Springer Texts in Business and Economics

The backup regressions are given below: These are performed using SAS

OLS REGRESSION OF LNC ON CONSTANT, LNP, AND LNY Dependent Variable: LNC

Analysis of Variance

Sum of

Mean

Source

DF

Squares

Square

F Value

Prob>F

Model

2

0.50098

0.25049

9.378

0.0004

Error

43

1.14854

0.02671

C Total

45

1.64953

RootMSE 0.16343 R-square 0.3037

DepMean 4.84784 Adj R-sq 0.2713

C. V. 3.37125

Parameter Estimates

Variable

DF

Parameter

Estimate

Standard

Error

T for H0: Parameter=0

Prob>|T|

INTERCEP

1

4.299662

0.90892571

4.730

0.0001

LNP

1

-1.338335

0.32460147

-4.123

0.0002

LNY

1

0.172386

0.19675440

0.876

0.3858

RESIDUAL

PLOT OF RESIDUAL VS. LNY

LNY

b. Regression for Glejser Test (1969)

Dependent Variable: ABS_E MODEL: Z1=LNYA(—1/

Analysis of Variance

Sum of

Mean

Source

DF

Squares

Square

F Value

Prob>F

Model

1

0.04501

0.04501

5.300

0.0261

Error

44

0.37364

0.00849

C Total

45

0.41865

Root MSE

0.09215

R-square

0.1075

Dep Mean

0.12597

Adj R-sq

0.0872

C. V.

73.15601

Parameter Estimates

Variable DF

Parameter

Estimate

Standard

Error

T for H0: Parameter=0

Prob>F

INTERCEP 1 Z1(LNYA - 1) 1

-0.948925

5.128691

0.46709261

2.22772532

-2.032

2.302

0.0483

0.0261

MODEL: Z2=LNYA(-0.5/ Dependent Variable: ABS_E

Analysis of Variance

Source DF

Sum of Squares

Mean

Square

F Value

Prob>F

Model 1 Error 44 C Total 45

0.04447

0.37418

0.41865

0.04447

0.00850

5.229

0.0271

Root MSE Dep Mean C. V.

0.09222

0.12597

73.20853

R-square Adj R-sq

0.1062

0.0859

Parameter Estimates

Variable DF

Parameter

Estimate

Standard

Error

T for H0: Parameter=0

Prob>|T|

INTERCEP 1 Z2 (LNYA - .5) 1

-2.004483

4.654129

0.93172690

2.03521298

-2.151

2.287

0.0370

0.0271

MODEL: Z3=LNYA(0.5)

Dependent Variable: ABS_E

Analysis

of Variance

Source DF

Sum of Squares

Mean

Square

F Value

Prob>F

Model 1 Error 44 C Total 45

0.04339

0.37526

0.41865

0.04339

0.00853

5.087

0.0291

Root MSE Dep Mean C. V.

0.09235

0.12597

73.31455

R-square Adj R-sq

0.1036

0.0833

Variable

DF

Parameter

Estimate

Standard

Error

T for H0: Parameter=0

Prob>|T|

INTERCEP

1

2.217240

0.92729847

2.391

0.0211

Z3 (LNYA 5)

1

-0.957085

0.42433823

-2.255

0.0291

MODEL: Z4=LNYA1 Dependent Variable: ABS_E

Analysis of Variance

Sum of

Mean

Source

DF

Squares

Square

F Value

Prob>F

Model

1

0.04284

0.04284

5.016

0.0302

Error

44

0.37581

0.00854

C Total

45

0.41865

Root MSE

0.09242

R-square

0.1023

Dep Mean

0.12597

Adj R-sq

0.0819

C. V.

73.36798

Parameter Estimates

Parameter

Standard

T for H0:

Variable

DF

Estimate

Error

Parameter=0

1—

A

_Q

о

CL

INTERCEP

1

1.161694

0.46266689

2.511

0.0158

Z4 (LNYA1)

1

-0.216886

0.09684233

-2.240

0.0302

c. Regression for Goldfeld and Quandt Test (1965) with first 17 obervations

Dependent Variable: LNC

Analysis of Variance

Sum of

Mean

Source

DF

Squares

Square

F Value

Prob>F

Model

2

0.22975

0.11488

2.354

0.1315

Error

14

0.68330

0.04881

C Total

16

0.91305

Root MSE

0.22092

R-square

0.2516

Dep Mean

4.85806

Adj R-sq

0.1447

C. V.

4.54756

Parameter Estimates

Parameter

Standard

T for H0:

