计量经济学英文课件(15)(20200617003533)
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计量经济学(英文版)精品PPT课件
(4.3a)
Expand and multiply top and bottom by n:
b2
=
nSxiyi - Sxi Syi nSxi2-(Sxi) 2
(4.3b)
Variance of b2
4.12
Given that both yi and ei have variance s2,
the variance of the estimator b2 is:
4. cov(ei,ej) = cov(yi,yj) = 0 5. xt c for every observation
6. et~N(0,s 2) <=> yt~N(b1+ b2xt,
The population parameters b1 and b2 4.4 are unknown population constants.
b2
+
nSxiEei - Sxi SEei nSxi2-(Sxi) 2
Since Eei = 0, then Eb2 = b2 .
An Unbiased Estimator
4.8
The result Eb2 = b2 means that the distribution of b2 is centered at b2.
4.6
The Expected Values of b1 and b2
The least squares formulas (estimators) in the simple regression case:
b2 =
nSxiyi - Sxi Syi nSxi22 -(Sxi) 2
b1 = y - b2x
金融计量经济学双语版全套课件.ppt
• However, the value of the autocovariances depend on the units
of measurement of yt.
• It is thus more convenient to use the autocorrelations which
are the autocovariances normalised by dividing by the
where ut is a zero mean white noise process with variance 2.
(i) Calculate the mean and variance of Xt (ii) Derive the autocorrelation function for this process (i.e.
Var(ut)= 2, then yt = + ut + 1ut-1 + 2ut-2 + ... + qut-q
is a qth order moving average model MA(q).
• Or using the lag operator notation:
Lyt = yt-1
Liyt = yt-i
TusTeful2aksm1aTpok2 rktm~ anm2teau
(general)
test
of
linear dependence in time series.
课件
5-7
An ACF Example (p234)
• Question: Suppose that we had estimated the first 5 autocorrelation coefficients using a series of length 100 observations, and found them to be (from 1 to 5): 0.207, -0.013, 0.086, 0.005, -0.022. Test each of the individual coefficient for significance, and use both the Box-Pierce and Ljung-Box tests to establish whether they are jointly significant.
计量经济学优秀课件
D
19 / 53
Law of Large numbers
log(Fertility)
0.5
1.0
1.5
பைடு நூலகம்
2.0
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Probability and Large sample Theory
8 / 53
Probability Theory Random variable
A function that assigns a numerical value to an outcome in an experiment. Associated with a probability Example
∞ −∞ g (x )fX (x )dx
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Variance, Covariance Var(X ) = E(X − E(X ))2 = E(X )2 − (E(X ))2 . Cov(X , Y ) = E(X − E(X ))(Y − E(Y )) = E(XY ) − E(X )E(Y )
Fertility
4
5
6
7
8
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q q q q q q q qq q q q q q q q q q q q q q q q q q q q
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Law of Large numbers
log(Fertility)
0.5
1.0
1.5
பைடு நூலகம்
2.0
5
6
7
8
9
10
7 / 53
Probability and Large sample Theory
8 / 53
Probability Theory Random variable
A function that assigns a numerical value to an outcome in an experiment. Associated with a probability Example
∞ −∞ g (x )fX (x )dx
16 / 53
Variance, Covariance Var(X ) = E(X − E(X ))2 = E(X )2 − (E(X ))2 . Cov(X , Y ) = E(X − E(X ))(Y − E(Y )) = E(XY ) − E(X )E(Y )
Fertility
4
5
6
7
8
3
q q q q q q q qq q q q q q q q q q q q q q q q q q q q
q
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q q q q q q q q qq q
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q qq q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q qq q qq q q q qqq q q q q q qq qq qq q q q q q q q q qq q qq q q q q q q q q q q q qq qq q q q q qq q q q q qq q q q q qq q q qq q q q q q qq q q q q q q qq q q q q q q qqqq q qq q
《计量经济学英文版》课件
2 ARMA模型
介绍ARMA模型的基本原 理和参数估计方法，以及 ARMA模型在经济数据分 析中的应用。
3 GARCH模型
