计量经济学英文课件(3)
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计量经济学(英文PPT)Chapter 21 Time Series Econometrics ⅠStationarity Unit roots and Cointegration
6
k
k
0
covariance at lag k variance
obviously when k 0, 1 0
1 1 k
plot against k, the graph we obtain is known as the population correlogram k
• Returning to the example given in figure 21.8,the value of the Q statistic up to lag 25 is about 793,the LB statistic is about 891,both are highly significant, the probability of obtaining such a high
• We can rewrite the functions above as,
Yt ( 1)Yt1 ut
(21.9.1)
• or,
• Yt Yt 1 ut
(-1.96*0.1066,1.96*0.1066) or (0.2089,0.2089)
10
• In figure 21.8,the left two lines of dots represent the 95% confidence interval.
the joint hypothesis test of k H0 : all the k are simultaneo usly equal to zero.
• This can be done by using the Q statistic developed by Box and Pierce,
k
k
0
covariance at lag k variance
obviously when k 0, 1 0
1 1 k
plot against k, the graph we obtain is known as the population correlogram k
• Returning to the example given in figure 21.8,the value of the Q statistic up to lag 25 is about 793,the LB statistic is about 891,both are highly significant, the probability of obtaining such a high
• We can rewrite the functions above as,
Yt ( 1)Yt1 ut
(21.9.1)
• or,
• Yt Yt 1 ut
(-1.96*0.1066,1.96*0.1066) or (0.2089,0.2089)
10
• In figure 21.8,the left two lines of dots represent the 95% confidence interval.
the joint hypothesis test of k H0 : all the k are simultaneo usly equal to zero.
• This can be done by using the Q statistic developed by Box and Pierce,
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
计量经济学(英文PPT)Chapter 11 HETEROSCEDASTICITY
n n
X iYi
X
2 i
(
X i Yi Xi )2
(11.2.1)
under the assumption of heterscedasticity namely:
var(2 ) (
xi2
2 i
xi2 )2
(11.2.2) return
under the assumption of homoscedasticity namely:：
(11.2.2)
The Method of Generalized Least
Squares(GLS)
The usual OLS method does not make use of the information, but GLS(generalized least squares) take such information into account
Consequences of Using OLS in the Presence of Heteroscedasticity
Suppose
we
use
2
,
and
use
the
variance
formula
given
in
(11.2.2),
which takes into account heteroscedasticity explicitly.
2
ui (Yi 1 2 Xi )2
(11.3.10)
But in GLS we minimize the expression(11.3.7),
which can also be written as：
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)
计量经济学导论第四版英文完整教学课件
Economics 20 - Prof. Anderson
7
The Question of Causality
Simply establishing a relationship between variables is rarely sufficient Want to the effect to be considered causal If we’ve truly controlled for enough other variables, then the estimated ceteris paribus effect can often be considered to be causal Can be difficult to establish causality
Need to use nonexperimental, or observational, data to make inferences
Important to be able to apply economic theory to real world data
Economics 20 - Prof. Anderson
3
Why study Econometrics?
An empirical analysis uses data to test a theory or to estimate a relationship
A formal economic model can be tested
Theory may be ambiguous as to the effect of some policy change – can use econometrics to evaluate the program
计量经济学(英文版)
●How to measure the economic growth?
(Measure GDP, Growth velocity, Fluctuation)
●Analysis the factors that impact GDP？
(Investment, Consumption, Exportation…..)
9
Contact Information
PPT download:
Public Email: econometrics_ly@ Password: fall2011
Contact Me: Email: liy@ Office：通博楼B208 Office hour：TW 1-3 pm
design the policy?
13
Case3：Share price analysis of Chinese Stocks
●How does share price change ?
（ Measure by stock index）
●What is the main effect factors
Course Arrangement and Requirement
Term mission (30 %):
10 terms are grouped by yourselves. Each term is responsible for one chapter (assign randomly).
VII. Autocorrelation (3)
5
Course Contents
VIII. IX. X. XI. Model Specification and Diagnostic testing (3) Autoregressive and distributed lag models (6) Simultaneous Equation Models (6) Time Series Econometrics (6)
(Measure GDP, Growth velocity, Fluctuation)
●Analysis the factors that impact GDP？
(Investment, Consumption, Exportation…..)
