eviews 3.1 user’s guide - Головна сторінка - volfy's...

EViews 3.1 Users Guide3rd Edition

Copyright 19941999 Quantitative Micro Software, LLC

All Rights Reserved

Printed in the United States of America

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Quantitative Micro Software, LLC

4521 Campus Drive, PMB 336, Irvine CA, 92612-2699

Telephone: (949) 856-3368

Fax: (949) 856-2044

e-mail: [email protected]

web:

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Table of Contents

PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

PART I. EVIEWS FUNDAMENTALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

CHAPTER 1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5

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CHAPTER 2. A DEMONSTRATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

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CHAPTER 3. EVIEWS BASICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

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CHAPTER 6. EVIEWS DATABASES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

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CHAPTER 9. STATISTICAL GRAPHS USING SERIES AND GROUPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

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CHAPTER 10. GRAPHS, TABLES, AND TEXT OBJECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

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CHAPTER 14. FORECASTING FROM AN EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305

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CHAPTER 15. SPECIFICATION AND DIAGNOSTIC TESTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329

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PART IV. ADVANCED SINGLE EQUATION ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .357

CHAPTER 16. ARCH AND GARCH ESTIMATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359

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CHAPTER 17. DISCRETE AND LIMITED DEPENDENT VARIABLE MODELS . . . . . . . . . . . . . . . . . . . . . . 381

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CHAPTER 18. THE LOG LIKELIHOOD (LOGL) OBJECT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431

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PART V. MULTIPLE EQUATION ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453

CHAPTER 19. SYSTEM ESTIMATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455

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CHAPTER 20. VECTOR AUTOREGRESSION AND ERROR CORRECTION MODELS . . . . . . . . . . . . . . . . . 477

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CHAPTER 21. STATE SPACE MODELS AND THE KALMAN FILTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505

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CHAPTER 22. POOLED TIME SERIES, CROSS-SECTION DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525

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Table of Contentsvii

CHAPTER 23. MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551

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APPENDIX A. MATHEMATICAL OPERATORS AND FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565

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APPENDIX B. GLOBAL OPTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579

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APPENDIX C. DATE FORMATS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583

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APPENDIX D. WILDCARDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587

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APPENDIX E. ESTIMATION ALGORITHMS AND OPTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591

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APPENDIX F. INFORMATION CRITERIA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599

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REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .601

INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .607

Preface

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Chapter 2. A Demonstration

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Dependent Variable: LOG(M1)Method: Least SquaresDate: 10/19/97 Time: 22:43Sample(adjusted): 1952:2 1992:4Included observations: 163 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob.

C 1.312383 0.032199 40.75850 0.0000LOG(GDP) 0.772035 0.006537 118.1092 0.0000

RS -0.020686 0.002516 -8.221196 0.0000DLOG(PR) -2.572204 0.942556 -2.728967 0.0071

R-squared 0.993274 Mean dependent var 5.692279Adjusted R-squared 0.993147 S.D. dependent var 0.670253S.E. of regression 0.055485 Akaike info criterion -2.921176Sum squared resid 0.489494 Schwarz criterion -2.845256Log likelihood 242.0759 F-statistic 7826.904Durbin-Watson stat 0.140967 Prob(F-statistic) 0.000000

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F-statistic 813.0060 Probability 0.000000Obs*R-squared 136.4770 Probability 0.000000

Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 10/19/97 Time: 22:45


C -0.006355 0.013031 -0.487683 0.6265LOG(GDP) 0.000997 0.002645 0.376929 0.7067

RS -0.000567 0.001018 -0.556748 0.5785DLOG(PR) 0.404143 0.381676 1.058864 0.2913RESID(-1) 0.920306 0.032276 28.51326 0.0000

R-squared 0.837282 Mean dependent var 1.21E-15Adjusted R-squared 0.833163 S.D. dependent var 0.054969S.E. of regression 0.022452 Akaike info criterion -4.724644Sum squared resid 0.079649 Schwarz criterion -4.629744Log likelihood 390.0585 F-statistic 203.2515Durbin-Watson stat 1.770965 Prob(F-statistic) 0.000000