Variable

DF

Estimate

Error

Parameter=0

Prob>|T|

INTERCEP

1

3.983911

4.51225092

0.883

0.3922

LNP

1

-1.817254

0.86970957

-2.089

0.0554

LNY

1

0.248409

0.96827122

0.257

0.8013

REGRESSION FOR GOLDFELD AND

QUANDT TEST (1965) w/last 17obs

Dependent Variable: LNC

Analysis ofVariance

Sum of

Mean

Source

DF

Squares

Square

F Value

Prob>F

Model

2

0.17042

0.08521

5.482

0.0174

Error

14

0.21760

0.01554

C Total

16

0.38803

Root MSE

0.12467

R-square

0.4392

Dep Mean

4.78796

Adj R-sq

0.3591

C. V.

2.60387

Parameter Estimates

Parameter

Standard

T for H0:

Variable

DF

Estimate

Error

Parameter=0

Prob>|T|

INTERCEP

1

6.912881

1.57090447

4.401

0.0006

LNP

1

-1.248584

0.39773565

-3.139

0.0072

LNY

1

-0.363625

0.31771223

-1.145

0.2716

. Data for Spearman Rank Correlation Test

OBS

STATE

LNC

RANKY

ABS_E RANKE

D

1

MS

4.93990

1

0.04196

11

10

2

UT

4.40859

2

0.41867

46

44

3

WV

4.82454

3

0.10198

21

18

4

NM

4.58107

4

0.28820

44

40

5

AR

5.10709

5

0.32868

45

40

6

LA

4.98602

6

0.21014

38

32

7

SC

5.07801

7

0.08730

19

12

8

OK

4.72720

8

0.10845

22

14

9

AL

4.96213

9

0.13671

30

21

10

ID

4.74902

10

0.11628

24

14

11

KY

5.37906

11

0.23428

40

29

12

SD

4.81545

12

0.11470

23

11

13

AZ

4.66312

13

0.22128

39

26

14

ND

4.58237

14

0.28253

43

29

15

MT

4.73313

15

0.17266

34

19

16

WY

5.00087

16

0.02320

5

-11

17

TN

5.04939

17

0.14323

31

14

18

IN

5.11129

18

0.11673

25

7

19

GA

4.97974

19

0.03583

10

-9

20

TX

4.65398

20

0.08446

18

-2

21

IA

4.80857

21

0.01372

3

-18

22

ME

4.98722

22

0.25740

41

19

23

WI

4.83026

23

0.01754

4

-19

24

OH

4.97952

24

0.03201

9

-15

25

VT

5.08799

25

0.20619

36

11

26

MO

5.06430

26

0.05716

15

-11

27

KS

4.79263

27

0.04417

12

-15

28

NE

4.77558

28

0.09793

20

-8

29

MI

4.94744

29

0.12797

28

-1

30

FL

4.80081

30

0.05625

14

-16

31

MN

4.69589

31

0.02570

8

-23

32

PA

4.80363

32

0.02462

6

-26

33

NV

4.96642

33

0.26506

42

9

34

RI

4.84693

34

0.11760

26

-8

35

VA

4.93065

35

0.04776

13

-22

36

WA

4.66134

36

0.00638

2

-34

37

DE

5.04705

37

0.20120

35

-2

38

CA

4.50449

38

0.14953

32

-6

39

IL

4.81445

39

0.00142

1

-38

40

MD

4.77751

40

0.20664

37

-3

41

NY

4.66496

41

0.02545

7

-34

42

MA

4.73877

42

0.12018

27

-15

43

NH

5.10990

43

0.15991

33

-10

44

DC

4.65637

44

0.12810

29

-15

45

CT

4.66983

45

0.07783

17

-28

46

NJ

4.70633

46

0.05940

16

-30

SPEARMAN RANK CORRELATION TEST

OBS R T

e. Harvey’s Multiplicative Heteroskedasticity Test (1976)

Dependent Variable: LNE_SQ

Analysis of Variance

Sum of

Mean

Source

DF

Squares

Square

F Value

Prob>F

Model

1

14.36012

14.36012

2.992

0.0907

Error

44

211.14516

4.79875

C Total

45

225.50528

Root MSE

2.19061

R-square

0.0637

Dep Mean

-4.97462

Adj R-sq

0.0424

C. V.

-44.03568

Parameter Estimates

Parameter

Standard

T for H0:

Variable

DF

Estimate

Error

Parameter=0

Prob>|T|

INTERCEP

1

24.852752

17.24551850

1.441

0.1566

LLNY

1

-19.082690

11.03125044

-1.730

0.0907

Variable

N

Mean

Std Dev

Minimum

Maximum

HV. TEMP

46

25.0589810 22.8713299

2.4583422

113.8840204

LNE_SQ

46

-4.9746160

2.2385773 -13.1180671

-1.7413218

HARVEY’S MULTIPLICATIVE HETEROSKEDASTICITY TEST (1976)

OBS HV. TEST

1 2.90997

f. Regression for Breusch and Pagan Test (1979)

Dependent Variable: X2

Analysis of Variance

Sum of

Mean

Source

DF

Squares

Square

F Value

Prob>F

Model

1

10.97070

10.97070

6.412

0.0150

Error

44

75.28273

1.71097

C Total

45

86.25344

RootMSE 1.30804 R-square 0.1272

DepMean 1.00001 Adj R-sq 0.1074

C. V. 130.80220

Parameter Estimates

Variable

DF

Parameter

Estimate

Standard

Error

T for H0: Parameter=0

Prob>|T|

INTERCEP

1

17.574476

6.54835118

2.684

0.0102

LNY

1

-3.470761

1.37065694

-2.532

0.0150

BREUSCH & PAGAN TEST (1979)

OBS RSSBP

1 5.48535

g. Regression for White Test (1979)

Dependent Variable: E_SQ

Analysis of Variance

Sum of

Mean

Source

DF

Squares

Square

F Value

Prob>F

Model

5

0.01830

0.00366

4.128

0.0041

Error

40

0.03547

0.00089

C Total

45

0.05377

Root MSE 0.02978 R-square

0.3404

Dep Mean 0.02497 Adj R-sq

0.2579

C. V.

119.26315

Parameter Estimates

Parameter

Standard

T for H0:

Variable

DF

Estimate

Error Parameter=0

Prob>|T|

INTERCEP

1

18.221989

5.37406002

3.391

0.0016

LNP

1

9.506059

3.30257013

2.878

0.0064

LNY

1

-7.893179

2.32938645

-3.389

0.0016

LNP. SQ

1

1.281141

0.65620773

1.952

0.0579

LNPY

1

-2.078635

0.72752332

-2.857

0.0068

LNY. SQ

1

0.855726

0.25304827

3.382

0.0016

Normality Test (Jarque-Bera) This chart was done with EViews.

Series:RESID

Sample 1 46

Observations 4 6

Mean

-9.95E-16

Median

0.007568

Maximum

0.328677

Minimum

-0.418675

Std. Dev.

0.159760

Skewness

-0.181935

Kurtosis

2.812520

Jarque-Bera

0.321137

Probability

0.851659

SAS PROGRAM Data CIGAR;

Input OBS STATE $ LNC LNP LNY; CARDS;

Proc reg data=CIGAR;

Model LNC=LNP LNY;

Output OUT=OUT 1 R=RESID;

Proc Plot data=OUT1 hpercent=85 vpercent=60;

Plot RESID*LNY=‘*’; run;

***** GLEJSER’S TEST (1969) *****;

*****************************************,

Data GLEJSER; set OUT1;
ABS_E=ABS(RESID);

Z1=LNY**-1;

Z2=LNY**-.5;

Z3=LNY**.5;

Z4=LNY;

Proc reg data=GLEJSER;

Model ABS_E=Z1;

Model ABS_E=Z2;

Model ABS_E=Z3;

Model ABS_E=Z4;

TITLE ‘REGRESSION FOR GLEJSER TEST (1969)’; LABEL Z1=‘LNY“(-1)’

Z2=‘LNY“(-0.5)’

Z3=‘LNY“(0.5)’

Z4=‘LNY“(1)’;

run;

***** GOLDFELD & QUANDT TEST (1965) *****; *******************************************************.

Proc sort data=CIGAR out=GOLDFELD;

By LNY;

Data GQTEST1; set GOLDFELD;

If_N_<18; OBS=_N_;

Data GQTEST2; set GOLDFELD;

