - - - -第 2 页,共 26 页精选学习资料 - - - - - - - - - often we have only a sample from this population. 8. Granted that the SRF is only an approximation of PRF. Can we find a method or a procedure that will make this approximation as close as possible. SRF 仅仅是 PRF 的近似,那么能不能找到一种方法使这种近似尽可能接近真实呢？9. Special meaning of “ linear”1Linearity in the variables 变量线性 The conditional mean value of the dependent variable is a linear function of the independent variables 2Linearity in the Parameters参数线性 The conditional mean of the dependent variable is a linear function of the parameters, the Bs; it may or may not be linear in the variables. 第三章1.Unless we are willing to assume how the stochastic U terms are generated, we will not be able to tell how good an SRF is as an estimate of the true PRF.只有假定了随 机误差的生成过程,才能判定 SRF 对 PRF 拟合的是好是坏；2.Classical Linear Regression Model 1 Assumption 1: The regression model is linear in the parameters. It may or may not be linear in the variables.回来模型是参数线性的, 但不肯定是变量线性的；2 Assumption 2: The explanatory variables X is uncorrelated with the disturbance term U. X s are nonstochastic, U is stochastic. 说明变量 X 与扰动 误差项 u 不相关 . X 是非随机的, U 是随机的；3 Assumption 3: Given the value of Xi, the expected, or mean value of the disturbance term U is zero.给定 Xi ,扰动项的期望或均值为零；Disturbance U represent all those factors that are not specifically introduced in the model 干扰项 U 代表了全部未纳入模型的影响因素；4Assumption 4:The variance of each Ui is constant, or homoscedastic. U的方差 为常数,或同方差；Homoscedasticity（同方差） : a. This assumption simply means that the conditional distribution of each Y population corresponding to the given value of X has the same variance. 该假定 说明,与给定的 X 相对应的每个 Y 的条件分布具有同方差；5b.The individual Y values are spread around their mean values with the same variance.即每个 Y 值以相同的方差分布在其均值四周；Assumption 5:There is no correlation between two error terms, this is the assumption of no-autocorrelation.无自相关假定,即两个误差项之间不相关；6Assumption 6:The regression model is correctly specified.回来模型是正确假 定的； There is no specification bias or specification error in the model.实证分析的模型不存在设定偏差或设定误差；This assumption can be explained informally as follows. An econometric investigation begins with the specification of the econometric model underlying the phenomenon of interest. 3.Variances and Standard errors of OLS estimators一般最小二乘估量量的方差与标 准误 :One immediate result of the assumptions introduced is that they enable us to 名师归纳总结 - - - - - - -第 3 页,共 26 页精选学习资料 - - - - - - - - - estimate the variances and standard errors of the OLS estimators given in Eq.2.16 and 2.17. 4.We should know: Variances of the estimators Standard errors of the estimators 5.What is the value of The homoscedastic is estimated from formula 6.Standard Error of the Regression SER 回来标准误 Is simply the standard deviation of the Y values about the estimated regression line. Y 值偏离估量回来的标准差；7.Summary of math S.A.T.score function 1 Interpretation The standard deviation, or standard error, is 0.000245, is a measure of variability of b2 from sample to sample. If we can say that our computed b2 lies within a certain number of standard deviation units from the true B2, we can state with some confidence how good the computed SRF is as an estimator of the true PRF. 2）Sampling Distribution 抽样分布 Once we determine the sampling distribution of our two estimators, the task of hypothesis testing becomes straightforward.一旦确定了两个估量量的抽样分布,那么假设检验就是举手之劳的事情；8.Why do we use OLS . The properties of OLS estimators The method of OLS is used popularly not only because it is easy to use but also because it has some strong theoretical properties. OLS 法得到广泛使用, 不仅是因 为它简洁易行,仍由于它具有很强的理论性质；9.Gauss-Markov theorem 高斯 -马尔科夫定理 Given the assumptions of the classical linear regression model CLRM, the OLS estimators have minimum variance in the class of linear estimators.The OLS estimators are BLUE best linear unbiased estimators满意古典线性模型的基本假 定,就在全部线性据计量中,OLS 估量两具有最小方差性,即 OLS 是最优线 性无偏估量量（ BLUE ）10.BLUE property 最优线性无偏估量量的性质 1B1 and B2 are linear estimators. B1 和 B2 是线性估量量 2They are unbiased , that is Eb1=B1, Eb2=B2. B1 和 B2 是无偏估量两 3The OLS estimator of the error variance is unbiased.误差方差的 OLS 估量量是无 偏的4b1 and b2 are efficient estimators.B1和 B2 是有效估量量 Varb1 is less than the variance of any other linear unbiased estimator of B1 Varb2 is less than the variance of any other linear unbiased estimator of B2 11.Monte Carlo simulation 蒙特卡洛模拟 Do the experiment at lab Do it by Excell. =NORMINVRAND,0,2 Do it by matlab.= NORMINVuniform,MU,SIGMA 名师归纳总结 - - - - - - -第 4 页,共 26 页精选学习资料 - - - - - - - - - Do it by Stata. =invnormuniform 12.Central Limit Theorems 中心极限定理 If there is a large number of independent and identically distributed iid random variables, then, with a few exceptions , the distribution of their sum tends to be a normal distribution as the number of such variables increases indefinitely. 