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Dependent Variable: LOG(M1)Method: Least SquaresDate: 10/19/97 Time: 22:48Sample(adjusted): 1952:3 1992:4Included observations: 162 after adjusting endpoints


C 0.071297 0.028248 2.523949 0.0126LOG(GDP) 0.320338 0.118186 2.710453 0.0075

RS -0.005222 0.001469 -3.554801 0.0005DLOG(PR) 0.038615 0.341619 0.113036 0.9101

LOG(M1(-1)) 0.926640 0.020319 45.60375 0.0000LOG(GDP(-1)) -0.257364 0.123264 -2.087910 0.0385

RS(-1) 0.002604 0.001574 1.654429 0.1001DLOG(PR(-1)) -0.071650 0.347403 -0.206246 0.8369


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Dependent Variable: LOG(M1)Method: Least SquaresDate: 10/19/97 Time: 22:52Sample(adjusted): 1952:3 1992:4Included observations: 162 after adjusting endpointsConvergence achieved after 14 iterations


C 1.050340 0.328390 3.198453 0.0017LOG(GDP) 0.794929 0.049342 16.11057 0.0000

RS -0.007395 0.001457 -5.075131 0.0000DLOG(PR) -0.008019 0.348689 -0.022998 0.9817

AR(1) 0.968100 0.018190 53.22283 0.0000


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Addendum: Matrix Object Reading and Writing

Addendum: Matrix Object Reading and Writing79

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Chapter 5. Working with Data

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Using Auto-series in Groups

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Working with Scalars

Working with Scalars99

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Chapter 6. EViews Databases

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An Overview

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Database Basics

What is an EViews Database?

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Part II. Basic Data Analysis

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Chapter 7. Series

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Descriptive Statistics

Histogram and Stats

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Descriptive Statistics for LWAGECategorized by values of MARRIED and UNIONDate: 10/15/97 Time: 01:11Sample: 1 1000Included observations: 1000

MeanMedianStd. Dev. UNIONObs. 0 1 All

0 1.993829 2.387019 2.0529721.906575 2.409131 2.0149030.574636 0.395838 0.568689

305 54 359

MARRIED 1 2.368924 2.492371 2.4001232.327278 2.525729 2.3978950.557405 0.380441 0.520910

479 162 641

All 2.223001 2.466033 2.2754962.197225 2.500525 2.3025850.592757 0.386134 0.563464

784 216 1000

Descriptive Statistics for LWAGECategorized by values of MARRIED and UNIONDate: 10/15/97 Time: 01:08Sample: 1 1000Included observations: 1000

UNION MARRIED Mean Median Std. Dev. Obs.0 0 1.993829 1.906575 0.574636 305

1 2.368924 2.327278 0.557405 479All 2.223001 2.197225 0.592757 784

1 0 2.387019 2.409131 0.395838 541 2.492371 2.525729 0.380441 162All 2.466033 2.500525 0.386134 216

All 0 2.052972 2.014903 0.568689 3591 2.400123 2.397895 0.520910 641All 2.275496 2.302585 0.563464 1000


Tests for Descriptive Stats

Simple Hypothesis Tests

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Hypothesis Testing for LWAGEDate: 10/15/97 Time: 01:14Sample: 1 1000Included observations: 1000

Test of Hypothesis: Mean = 2

Sample Mean = 2.275496Sample Std. Dev. = 0.563464

Method Value Probabilityt-statistic 15.46139 0.00000

2

2

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Series Views151

Equality Tests by Classification

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Hypothesis Testing for LWAGEDate: 10/14/97 Time: 23:23Sample: 1 1000Included observations: 1000

Test of Hypothesis: Median = 2.25

Sample Median = 2.302585

Method Value ProbabilitySign (exact binomial) 532 0.046291Sign (normal approximation) 1.992235 0.046345Wilcoxon signed rank 1.134568 0.256556van der Waerden (normal scores) 1.345613 0.178427

Median Test Summary

Category Count Mean Rank

Obs > 2.25 532 489.877820Obs < 2.25 468 512.574786Obs = 2.25 0

Total 1000


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Series Views153

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Median Equality Tests

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Test for Equality of Means of LWAGECategorized by values of MARRIED and UNIONDate: 10/14/97 Time: 12:28Sample: 1 1000Included observations: 1000

Method df Value Probability

Anova F-statistic (3, 996) 43.40185 0.0000

Analysis of Variance

Source of Variation df Sum of Sq. Mean Sq.