If _N_>29; OBS=_N_-29;

Proc reg data=GQTEST1;

Model LNC=LNP LNY;

Output out=GQ_OUT1 R=GQ_RES1;

TITLE ‘REGRESSION FOR GOLDFELD AND QUANDT TEST (1965) w/ first 17 obs’;

Proc reg data=GQTEST2;

Model LNC=LNP LNY;

Output out=GQ_OUT2 R=GQ_RES2;

TITLE ‘REGRESSION FOR GOLDFELD AND QUANDT TEST (1965) w/last 17 obs’;

run;

***** SPEARMAN’S RANK CORRELATION TEST *****; ***************************************************************.

Data SPEARMN1; set GOLDFELD;

RANKY=_N_;

Proc sort data=GLEJSER out=OUT2;

By ABS_E;

DataTEMP1; setOUT2;

RANKE=_N_;

Proc sort data=TEMP1 out=SPEARMN2;

By LNY;

Data SPEARMAN;

Merge SPEARMN1 SPEARMN2;

By LNY;

D=RANKE-RANKY;

* Difference b/w Ranking of —RES— and Ranking of LNY; D_SQ=D**2;

Proc means data=SPEARMAN NOPRINT;

Var D_SQ;

Output out=OUT3 SUM=SUM_DSQ;

Data SPTEST; Set OUT3;

R=1-((6*SUM_DSQ)/(46**3-46));

T=SQRT (R**2*(46-2)/(1-R**2));

Proc print data=SPEARMAN;

Var STATE LNC RANKY ABS_E RANKE D;

TITLE ‘DATA FOR SPEARMAN RANK CORRELATION TEST’;

Proc print data=SPTEST;

Var R T;

TITLE ‘SPEARMAN RANK CORRELATION TEST’; run;

‘HARVEY’S MULTIPLICATIVE HETEROSKEDASTICITY TEST (1976) **;

A**********************************************************************************.

Data HARVEY; setOUTI;

E_SQ=RESID‘‘2;

LNE_SQ=LOG(E_SQ);

LLNY=LOG(LNY);

Proc reg data=HARVEY;

Model LNE_SQ=LLNY;

Output out=OUT4 R=RLNESQ;

TITLE ‘HARVEY’ ‘S MULTIPLICATIVE HETEROSKEDASTICITY TEST (1976)’;

Data HARVEY1; set OUT4;

HV_TEMP=LNE_SQ‘‘2-RLNESQ‘‘2;

Proc means data=HARVEY1;

Var HV_TEMP LNE. SQ;

Output out=HARVEY2 SUM=SUMTMP SUMLNESQ;

Data HARVEY3; set HARVEY2;

HV_TEST=(SUMTMP-46* (SUMLNESQ/46)‘‘2)/4.9348;

Proc print data=HARVEY3;

Var HV_TEST;

TITLE ‘HARVEY’ ‘S MULTIPLICATIVE HETEROSKEDASTICITY TEST (1976)’;

***** BREUSCH & PAGAN TEST (1979) *****; ***************************************************,

Proc means data=HARVEY;

Var E_SQ;

Output out=OUT5 MEAN=S2HAT;

TITLE ‘BREUSCH & PAGAN TEST (1979)’;

Proc print data=OUT5;

Var S2HAT;

Data BPTEST; set HARVEY;

X2=E_SQ/0.024968;

Proc reg data=BPTEST;

Model X2=LNY;

Output out=OUT6 R=BP_RES;

TITLE ‘REGRESSION FOR BREUSCH & PAGAN TEST (1979)’;

Data BPTEST1; set OUT6;

BP_TMP=X2**2-BP_RES**2;

Proc means data=BPTEST1;

Var BP_TMP X2;

Output out=OUT7 SUM=SUMBPTMP SUMX2;

Data BPTEST2; set OUT7;

RSSBP=(SUMBPTMP-SUMX2**2/46)/2;

Proc print data=BPTEST2;

Var RSSBP;

***** WHITE’S TEST (1980) *****;

*************************************.

Data WHITE; set HARVEY;

LNP_SQ=LNP**2;

LNY_SQ=LNY**2;

LNPY=LNP*LNY;

Proc reg data=WHITE;

Model E_SQ=LNP LNY LNP. SQ LNPY LNY_SQ; TITLE ‘REGRESSION FOR WHITE TEST (1979)’; run;

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