讲解GARCH模型的原理 和估计方法，以及 GARCH模型在金融市场 波动预测中的应用。
计量经济模型的应用
金融市场分析
应用计量经济模型进行金融市 场的预测和分析。
政策评估
利用计量经济模型评估政策的 效果和影响。
面板数据模型
1
面板数据概述
介绍面板数据的特点和应用领域，以及面板数据模型的基本概念。
2
固定效应模型
讲解固定效应模型的估计和推断方法，以及固定效应模型的优缺点。
3
随机效应模型
介绍随机效应模型的估计和推断方法，以及随机效应模型与固定效应模型的比较。
时间序列模型
1 时间序列数据基本特
征
描述时间序列数据的基本 特征，如趋势、季节性和 周期性。
《计量经济学英文版》 PPT课件
本课程介绍了计量经济学的基本概念和分析方法。涵盖了经济数据与计量分 析、经典线性回归模型、面板数据模型、时间序列模型和计量经济模型的应 用。
课程概述
本节将概述本课程的内容，包括学习目标和涵盖的主要内容。通过本课程的学习，您将掌握计量经济学的基本 理论和实际应用。
经济数据与计量分析
企业ቤተ መጻሕፍቲ ባይዱ策
运用计量经济模型辅助企业的 决策制定。
总结
通过本课程的学习，您将获得计量经济学分析的基本知识和技能，能够应用计量经济模型进行实证研究，并在 实际问题中运用计量经济学的方法和工具。
• 经济数据的概念与特点 • 统计概率基础 • 经济计量分析的目的与意义
经典线性回归模型
普通最小二乘法
计量经济学英文课件共35页
8
One-Sided Alternatives (cont)
Having picked a significance level, a, we look up the (1 – a)th percentile in a t distribution with n – k – 1 df and call this c, the critical value We can reject the null hypothesis if the t statistic is greater than the critical value If the t statistic is less than the critical value then we fail to reject the null
Under the CLM assumptions, conditional on the sample values of the independent variable s
bˆ j ~ Normal b j ,Var bˆ j , so that
bˆ j b j sd bˆ j ~ Normal 0,1
7
t Test: One-Sided Alternatives
Besides our null, H0, we need an alternative hypothesis, H1, and a significance level H1 may be one-sided, or two-sided
because we have to estimate s 2by sˆ 2
Note the degrees of freedom : n k 1
5
The t Test (cont)
One-Sided Alternatives (cont)
Having picked a significance level, a, we look up the (1 – a)th percentile in a t distribution with n – k – 1 df and call this c, the critical value We can reject the null hypothesis if the t statistic is greater than the critical value If the t statistic is less than the critical value then we fail to reject the null
Under the CLM assumptions, conditional on the sample values of the independent variable s
bˆ j ~ Normal b j ,Var bˆ j , so that
bˆ j b j sd bˆ j ~ Normal 0,1
7
t Test: One-Sided Alternatives
Besides our null, H0, we need an alternative hypothesis, H1, and a significance level H1 may be one-sided, or two-sided
because we have to estimate s 2by sˆ 2
Note the degrees of freedom : n k 1
5
The t Test (cont)
计量经济学(英文PPT)Chapter 15 Qualitative Response Regression Model
The probability distribution of ui is :
Obviously, they follow the Bernoulli distribution. The OLS point estimates still remain unbiased. As the sample size increases indefinitely, the OLS estimators tend to be normally distributed generally.
Ask: Eui ? var(ui) ?
2. Heteroscedastic Variances of the Disturbances.
Answer : Eui Pi(1 1 2 Xi) (1 Pi)(1 1 2 Xi)
Pi 1 2 Xi
• Step 1: Run the OLS regression (15.2.1) despite the
heteroscedasticity problem and obtain Yi = estimate of the true
E
(Yi
|
Xi).
Then
obtain
Wi
Yi(1 Yi)
• The qualitative variable can be divided into three kind.
1. Dichotomous Variable
for example:
if male, Y=1 if female, Y=0
if vote for the Democratic Party, Y=1 if vote for the Republican Party, Y=0
Obviously, they follow the Bernoulli distribution. The OLS point estimates still remain unbiased. As the sample size increases indefinitely, the OLS estimators tend to be normally distributed generally.
Ask: Eui ? var(ui) ?
2. Heteroscedastic Variances of the Disturbances.
Answer : Eui Pi(1 1 2 Xi) (1 Pi)(1 1 2 Xi)
Pi 1 2 Xi
• Step 1: Run the OLS regression (15.2.1) despite the
heteroscedasticity problem and obtain Yi = estimate of the true
E
(Yi
|
Xi).
Then
obtain
Wi
Yi(1 Yi)
• The qualitative variable can be divided into three kind.