Between 3 36.66990 12.22330Within 996 280.5043 0.281631

Total 999 317.1742 0.317492

Category Statistics

Std. Err.UNION MARRIED Count Mean Std. Dev. of Mean

0 0 305 1.993829 0.574636 0.0329040 1 479 2.368924 0.557405 0.0254681 0 54 2.387019 0.395838 0.0538671 1 162 2.492371 0.380441 0.029890

All 1000 2.275496 0.563464 0.017818

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Tabulation Summary

Variable CategoriesLWAGE 5UNION 2MARRIED 2Product of Categories 20

Test Statistics df Value ProbPearson X2 4 174.5895 0.000000Likelihood Ratio G2 4 167.4912 0.000000

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ri yi a xi b( )2

i 1=

N

yi xi r

r 1 ei2 36m2( )( )

2for ei 6m 1

,;2@4#$$9A

,>

3532------ 1 u2( )

3I u 1( )

4---

2---u

I u 1( )cos

I

h 0.15 XU XL( )=

XU XL( )

M 100=XL XU[ , ]

xi XL iXU XLM

---------------------- for i+ 0 1 M 1, ,= =

xi Xj Yj,( )j 1 2 N, , ,=

Xj


,4

'

Y

>

.,;&;$'P

PP5

8) #) >

Example

" 5@#$$#A

series x=rnd

series y=sin(2*pi*x^3)^3+nrnd*(0.1^.5)

G__GL,=

DEG

+, >

GLG

LJ

5LG,

. .$ $2$4

$(

-2

-1

0

1

2

0.0 0.2 0.4 0.6 0.8 1.0

Y

X

x 0.6= x 0.9=x 0.8=

Commands213

'

=

1

,,

LN#;

group aa age lwage

aa.linefit(yl,xl)

""("3"3

("3"3

-2

-1

0

1

2

0.0 0.2 0.4 0.6 0.8 1.0

X

Y

LOESS Fit (degree = 1, span = 0.3000)

-2

-1

0

1

2

0.0 0.2 0.4 0.6 0.8 1.0

XY

Kernel Fit (Epanechnikov, h = 0.1494)


aa.linefit(yl,d=3)

("3"3

aa.nnfit

aa.kerfit

@A>,>

""

Chapter 10. Graphs, Tables, and Text Objects

'

216Chapter 10. Graphs, Tables, and Text Objects

Graph Type

+

@ A

4

.

.$*-

=

C ,.$

C &,

-

C ;.$

C &;

C /";E,

C 02?

Graphs217

C A>

@A

*

>>

C $>

Graph Attributes

G.$

, G

???

Bars and Lines

G'

,,,

.$'>

(

'

Graph Scaling Options

2

2>

=

C :

C $2$: ?

C ,2$2

C :0?


8/2

3

4

@A4LG

?

@A

+

'

Line Graph Options

Graphs219


L>

G>

"

LN9GN2>

>>

>

G

>

",

,,

Adding Shading

G

4

.

,$

Customizing Axis Labels

.,?

,,

,

G

,,

4 33 3

Graphs221

Customizing Legends

.,

=

C

C

J-

C ,,,,2;"

C

C -

4

6,

G

Removing Graph Elements

?

4

, "

-

Graph Templates

5

,


Graph Commands

4 >

'

?

4

Multiple Graph Objects

,

Printing Graphs223

A


Printing Graphs as PostScript Files

'(

(,!($)

4, 2 6,

,",,-(

5-K9"

(-@,>

A

,

;4.=(

((

DE

(

'

Copying Graphs to Other Windows Programs

G'

(

, -

'J3

G

(,G:

(

,>>

.