9
Contact Information
PPT download:
Public Email: econometrics_ly@ Password: fall2011
Contact Me: Email: liy@ Office：通博楼B208 Office hour：TW 1-3 pm
design the policy?
13
Case3：Share price analysis of Chinese Stocks
●How does share price change ?
（ Measure by stock index）
●What is the main effect factors
Course Arrangement and Requirement
Term mission (30 %):
10 terms are grouped by yourselves. Each term is responsible for one chapter (assign randomly).
VII. Autocorrelation (3)
5
Course Contents
VIII. IX. X. XI. Model Specification and Diagnostic testing (3) Autoregressive and distributed lag models (6) Simultaneous Equation Models (6) Time Series Econometrics (6)
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 2 TWO-VARIABLE REGRESSION ANALYSIS SOME BASIC IDEAS
As the X value increases, the conditional mean value of Y increases, too. The dark circled points in Figure 2.1 show the conditional mean values of Y against the various X values.
is a linear function of X i ,say, of the type
E(Y | X i ) 1 2 X i (2.2.2)
1 and 2 are known as the regression coefficients. Equation（2.2.2）itself is known as the linear population regression function or simply linear population regression.
If we want to get the relationship between weekly family consumption expenditure (Y) and weekly family income (X).
In the hypothetical community, there is a total population of 60 families. The 60 families are divided into 10 income groups (from $80 to $260) . And assume that we get the observations given in Table 2.1.
Therefore, we can express the deviation of an individual Yi around its expected value as follows:
is a linear function of X i ,say, of the type
E(Y | X i ) 1 2 X i (2.2.2)
1 and 2 are known as the regression coefficients. Equation（2.2.2）itself is known as the linear population regression function or simply linear population regression.
If we want to get the relationship between weekly family consumption expenditure (Y) and weekly family income (X).
In the hypothetical community, there is a total population of 60 families. The 60 families are divided into 10 income groups (from $80 to $260) . And assume that we get the observations given in Table 2.1.
Therefore, we can express the deviation of an individual Yi around its expected value as follows:
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：
计量经济学英文课件 (3)
Z
b2 2
2
xi x
2
~ N 0,1
(3.1)
The standardized random variable Z is normally distributed with mean 0 and variance 1.
Slide 3-4
Principles of Econometrics, 3rd Edition
and its standard error
se(b2 ) var(b2 ) 4.38 2.09
Principles of Econometrics, 3rd Edition
Slide 3-12
A “95% confidence interval estimate” for 2:
The critical value tc for degrees of freedom m is the percentile value t1 2,m .
Principles of Econometrics, 3rd Edition
Slide 3-9
Figure 3.1 Critical Values from a t-distribution
Principles of Econometrics, 3rd Edition
Slide 3-16
The Null Hypothesis
parameter.
The null hypothesis, which is denoted H0 (H-naught), specifies a value for a regression The null hypothesis is stated H 0 : k c, where c is a constant, and is an important value in the context of a specific regression model.
计量经济学(共11张PPT)
分析与模型应 用阶段
是否可用于决策？ 应用
修改整理模型
结构分析
预测未来
模拟
检验发展理论
第五节 经济计量学和其它学科的关系
数理经济学是运用数学研究有关经济理论
数理统计学是运用数学研究统计问题 经济统计学是对经济现象的统计研究
经济计量学是经济学、统计学、数学三者结合在一起的交叉学科。
经济学
数理经济学
经济统计学
四、我国经济计量学的发展
70－80年代
80－90年代 1998年
开始介绍《经济计量学》的学科内 容和国外发展情况
1995年《经济计量学》的教学大纲 正式发表；全国许多高校相继开设 《经济计量学》课程。
将《经济计量学》列入经济类各专 业八门公共核心课程之一
五、经济计量学的内容体系
按照研究的方 法不同
《Econometrics》。
从30年代到今天，尤其是二次大战以后，计量经济学在西方各 国的影响迅速扩大。曾说：“二次世界大战以后的经济学是计量经 济学的时代”。1969年首届诺贝尔经济学奖授予弗里希和丁伯根。 自1996年设立诺贝尔经济学奖至1989年27为获奖者中有15位是计量 经济学家，其中10位是世界计量经济学会的会长。
（时间序列数据、截面数据）
二、参数估计
三、模型检验（拟合优度、t 检验、F 检验） 四、模型应用（预测、结构分析、 模拟）
第三节 经济计量学的特点
1.它是研究经济现象的，它不但给出质的解释，而且给出确切的量的 描述，从而使经济学成为一门精密的科学。 定性分析－定量分析（简单的数量对比－模型分析）
2.能综合考虑多种因素，通过描述客观经济现象中极为复杂的因果关系，对 影响某一经济现象的众多因素（哪些是主要、次要因素）给出一目了然的 回答。
Stock 计量经济学ppt一到三章
Introduction to Econometrics
The Statistical Analysis of Economic (and related) Data
Brief Overview of the Course
Economics suggests important relationships, often with policy implications, but virtually never suggests quantitative magnitudes of causal effects. What is the quantitative effect of reducing class size on student achievement? How does another year of education change earnings? What is the price elasticity of cigarettes? What is the effect on output growth of a 1 percentage point increase in interest rates by the Fed? What is the effect on housing prices of environmental improvements?