1. Dichotomous Variable
for example:
if male, Y=1 if female, Y=0
if vote for the Democratic Party, Y=1 if vote for the Republican Party, Y=0
计量经济学ppt第一章
1.2 What is Econometrics About
◆计量经济学家时常被指责为：使用大铁锤去砸开花 生，却对数据不足以及成功运用这些技术所需的但却 不可靠的许多假设熟视无睹。
“计量经济理论就像仔细斟酌过的法国食谱，清楚、精确地 说明了混合调味料需要调几次，需要多少克拉的香料，以及在恰 好474度下需要多少毫秒烘烤混合物。可是，当统计学的”厨师“ 转向原材料时，却发现没有仙人掌水果的核，因此用几块哈密瓜 代替；当食谱要求采用粉条时他却用麦片；他还用绿色胡椒代替 咖喱，用鹌鹑蛋代替海龟蛋，还用一罐松脂油代替1883的 Chalifougnac。”（Valavanis，1959）
Page 5
1.1 什么是计量经济学
Principles of Econometrics, 4th Edition
Chapter 1: An Introduction to Econometrics
Page 6
1.1.1 计量经济学的概念
计量经济学（ Econometrics）：是经济理论、统计学和数学 的结合。
原因之三：
新的检验要求新的计量经济学方法，从
而催生新的理论的诞生。 这也提示我们，在学习计量经济学时，应回到经济学 之中，应与经济现实相结合，对感兴趣的经济理论或假
设进行检验。
Principles of Econometrics, 4th Edition
Chapter 1: An Introduction to Econometrics Page 15
Principles of Econometrics, 4th Edition
Chapter 1: An Introduction to Econometrics Page 10
计量经济学(英文版).
Chapter 4 Statistical Properties of the OLS Estimators
Xi’An Institute of Post & Telecommunication Dept of Economic & Management Prof. Long
Simple Linear Regression Model y t = b1 + b 2 x t + e t
b1 + b2 x t
Assumptions of the Simple Linear Regression Model yt = b1 + b2x t + e t 2. E(e t) = 0 <=> E(yt) = b1 + b2x t
1.
3. var(e t)
4.3
=
4.
5.
cov(e i,e j)
x t c for every observation
= cov(yi,yj)
s 2 = var(yt)
= 0
6.
e t~N(0,s 2) <=> yt~N(b1+ b2x t,
The population parameters b1 and b2 are unknown population constants.
4.2
yt = household weekly food expenditures
x t = household weekly income
For a given level of x t, the expected level of food expenditures will be: E(yt|x t) =
Xi’An Institute of Post & Telecommunication Dept of Economic & Management Prof. Long
Simple Linear Regression Model y t = b1 + b 2 x t + e t
b1 + b2 x t
Assumptions of the Simple Linear Regression Model yt = b1 + b2x t + e t 2. E(e t) = 0 <=> E(yt) = b1 + b2x t
1.
3. var(e t)
4.3
=
4.
5.
cov(e i,e j)
x t c for every observation
= cov(yi,yj)
s 2 = var(yt)
= 0
6.
e t~N(0,s 2) <=> yt~N(b1+ b2x t,
The population parameters b1 and b2 are unknown population constants.
4.2
yt = household weekly food expenditures
x t = household weekly income
For a given level of x t, the expected level of food expenditures will be: E(yt|x t) =
计量经济学(英文PPT)Chapter 0 Introduction
consumption
is：2
,
namely,
－231.8
and
0.7194.
Thus,
the
estimated
Yˆ 231.8 0.7194 X
We see that，for the period 1980—1992, MPC≈0.72 in America, suggesting that for the sample period an increase in real income of 1 dollar led, on average, to an increase of about 72 cents in real
However, the establishment of World Econometric Society in December 29th, 1930 and the publication of its academic journal Econometrics in 1933 are generally acknowledged as a landmark of econometrics as a separate discipline.
Why a separate discipline?
Economic theory makes statements or hypotheses that are mostly qualitative in nature; It is the job of the econometrician to provide such numerical estimates.
Example: Keynesian theory of consumption
is：2
,
namely,
－231.8
and
0.7194.
Thus,
the
estimated
Yˆ 231.8 0.7194 X
We see that，for the period 1980—1992, MPC≈0.72 in America, suggesting that for the sample period an increase in real income of 1 dollar led, on average, to an increase of about 72 cents in real
However, the establishment of World Econometric Society in December 29th, 1930 and the publication of its academic journal Econometrics in 1933 are generally acknowledged as a landmark of econometrics as a separate discipline.
Why a separate discipline?
Economic theory makes statements or hypotheses that are mostly qualitative in nature; It is the job of the econometrician to provide such numerical estimates.
Example: Keynesian theory of consumption
计量经济学(英文PPT)Chapter 3 TWO-VARIABLE REGRESSION MODEL-THE PROBLEM OF ESTIMATION
Chapter 3 TWO-VARIABLE REGRESSION MODEL:
THE PROBLEM OF ESTIMATION
§3.1 THE METHOD OF ORDINARY LEAST SQUARES
The Method of ordinary least squares is attributed to Carl Friedrich Gauss, a German mathematician.
Ⅱ．The estimators which are point estimators are different from interval estimators.