/&'

.

((-

?G

,

Tables

"

;K

=

Copying Tables to Other Windows Programs225

Table Options

"

>>

.>

C

C )+0@)0A

C $@$A>

C @A

"$"+

+

J$

F'

GF'-


",

' @04A

>>'

(

04

=

.

Text Objects

:L>##

Commands227

?30-#

30"#

freeze(gra1) grp1.scat

Part III. Basic Single Equation Analysis

##H#)':

C

##10B

:'

C

#7"0B:

>:::

C

#20B:>

:=

"0""0."L

C

#9B'

C

#)4B'

:

"::,>

-.'-'

:

Chapter 11. Basic Regression

:>

:

:'=>

:

?::>:@A

:"0."F"0."L?

@3A3"05:

:

G ,

::

,

@A=

C -,0@#$$#A

C K6+@#$$%A

C 3@#$$%A

C 6M@#$$2A

(

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Equation Objects

:'(

):

232Chapter 11. Basic Regression

>>:::

>:

Specifying an Equation in EViews

(:

G

=:>

.

>

:=@>

A@>

A>

:=>

J

Specifying an Equation by List

:

:4

4

.+

:=

cs c inc

+>'

'>

@:A

,

:.#

>

G>

Specifying an Equation in EViews233

B4

=

cs cs(-1) c inc

'.+

@#A@7A

.+@2A

Gto4

cs c cs(-1 to -4) inc

@>#A@>7A@>2A@>9A.+.T

,?4

cs c inc(to -2) inc(-4)

.+.+@>#A.+@>7A.+@>9A

G>.>

4

log(cs) c log(cs(-1)) ((inc+inc(-1)) / 2)

.+

,

.'4>

,,+ 0>,

(>

, 3!:

J

Specifying an Equation by Formula

G:

:

":' >

:


':

:

(:'::

4

log(cs) c log(cs(-1)) log(inc)

'

log(cs) = c(1) + c(2)*log(cs(-1)) + c(3)*log(inc)

::

N=

log(urate) + c(1)*dmr = c(2)

:=

@###A

'?>>:

.:

:.:' >

4 :

c(1)*x + c(2)*y + 4*z

'?:

@@#AOLY@7AOGY9ORA('

@0>:A

::

:4

x + c(1)*y = c(2)*z

'@#A@7A?:@LY@#AOGH

@7AORA:=

x = -c(1)*y + c(2)*z

:

4

>

L

=

urate( )log c 1( )dmr c 2( )=

Estimating an Equation in EViews235

y = c(1) + c(2)*x + c(3)*x(-1) + c(4)*x(-2) +(1-c(2)-c(3)-

c(4))*x(-3)

'

:4

#7D+:E 7&8

G

!/"++'

,(./"

''+

>:

:>

:

::>

:3"05

+:

:"0"

Estimation Sample

G'

,>

Equation Output237

Equation Output

(,(:':

=

! =

@##7A

yT>XT

k k> T>>

Tk>

.y@#[email protected]

Coefficient Results

Regression Coefficients

DE:

b;

@##2A

.:D'E

J:'

@#A@7A

4

.

B

Dependent Variable: LOG(M1)Method: Least SquaresDate: 08/18/97 Time: 14:02Sample: 1959:01 1989:12Included observations: 372


C -1.699912 0.164954 -10.30539 0.0000LOG(IP) 1.765866 0.043546 40.55199 0.0000

TB3 -0.011895 0.004628 -2.570016 0.0106


y X +=

T 372= k 3=

b XX( ) 1 Xy=


?

Standard Errors

DE

B>

.

72

$)#88

@##9A

:

G

/"

t-Statistics

t>:?t>

t>:

?

Probability

t>

, 3p>

?4

)Qp>8),

>

>'

4 12?t>

var b( ) s2 XX( ) 1 s2; T k( ) ; y Xb= = =

T k

Equation Output239

Summary Statistics

R-squared

0>:@ A

.

:?

.

>

>:

'@A

@##)A

@>A

Adjusted R-squared

;

.