9
Initial data analysis: Compare districts with “small” (STR < 20) and “large” (STR ≥ 20) class sizes:
Class Size Average score (Y ) Small 657.4 Large 650.0 Standard deviation (sBYB) 19.4 17.9 n 238 182
The Statistical Analysis of Economic (and related) Data
Brief Overview of the Course
Economics suggests important relationships, often with policy implications, but virtually never suggests quantitative magnitudes of causal effects. What is the quantitative effect of reducing class size on student achievement? How does another year of education change earnings? What is the price elasticity of cigarettes? What is the effect on output growth of a 1 percentage point increase in interest rates by the Fed? What is the effect on housing prices of environmental improvements?
9
Initial data analysis: Compare districts with “small” (STR < 20) and “large” (STR ≥ 20) class sizes:
Class Size Average score (Y ) Small 657.4 Large 650.0 Standard deviation (sBYB) 19.4 17.9 n 238 182
计量经济学课程的英语
计量经济学课程的英语Econometrics is a course that marries economics with statistical methods to analyze economic data. It's like a compass for economists, guiding them through the sea of data to find the hidden treasures of economic relationships.In this course, we learn to use mathematical models to test theories and make predictions. It's not just about crunching numbers; it's about understanding the stories behind them. Each model we construct is like a puzzle piece that helps us see the bigger picture of the economy.One of the most exciting aspects of econometrics is its practicality. We don't just learn theories; we apply them to real-world problems. Whether it's predicting the stock market or analyzing the impact of a new policy, econometrics gives us the tools to make informed decisions.But this course isn't just about the destination; it's about the journey. The process of learning econometrics is a journey of discovery. Each new concept or technique we learn opens up a new way of looking at the world, and each problem we solve is a step forward in our understanding.The language of econometrics is English, but the lessons are universal. Students from all over the world come together in this course, united by a common goal: to understand the complex interactions of the economy and to use thatunderstanding to make a difference.As we progress through the course, we learn not onlyabout econometrics but also about ourselves. We discover our strengths and weaknesses, our passions and interests. And in the end, we come out not just as better economists, but as better thinkers, ready to tackle any challenge that comes our way.In conclusion, the econometrics course is more than justa class; it's an adventure into the heart of the economy.It's a journey that challenges us, teaches us, and ultimately, transforms us. And for those who embrace it, it's a journey that will last a lifetime.。
计量经济学(英文PPT)Chapter 22 TIME SERIES CONOMETRICS FORECASTING
1.Single Exponential Smoothing 2.Holt’s Linear Method 3.Holt winter’s Method
and their variations.
We will not discuss them in this chapter.
§22.1 APPROACHES TO ECONOMIC
Step3.Diagnostic checking. That is, test whether the chosen model fits
the data reasonably well. Choosing the right model needs not only
the science,but also considerable skills and the art.
The prerequisite of using BJ methodology to model an ARMA process,is that we must have either a stationary time series or a time series that is stationary after one or more differencings.
In short,a moving average process is simply a linear combination of white noise error term.
Autoregressive and Moving Average (ARMA) Process
It is quite likely that Y has characteristics of both
form knowledge directly perceived through the senses
and their variations.
