计量经济学(英文)重点知识点考试必备

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)

4)

U may also represent errors of measurement. U

还代表了度量误差

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 possi ble.

“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

< br>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

“

< br>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

4

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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

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 mod el

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

5

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the same v ariance.

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-autocorrel ation.

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.

and Standard errors of OLS estimators< /p>

普通最小二乘估计量的方差与标准

误

:O ne

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. and .

should know:

Variances of the estimators

Standard errors of the estimators

is the value of

σ

The homoscedastic

σ

is estimated from formula

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。

of math function

1)

Interpretation

The standard deviation, or standard error, is , is a measure of

variability of b2 from sample to sample.

6

If we can say that our computed b2 lies within a certain number

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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 stra ightforward.

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。

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。

theorem

< br>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 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

）

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

< br>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

< br>

4)

b1 and b2 are efficient

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

7

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of B2

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)

Do it by Stata. =invnorm(uniform())

l Limit Theorem

’

s

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服从正态 分布

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 回归模型的其他所有因素的影响。

因为在这些影响中，

每

种因素对

Y

的影响都很微弱

< br>

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 di stribution.

如果所有这些影响因素都是随机的，用

U

代表所有这些影响因素之和，

那么根据中心极限定理，

可以假定误差项服从正态

分布。

r 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.

8

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正态变量的性质函数仍服从正态分布。

esis testing

假设检验

Having

known

the

distribution

of

OLS

estimators

b1

and

b2,

we

can

proceed

the topic of hypothesis testing.

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< /p>

以选择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。

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=, we can find out

the

probability

of

obtaining

such

a

value

from

the

Z,

the

standard

normal

d istribution.

如果零假设为

B2=0

，计算得到

b2=

，那么根据标准正态分布

Z

，

能够求得获此

b2

值的概率

If the probability is very small, we can reject

the

null

hypothesis.

如 果这个概率非常小，

则拒绝零假设。

If

the

probability

is larger, say , greater than 10 percent, we may not reject the null

hyp othesis.

如果这概率比较大，比如大于

10%

，就不拒绝零假设。

don

’

t know the

σ

2

We must know the true

σ

2, but we can estimate it by using

?

will happen if we replace

σ

by its estimator

σ

-hat

b

2

?

B

2< /p>

2

?

t

n

?

2

?

x

i

or

,

more

?

generally

b

2

?

B

2