@##*A

Log Likelihood

',@A

,

,,>

:

,

@##$A

(''

Durbin-Watson Statistic

6>(>

@###8A

K6+@#$$%6)A>

6>(

"6(7

6(

#2 6>(

:

.

#2Q>

1>3

6>(

Mean and Standard Deviation (S.D.) of the Dependent Variable

y=

yi Xib( )2

t 1=

T

=

lT2--- 1 2( )log T( )log+ +( )=

DW

t t 1( )2

t 2=

T

t2

t 1=

T

-------------------------------------=

Equation Output241

@####A

Akaike Information Criterion

",,.@".A=

@###7A

,@:@##$A798A

".>B".

4 >

"."

4 )$$

Schwarz Criterion

?@A".>

=

@###2A

F-Statistic and Probability

+>@

A?4:+>

@###9A

!+>

p>6+7>

+>.p>8)?

?++>>

+>

Working With Regression Statistics

:

V>G

.

+"

y ytt 1=

T

T sy yt y( )2 T 1( )t 1=

T

=;=

AIC 2l T 2k T+=

l

SC 2l T k Tlog( ) T+=

FR

2k 1( )

1 R2( ) T k( )------------------------------------------=

k 1 T k


,V>=>

Keywords that return scalar values

Keywords that return vector or matrix objects

.:

Working with Equations243

G6>(>

:

(:(:#

4


+

4

4.$

'

>

.$

:

.$

>

/"6

Working with Equations245

Default Equation

4'

:

#)

#972

!:,G:>

::,

;:


t>:#

eq1.@tstats(2)

#

sym ccov1 = eq1.@cov

D0E 79)

Storing and Retrieving an Equation

">,

':,

G:,>

2&

.>

!:

8''34

Estimation Problems247

"@coefs

:@

A4

series cshat=eq1.@coefs(1)+eq1.@coefs(2)*gdp

'

:

equation eq01.ls y=c(10)+b(5)*y(-1)+a(7)*inc

1"

eq01.@coefs(1)@#8A

eq01.@coefs(2)1@)A

eq01.@coefs(3)"@%A

@stderrs:@"

" )&)A@coefs

.:

4

1"

equation eq02.ls cs=beta(1)+beta(2)*gdp

series cshat=beta(1)+beta(2)*gdp

1""@coefs

87"

1" 8''3:

+':eq02.beta(1)

eq02.beta(2AG eq02.@coefs(1)eq02.@coefs(2)

Estimation Problems

Exact Collinearity

.'

.'D+ E

(,">

! X>

,;


G >

"

4

:>

y c x @seas(1) @seas(2) @seas(3) @seas(4)

'D+ E:>

=

c = @seas(1) + @seas(2) + @seas(3) + @seas(4)

.

,

Commands

:

Chapter 12. Additional Regression Methods

:,

>:@A

:?@3A+>

:J

#$

-

@"0A

@"A

#2

Weighted Least Squares

,,w

G

:w,>

':

?

,>

?':

>

:

?>>:

@#7#A

k> . W

w?

yX>>

:

@#77A

@#72A

::

1& 3!,=,36,

S ( ) wt2yt xt( )

2

t=

bWLS XWWX( )1XWWy=

WLS s2XWWX( ) 1=

250Chapter 12. Additional Regression Methods

/7 :

,2$, *,

4,2$%,

(,(:

'

@#79A

Dependent Variable: LOG(X)Method: Least SquaresDate: 10/15/97 Time: 11:10Sample(adjusted): 1891 1983Included observations: 93 after adjusting endpointsWeighting series: POP


C 0.004233 0.012745 0.332092 0.7406LOG(X(-1)) 0.099840 0.112539 0.887163 0.3774LOG(W(-1)) 0.194219 0.421005 0.461322 0.6457

Weighted Statistics

R-squared 0.016252 Mean dependent var 0.009762Adjusted R-squared -0.005609 S.D. dependent var 0.106487S.E. of regression 0.106785 Akaike info criterion -1.604274Sum squared resid 1.026272 Schwarz criterion -1.522577Log likelihood 77.59873 F-statistic 0.743433Durbin-Watson stat 1.948087 Prob(F-statistic) 0.478376

Unweighted Statistics

R-squared -0.002922 Mean dependent var 0.011093Adjusted R-squared -0.025209 S.D. dependent var 0.121357S.E. of regression 0.122877 Sum squared resid 1.358893Durbin-Watson stat 2.086669

ut wt yt xtbWLS( )=

Heteroskedasticity and Autocorrelation Consistent Covariances251

@A

@#7)A

40.6

.