We will not discuss them in this chapter.
§22.1 APPROACHES TO ECONOMIC
Step3.Diagnostic checking. That is, test whether the chosen model fits
the data reasonably well. Choosing the right model needs not only
the science,but also considerable skills and the art.
The prerequisite of using BJ methodology to model an ARMA process,is that we must have either a stationary time series or a time series that is stationary after one or more differencings.
In short,a moving average process is simply a linear combination of white noise error term.
Autoregressive and Moving Average (ARMA) Process
It is quite likely that Y has characteristics of both
form knowledge directly perceived through the senses
计量经济学(英文PPT)Chapter 10 Multicollinearity
errors are infinite。To a three-variable regression model：
yi 2 x2i 3 x3i uˆi
(10.2.1)
From chapter 7 we obtain：
( 2
yi x2i )( x32i ) ( yi x3i )( x2i x3i ) ( x22i )( x32i ) ( x2i x3i )2
Estimation in the presence of perfect multicollinearity
In the case of perfect muiticollinearity the regression
coefficients remain indeterminate and their standard
Chapter 10 Multicollinearity
The Nature of Multicollinearity
Mean: originally it meant the existence of a perfect ,or exact, linear relationship among some or all explanatory
Theoretical consequences of multicollinearity
It is true that even in the case of near multicollinearity the OLS estimators are unbiased. But unbiasedness is a multisample or repeated sampling property Collinearity does not destroy the property of minimum variance. But this does not mean that the variance of an OLS estimator will necessarily be small in any given sample
计量经济学英文课件 (1)
– The owner of a local Pizza Hut must decide how much advertising space to purchase in the local newspaper, and thus must estimate the relationship between advertising and sales
1.2 What is Econometrics About
1.2.1 Some Examples
•
Every day, decision-makers face ‘‘how much’’ questions
: (Continued)
– A real estate developer must predict by how much population and income will increase to the south of Baton Rouge, Louisiana, over the next few years, and whether it will be profitable to begin construction of a gambling casino and golf course
– You must decide how much of your savings will go into a stock fund, and how much into the money market. This requires you to make predictions of the level of economic activity, the rate of inflation, and interest rates over your planning horizon
1.2 What is Econometrics About
1.2.1 Some Examples
•
Every day, decision-makers face ‘‘how much’’ questions
: (Continued)
– A real estate developer must predict by how much population and income will increase to the south of Baton Rouge, Louisiana, over the next few years, and whether it will be profitable to begin construction of a gambling casino and golf course
– You must decide how much of your savings will go into a stock fund, and how much into the money market. This requires you to make predictions of the level of economic activity, the rate of inflation, and interest rates over your planning horizon
计量经济学(英文PPT)Chapter 5 Interval Estimation and Hypothesis Testing
likely to differ from the true value, although E(ˆ2 ) 2 . Therefore, instead of
relying on the point estimate alone, we may construct a interval around the point estimate, such that this interval has a certain probability of the true parameter value. This is the idea behind the interval estimation.
ˆ2 t / 2se(ˆ2 )
Example: P123
Second , confidence interval for 1
By the virtue of E(ˆ1 ) 1 and
2 ˆ1 n
Xi2 xi 2
2
,we
can
get
the
equations
as
Equation（5.2.1）shows that the interval has a probability 1 of including the
true 2. The interval estimator thus give a ranger of values within which the true
§5.3confidence intervals for regression
Coefficients 1 and 2
First, confidence interval for 2
It is shown before that the OLS estimator ˆ1 and ˆ2 are themselves normally
relying on the point estimate alone, we may construct a interval around the point estimate, such that this interval has a certain probability of the true parameter value. This is the idea behind the interval estimation.
ˆ2 t / 2se(ˆ2 )
Example: P123
Second , confidence interval for 1
By the virtue of E(ˆ1 ) 1 and
2 ˆ1 n
Xi2 xi 2
2
,we
can
get
the
equations
as
Equation（5.2.1）shows that the interval has a probability 1 of including the
true 2. The interval estimator thus give a ranger of values within which the true
§5.3confidence intervals for regression
Coefficients 1 and 2
First, confidence interval for 2
It is shown before that the OLS estimator ˆ1 and ˆ2 are themselves normally
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