Econometric Analysis of Panel Data, 5th Edition , Badi H. Baltagi , Solution Manual.pdf

For exam and test prep, contact excellentessaywriters@gmail.com Type:

Solution Manual

Resource:

Econometric Analysis of Panel Data

Edition:

5th Edition

Author(s):

Badi H. Baltagi

1

Chapter 2 The One-way Error Component Regression Model 2.2

2.5

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

2

2.7

2.10

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

3

2.11

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

4

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

5

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

6

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

7

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

8

/* SAS Output for Grunfield Data

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

9

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

10

The following output was produced using EViews 5.0. This should replicate Table 2.1 and differs from the above SAS output in that degrees of freedom adjustments are made when estimating the variance components.

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

11

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

12

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

13

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

14

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

15

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

16

2.12

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

17

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

18

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

19

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

20

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

21

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

22

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

23

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

24

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

25

2.14

2.15

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

26

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

27

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

28

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

29

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

30

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

31

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

32

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

33

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

34

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

1

Chapter 3 The Two-way Error Component Regression Model 3.2

Q, defined in (3.3), is idempotent and is its own generalized-inverse. Therefore, the same proof holds for the two-way fixed effects model as for the one-way fixed effects model given in problem 2.2 with this new Q.

3.4

3.7

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

2

3.8

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

3

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

4

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

5

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

6

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

7

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

8

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

9

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

10

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

11

3.9

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

12

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

13

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

14

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

15

3.10

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

16

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

17

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

18

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

19

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

20

3.13

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

1

Chapter 4 Test of Hypotheses with Panel Data

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

2

4.9

This solution gives the SAS program to replicate Table 4.1 using Grunfeld data.

DATA GRABIN; INFILE ‘A:\GRUNFELD.FIL’; INPUT FIRM YEAR INVEST FIRMV CAPITALV; DATA TOUSE; SET GRABIN; PROC SORT DATA=TOUSE;

BY FIRM YEAR; DATA INDEX; SET TOUSE; KEEP FIRM YEAR; ****************************************; * OLS FOR INDIVIDUAL FIRMS; ****************************************; * PROC REG DATA=TOUSE ; * MODEL INVEST=FIRMV CAPITALV; *

BY FIRM; * TITLE 'OLS FOR INDIVIDUAL'; ****************************************; * FOR OLS OF THE POOLING MODEL; ****************************************; * PROC REG DATA=TOUSE ;

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

3 * MODEL INVEST=FIRMV CAPITALV; * TITLE 'OLS FOR POOLING MODEL'; *********************************************; * IML MATRIX TRANSFORMATION FOR THETA; *********************************************; PROC IML; RESET AUTONAME; START MAIN; ********************************************; * INPUT DATA AND GENERATE P & Q; ********************************************; USE TOUSE VAR{INVEST}; READ ALL INTO Y; USE TOUSE VAR{FIRMV CAPITALV}; READ ALL INTO XRAW; N =10 ; T =20 ; K =NCOL(XRAW); EN=I(N)-J(N,N,1)/N; ET=I(T)-J(T,T,1)/T; DN=I(N)@J(T,T,1) ; DT=J(N,N,1)@I(T) ; P1=I(N)@ET; P2=EN@I(T); Q1=EN@ET; Q2=EN@(J(T,T,1)/T); Q3=(J(N,N,1)/N)@ET; PQ2=I(N)@ET; PQ3=EN@I(T); JNTBAR=J(N*T,N*T,1)/(N*T); ENT=I(N*T)-JNTBAR; X=J(N*T,1,1)||XRAW; YIBAR=(I(N)@(J(T,T,1)/T))*Y; YTBAR=((J(N,N,1)/N)@I(T))*Y; YITBAR=JNTBAR*Y; XIBAR=(I(N)@(J(T,T,1)/T))*X; XTBAR=((J(N,N,1)/N)@I(T))*X; XITBAR=JNTBAR*X; FP=INV(X`*X); BOLS=FP*X`*Y; ROLS=Y-X*BOLS; DF=N*T-K-1; MSE=ROLS`*ROLS/DF; VARBOLS=MSE*VECDIAG(FP); SDBOLS =SQRT(VARBOLS); TBOLS =BOLS/SDBOLS; LOOK1=BOLS||SDBOLS||TBOLS; CTITLE={'PARAMETER' 'STANDARD ERROR' 'T-STATISTICS'}; RTITLE={'INTERCEPT' 'FIRMV' 'CAPITALV'}; PRINT 'RESULTS OF OLS',, LOOK1 (|COLNAME=CTITLE ROWNAME=RTITLE FORMAT=8.5|); LROLS=-(N*T/2)*LOG(ROLS`*ENT*ROLS); ***Test for Individual or Time Effects***; ***BREUSCH-PAGAN TEST (Section 4.2.1.)***; LM1=N*T/(2*(T-1))* (1-(ROLS`*DN*ROLS)/(ROLS`*ROLS))**2; /* equation (4.23) */ LM2=N*T/(2*(N-1))* (1-(ROLS`*DT*ROLS)/(ROLS`*ROLS))**2; /* equation (4.24) */ LM =LM1+LM2;

