发布时间 : 星期四 文章计量经济学（英文）重点知识点考试必备更新完毕开始阅读
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 ? Three 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 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独立或解释变量（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 ? In 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 ? That is, on average, how the dependent variable responds to a unit change in the
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.
第二章
1. The meaning of regression（回归）
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
1)Estimate the mean, or average, and the dependent values given the independent values
2)Test hypotheses about the nature of the dependence -----hypotheses suggested by the underlying economic theory
3)Predict or forecast the mean value of the dependent variable given the values of the independents
4)One 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 student’s S.A.T. score, say, the ith individual, corresponding to a specific family income can be expressed as the sum of two components 1) The component can be called the systematic, or deterministic, component. 2) May be called the nonsystematic or random component 6. What is the nature of U(stochastic error) term？
1)The 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
2)Some intrinsic randomness in the math score is bound to occur that can not be explained even we include all relevant variables.即使模型包括了决定性数学分数的所有变量，内在随机性也不可避免，这是做任何努力都无法解释的。 3)U may also represent errors of measurement. U还代表了度量误差
4)The 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.“奥卡姆剃刀原则”，描述应该尽可能简单，只要不遗漏重要信息。这表明回归模型应尽可能简单。
7. How do we estimate the PRF（population regression function）?
Unfortunately, in practice, We rarely have the entire population in our disposal,
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” 1)Linearity in the variables变量线性
The conditional mean value of the dependent variable is a linear function of the independent variables
2)Linearity in the Parameters参数线性
The conditional mean of the dependent variable is a linear function of the parameters, the B’s; 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.回归模型是参数线性的，但不一定是变量线性的。 2) Assumption 2: The explanatory variables X is uncorrelated with the disturbance term U. X’s are nonstochastic, U is stochastic. 解释变量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代表了所有未纳入模型的影响因素。
4) Assumption 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. 该假定表明，与给定的X相对应的每个Y的条件分布具有同方差。
b. 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周围。
5) 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。 6) Assumption 6:The regression model is correctly specified.回归模型是正确假定的。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普通最小二乘估计量的方差与标准误:One immediate result of the assumptions introduced is that they enable us to
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 σ
? The homoscedastic σ is estimated from formula 6.Standard Error of the Regression (SER) 回归标准误
? Is simply the standard deviation of the Y values about the estimated regression line. Y值偏离估计回归的标准差。 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.一旦确定了两个估计量的抽样分布，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，不仅是因为它简单易行，还因为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)满足古典线性模型的基本假定，则在所有线性据计量中，OLS估计两具有最小方差性，即OLS是最优线性无偏估计量（BLUE）
10.BLUE property 最优线性无偏估计量的性质
1) B1 and B2 are linear estimators. B1和B2是线性估计量
2) They are unbiased , that is E(b1)=B1, E(b2)=B2. B1和B2是无偏估计两
3) The OLS estimator of the error variance is unbiased.误差方差的OLS估计量是无偏的
4) b1 and b2 are efficient estimators.B1和B2是有效估计量
Var(b1) is less than the variance of any other linear unbiased estimator of B1 Var(b2) 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. =NORMINV(RAND(),0,2)
? Do it by matlab.= NORMINV(uniform(),MU,SIGMA)