Ⅲ．Once the OLS estimators are obtained from the sample data, the sample regression line can be easily obtained. The regression line thus obtained has the following properties:
Yˆi ˆ1 ˆ2 X i (Y ˆ2 X ) ˆ2 X i Y ˆ2 ( X i X )
while ∵ (Xi X ) 0
∴sum the equation above for the sample value on both sides and divide the result through by n( sum for i，then dived by n),
least-squares estimators, for they are derived from the least-
squares principle.
note：
THE PROBLEM OF ESTIMATION
§3.1 THE METHOD OF ORDINARY LEAST SQUARES
The Method of ordinary least squares is attributed to Carl Friedrich Gauss, a German mathematician.
Ⅱ．The estimators which are point estimators are different from interval estimators.
Ⅲ．Once the OLS estimators are obtained from the sample data, the sample regression line can be easily obtained. The regression line thus obtained has the following properties:
Yˆi ˆ1 ˆ2 X i (Y ˆ2 X ) ˆ2 X i Y ˆ2 ( X i X )
while ∵ (Xi X ) 0
∴sum the equation above for the sample value on both sides and divide the result through by n( sum for i，then dived by n),
least-squares estimators, for they are derived from the least-
squares principle.
note：
计量经济学(英文版)
3. The coefficients of the model chosen should satisfy certain a priori expectations. For example, if we are considering the demand for automobiles as a function of price and some other variables, we should expect a negative coefficient for the price variable.
Some practical model
To grasp the ideas developed in this section, consider the data given in table 6.2, Refers to U.S. gross private domestic investment (GPDI) and gross domestic product (GDP), in billions as well as millions of (chained) 1992 dollars.
4. Sometime more than one model may fit a given set of data reasonably well. In the modified Phillips curve, we fitted both a linear and a reciprocal model to the same data. In both cases the coefficients were in line with prior expectations and they were all statistically significant. One major difference was that the r2 value of the linear model was larger than that of the reciprocal model. One may therefore give a slight edge to the linear model over the reciprocal model. But make sure that in comparing two r2 values the dependent variable, or the regressand, of the two models is the same; the regressor(s) can take any form.
计量经济学全册课件(完整)pptx
预测与置信区间
阐述如何利用一元线性回归模型进行 预测，并给出预测值的置信区间，以 评估预测的不确定性。
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多元线性回归模型
模型设定与参数估计
介绍多元线性回归模型的基本形 式，解释多个自变量对因变量的 影响，以及最小二乘法在多元线 性回归中的应用。
模型的统计性质
探讨多元线性回归模型的统计性 质，包括回归系数的解释、拟合 优度的度量、多重共线性的诊断 与处理等。
经典线性回归模型
REPORTING
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一元线性回归模型
模型设定与参数估计
介绍一元线性回归模型的基本形式， 解释因变量、自变量和误差项的含义 ，阐述最小二乘法（OLS）进行参数 估计的原理。
模型的统计性质
探讨一元线性回归模型的统计性质， 包括回归系数的解释、拟合优度的度 量（如R方）、回归系数的显著性检 验等。
贝叶斯计量经济学的定义
贝叶斯计量经济学是应用贝叶斯统计推断方法，对经济模 型进行参数估计、假设检验和预测的一门学科。
贝叶斯计量经济学的研究对象
贝叶斯计量经济学主要关注经济模型的参数估计和不确定 性问题，如线性回归模型、时间序列模型、面板数据模型 等。
贝叶斯计量经济学的研究方法
贝叶斯计量经济学的研究方法主要包括先验分布的设定、 后验分布的推导、马尔科夫链蒙特卡罗模拟（MCMC）等 。
介绍如何在EViews中导入数据，进行 数据清洗、转换和预处理等操作。
计量经济学模型估计
介绍如何在EViews中建立计量经济学 模型，进行参数估计、模型检验和预 测等操作。
24
Stata软件介绍及操作指南
Stata软件概述
Stata是一款流行的计量经济学软件，具有强大 的数据处理和统计分析功能。
计量经济学(英文版)
Some practical model
To grasp the ideas developed in this section, consider the data given in table 6.2, Refers to U.S. gross private domestic investment (GPDI) and gross domestic product (GDP), in billions as well as millions of (chained) 1992 dollars.
Chapter 7 Multi variable regression
Xi’An Institute of Post & Telecommunication Dept of Economic & Management Prof. Long
• SCALING AND UNITS OF MEASUREMENT
Model 2
Some practical models
Model 3
Model 4
Note: CM=Child mortality, the number of deaths of children under age 5 in a year per 1000 live births. FLFP=Female literacy rate, percent. PGNP=per capita GNP in 1980. TFR=total fertility rate, 1980–1985, the average number of children born to a woman, using age-specific fertility rates for a given year.