,.

,t $

:"0"+

Heteroskedasticity and Autocorrelation Consistent Covariances

(,,>

:;>

,;

1:5"=

C !(,+>(5"

>

C ,,>

4 :

(+>(

Heteroskedasticity Consistent Covariances (White)

(@#$*8A, >

,

,( =

@#7&A

Tk :

ut yt xtbWLS=

wt

WT

T k------------ XX( ) 1 ut

2xtxt

t 1=

T

XX( ) 1=

ut


'(

;;::

+ ,, #&-

,$",(:

':(I>

G'(

=

HAC Consistent Covariances (Newey-West)

( :>

+(@#$*%A

,

,+>(

@#7%A

@#7*A

q; 4+(

'q

@#7$A

+>( ,

#&--+>

Dependent Variable: LOG(X)Method: Least SquaresDate: 10/15/97 Time: 11:11Sample(adjusted): 1891 1983Included observations: 93 after adjusting endpointsWeighting series: POPWhite Heteroskedasticity-Consistent Standard Errors & Covariance


C 0.004233 0.012519 0.338088 0.7361LOG(X(-1)) 0.099840 0.137262 0.727369 0.4689LOG(W(-1)) 0.194219 0.436644 0.444800 0.6575

NWT

T k------------ XX( ) 1 XX( ) 1=

T

T k------------ ut

2xtxt

t 1=

T

1 vq 1+-------------

xtutut v xt v xt v ut v utxt+( )t v 1+=

T

v 1=

q

+

=

ut

q floor 4 T 100( )2 9( )=

Two-Stage Least Squares253

Two-Stage Least Squares

">>

.;

>

=

C >:

C 0>

4

"

>

: >

@#A

:@7A>

>>

>:@A"

>:.

;

:

>

G'

:Z

yX >:

@#7#8A

@#7##A

@:A

bTSLS XZ ZZ( )1ZX( )

1XZ ZZ( ) 1 Zy=

TSLS s2XZ ZZ( ) 1 ZX( )

1=

s2


Estimating TSLS in EViews

>::

3!1& 3!*,/$%

.

>

,=

C .

>

:,

6M@#$$9AK6+@#$$%A>

C 4>

C '

4

:>

@;+A@36-A@;+@H#AA

@.A@A36->

G @3A

@A.

G:

cons c gdp cons(-1) time


c gov cons(-1) time lm

:

@A@A:

4:>

@;+@H#A.A

:

+'>

Output from TSLS

1;3@A;3@36-A

;3@@>#AA;3@36-@>#AA=

'

t>p>

>

##14

K6+@#$$%

2))H

2)*A6M@#$*9

77#H779A

' >

4 >

@#7#7A

>

Dependent Variable: LOG(CS)Method: Two-Stage Least SquaresDate: 10/15/97 Time: 11:32Sample(adjusted): 1947:2 1995:1Included observations: 192 after adjusting endpointsInstrument list: C LOG(CS(-1)) LOG(GDP(-1))


C -1.209268 0.039151 -30.88699 0.0000LOG(GDP) 1.094339 0.004924 222.2597 0.0000

R-squared 0.996168 Mean dependent var 7.480286Adjusted R-squared 0.996148 S.D. dependent var 0.462990S.E. of regression 0.028735 Sum squared resid 0.156888F-statistic 49399.36 Durbin-Watson stat 0.102639Prob(F-statistic) 0.000000

ut yt xtbTSLS=

s2

ut2

T k( )t=


:

>

(4

:

:

Weighted TSLS

G

2$, *,

(>:

:>

'

@#7#2A

@#7#9A

TSLS with AR errors

G


>

First-order AR errors

=

@#7#)A

.