随着变量个数的无限增加,独立同分布随机变量近似听从正态分布13.Recall U, the error term represents the influence of all those forces that affect Y but are not specifically included in the regression model because there are so many of them and the individual effect of any one such force on Y may be too minor. 误差项代表了未纳入回来模型的其他全部因素的影响；由于在这些影响中, 每 种因素对 Y 的影响都很柔弱 If all these forces are random, if we let U represent the sum of all these forces, then by invoking the CLT, we can assume that the error term U follows the normal distribution.假如全部这些影响因素都是随机的,用 U 代表全部这些影响因素之 和,那么依据中心极限定理,可以假定误差项听从正态分布；14.Another property of normal distribution 另一个正态分布的性质 Any linear function of a normally distributed variable is itself normally distributed. 正态变量的性质函数仍听从正态分布；15.Hypothesis testing 假设检验 Having known the distribution of OLS estimators b1 and b2, we can proceed the topic of hypothesis testing. 16.Null hypothesis 零假设“ zero”null hypothesis is deliberately chosen to find out whether Y is related to X al all, which is also called straw man hypothesis.之所以挑选这样一个假设是为了确 定 Y 是否与 X 有关,也称为稻草人假设；17.We need some formal testing procedure to reject or receive the null hypothesis and make the skeptical guys shut up.需要正规的检验过程拒绝或接受零假设 18. If our null hypothesis is B2=0 and the computed b2=0.0013, we can find out the probability of obtaining such a value from the Z, the standard normal distribution.如 果零假设为 B2=0,运算得到 b2=0.0013,那么依据标准正态分布 Z,能够求得获 此 b2 值的概率 If the probability is very small, we can reject the null hypothesis.假如这个概率特别小,就拒绝零假设；If the probability is larger, say , greater than 10 percent, we may not reject the null hypothesis.假如这概率比较大,比如大于 就不拒绝零假设；10%,19.We dont know the 2 We must know the true 2, but we can estimate it by using . 220.What will happen if we replace by its estimator -hat 名师归纳总结 b 2B 2:ttn2第 5 页,共 26 页2 x ior moregenerallyb2B 2:n2se b 2- - - - - - -精选学习资料 - - - - - - - - - 21.Let us assume that , the level of significance or the probability of committing a type I error, is fixed at 5 percent. 假定 ,显著水平成犯第一类错误的概率为 5%；22.red area = rejection region for 2-sided test ft a/2 1-a a/2 -t0 tt c c 23.Loop and ball a. This is a 95% confidence interval for B2 给出了 B2 的一个 95%的置信区间；b. in repeated applications 95 out of 100 such intervals will include the true B2 重复上述过程,100 个这样的区间中将有 95 个包括真实的 B2；c. Such a confidence interval is known as the region of acceptance of H0 and the area outside the confidence interval is known as the rejection region of H0用假设检验的语言把这样的置信区间称为（H0 的）接受区域,把置信区间以外的区间成为（H0 的）拒绝区域24.回来系数的假设检验 目的：简洁线性回来中,检验 X 对 Y 是否真有显著影响 基本概念回忆 : 临界值与概率、大致率大事与小概率大事相对于显著性水平*t的临界值为 : t（单侧）或t2（双侧）运算的统计量为:（ 小 概 率t2（ 大 概 率 事t2大事）件）1统计0 *t量 t 25.Conclusions Since this interval does not include the null-hypothesized value of 0.由于这个区间没有包括零假名师归纳总结 - - - - - - -第 6 页,共 26 页精选学习资料 - - - - - - - - - 设值 0； We can reject the null hypothesis that annual family income is not related to math S.A.T. Scores.所以拒绝假设：家庭年收入对数学SAT 没有影响； Put positively, income does have a relationship to math S.A.T. scores. 换言之,收入的确与数学 SAT 有关系；26.A cautionary note Although the statement given is true, we cannot say that the probability is 95 percent that the particular interval includes B2, for this interval is not a random interval, it is fixed, therefore, the probability is either 1 ore 0 that the interval includes B2. 区间式 3.27 包括真实 B2 的概率为 95%,由于与式子虽然式子 3.26 为真,但不能说某个特定 3.26 不同,式 3.27 是固定的,而不是一根随机区间, 所以区间 3.27 包括 B2 的概率为 1 或 0.We can only say that if we construct 100 intervals like this interval, 95 out of 100 such intervals will include the true B2. 我们只能说, 假如建立 100 个像式 3.27 这样的区间,就有 95 个区间包括真实的B2.We can not guarantee that this particular interval will necessarily includes B2.并不能保证某个区间肯定有B2. 27.The test of significance approach to hypothesis testing 假设检验的显著性检验方法Hypothesis testing is that of a test statistic and the sampling distribution of the test statistic under the null hypothesis, H0. 假设检验方法涉及两个重要的概念检验统计量和零假设下检验统计量 的抽样分布； The decision to accept or reject H0 is made on the basis of the value of the test statistic obtained from the sample data.依据从样本数据求得的检验统计量的值打算接受或拒 绝零假设；28.T test We can use the t value computed here ad the test statistic, which follows the t distribution with n-2 d.f. 可以运算出t 值作为检验统计量,它听从自由度为（n-2）的 t 分布；29.Instead of arbitrarily choosing the value , we can find the p value the exact level of significance and reject the null hypothesis if the computed P value is sufficiently low. 为了防止选择显著水平的随便性,通常求出 p 值（精确的显著水平） ,假如运算的 p 值充分小,就拒绝零假设；30.Conclusions In the case of two-sided t test 双边检验情形中If the computed |t|, the absolute value of t, exceeds the critical t value at the chosen level of significance, we can reject the null hypothesis. 如果运算得到的 |t|值超过临界 t 值,就拒绝零假设；31.P value The P value of that t statistic of 5.4354 is about 0.0006. t统计量（ 5.4354）的 p 值（概率值）约为 0.0006；The smaller the p value, the more confident we ar