.:4@#$%8A

,>

.

@#7#&A

':4@#$*9A"

>>

Dependent Variable: LOG(CS)Method: Two-Stage Least SquaresDate: 10/15/97 Time: 11:42Sample(adjusted): 1947:2 1995:1Included observations: 192 after adjusting endpointsConvergence achieved after 4 iterationsInstrument list: C LOG(CS(-1)) LOG(GDP(-1))


C -1.420705 0.203266 -6.989390 0.0000LOG(GDP) 1.119858 0.025116 44.58782 0.0000

AR(1) 0.930900 0.022267 41.80595 0.0000

R-squared 0.999611 Mean dependent var 7.480286Adjusted R-squared 0.999607 S.D. dependent var 0.462990S.E. of regression 0.009175 Sum squared resid 0.015909F-statistic 243139.7 Durbin-Watson stat 1.931027Prob(F-statistic) 0.000000

Inverted AR Roots .93

yt xt wt ut+ +=

ut 1ut 1 t+=

xt wtzt

wt

yt 1 xt 1 wt 1, ,( )

wt zt yt 1 xt 1 wt 1, , , ,( )


Higher Order AR errors

"0@#A 4

"0@9A

@#7#%A

."0#9

@#7#*A

(

@4@#$*97#9A

6M@#$$2

777>779AA.

"0>

.>'

J

>

Examples

>:>

>G>:

cons c gdp ar(1)

c gov log(m1) time cons(-1) gdp(-1)

+@;+@H#A36-@H#AA

cons c cons(-1) gdp ar(1)

"

c gov log(m1) time cons(-1) cons(-2) gdp(-1)

5>>

wt zt yt 4 xt 4 wt 4, , , ,( )

wt zt yt 1 y, , t 4 xt 1 x, , t 4 wt 1 w, , t 4, , , ,( )


cons c gdp ar(1) ar(2) ar(3) ar(4)

.DE

c gov log(m1) time cons(-1) cons(-2) cons(-3) cons(-4) gdp(-1)

gdp(-2) gdp(-3) gdp(-4)

"@A

c gov log(m1) time

3;'

;3@#A.;+J36-

TSLS with MA errors

G>:"

"

>

Illustration

>:

>G>:

cons c gdp ma(1)

c gov log(m1) time

.;+36->

Technical Details

"0'>

@,

A

:

"

"

G


Nonlinear Least Squares

@#7#$A

:?:=

@#778A

(

J

4

@#77#A

:

.:

@#777A

:?>>:

(::

+:?>>:

(

>=

@#772A

@

GXA

@#779A

4

-,0@#$$#

72#>79)A6M@#$$2A

Estimating NLS Models in EViews

.'

:'

::

yt f xt ,( ) t+=

f xt

S ( ) yt f xt ,( )( )2

t y f X ,( )( ) y f X ,( )( )= =

f

yt 1 2 Ltlog 3 Ktlog t+ + +=

yt 1Lt2Kt

3 t+=

G ( )( ) y f X ,( )( ) 0=

G ( ) f X ,( )

NLLS s2G bNLLS( )G bNLLS( )( )

1=

bNLLS

Nonlinear Least Squares261

3:

: ,(',

""

Specifying Nonlinear Least Squares

4:

' G

@@#A@7A@29A@*%AA>

4

y = c(1) + c(2)*(k^c(3)+l^c(4))

>

/"++' ''

G

4 4>

y = cf(11) + cf(12)*(k^cf(13)+l^cf(14))

4

G=

y = c(11) + c(12)*(k^cf(1)+l^cf(2))

4

.'4

y = (c(1)*x + c(2)*z + 4)^2

'?

@#77)A

.:

4

(c(1)*x + c(2)*z + 4)^2

yt c 1( )xt c 2( )zt 4+ +( )2

t+=

S c 1( ) c 2( ),( ) yt c 1( )xt c 2( )zt 4+ +( )2( )

2

t=


' '?

@#77&A

(':

:

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