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

4 PRINT 'BREUSCH-PAGAN TEST',, LM1 LM2 LM; **HONDA TEST AND KING-WU TEST (Section 4.2.2)**; A =SQRT(N*T/(2*(T-1)))* ((ROLS`*DN*ROLS)/(ROLS`*ROLS)-1); /* equation (4.25) */ B =SQRT(N*T/(2*(N-1)))* ((ROLS`*DT*ROLS)/(ROLS`*ROLS)-1); /* equation (4.29) */ C =(A+B)/SQRT(2); KW =SQRT((T-1)/(N+T-2))*A +SQRT((N-1)/(N+T-2))*B; /* equation (4.30) */ PRINT 'HONDA TEST',, A B C ; PRINT 'KING-WU TEST',, A B KW; **STANDARD LAGRANGE MULTIPLIER TEST (Section 4.2.2.)**; P = N*T-(K+1); PXBAR=I(N*T)-X*INV(X`*X)*X`; DA= ROLS`*DN*ROLS/(ROLS`*ROLS); EDA=TRACE(DN*PXBAR)/P; /* equation (4.27) */ VARDA=2*(TRACE(DN*PXBAR*DN*PXBAR)/P-EDA**2)/(P+2); /* equation (4.28) */ DB= ROLS`*DT*ROLS/(ROLS`*ROLS); EDB=TRACE(DT*PXBAR)/P; VARDB=2*(TRACE(DT*PXBAR*DT*PXBAR)/P-EDB**2)/(P+2); SLMA= (DA-EDA)/SQRT(VARDA);

/* equation (4.26) */

SLMB= (DB-EDB)/SQRT(VARDB); PRINT 'STANDARD LAGRANGE MULTIPLIER TEST',, SLMA SLMB; ***GHM TEST (Section 4.2.3.)***; GHM1 = LM1; IF A < 0 THEN GHM1 = 0; GHM2 = LM2; IF B < 0 THEN GHM2 = 0; GHM = GHM1 +GHM2;

/* equation (4.33) */

PRINT 'GHM TEST',, GHM; ***ANOVA F-tests (Section 4.2.4)***; FP=INV(XRAW`*Q1*XRAW); BWITHIN=FP*XRAW`*Q1*Y; RWITHIN=Y-XRAW*BWITHIN; DFW=(N-1)*(T-1)-K; MSEW=RWITHIN`*Q1*RWITHIN/DFW; VARBWI=MSEW*VECDIAG(FP); SDBWI =SQRT(VARBWI); TBWI =BWITHIN/SDBWI; LOOK1=BWITHIN||SDBWI||TBWI; RTITLEW={ 'FIRMV' 'CAPITALV'}; PRINT 'RESULTS OF WITHIN ESTIMATION',, LOOK1 (|COLNAME=CTITLE ROWNAME=RTITLEW FORMAT=8.5|); FP=INV(XRAW`*PQ2*XRAW); BNWITHIN=FP*XRAW`*PQ2*Y; RNWITHIN=Y-XRAW*BNWITHIN; DFNW= N*(T-1)-K; MSENW=RNWITHIN`*PQ2*RNWITHIN/DFNW; VARBNW=MSENW*VECDIAG(FP);

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

5 COVBNW=MSENW*FP; PRINT 'WITHIN ESTIMATES ACROSS FIRMS',, BNWITHIN, COVBNW; FP=INV(XRAW`*Q2*XRAW); BNBETW=FP*XRAW`*Q2*Y; RNBETW=Y-XRAW*BNBETW; DFNB= N-1-K; MSENB=RNBETW`*Q2*RNBETW/DFNB; VARBNB=MSENB*VECDIAG(FP); COVBNB=MSENB*FP; PRINT 'BETWEEN ESTIMATES ACROSS FIRMS',, BNBETW, COVBNB; FP=INV(XRAW`*PQ3*XRAW); BTWITHIN=FP*XRAW`*PQ3*Y; RTWITHIN=Y-XRAW*BTWITHIN; DFTW=(N-1)*T-K; MSETW=RTWITHIN`*PQ3*RTWITHIN/DFTW; *************************************; * F-TEST; *************************************; FN =((MSE*DF-MSENW*DFNW)/(DF-DFNW))/MSENW; /* equation (4.38) */ FT =((MSE*DF-MSETW*DFTW)/(DF-DFTW))/MSETW; FNT=((MSE*DF-MSEW*DFW)/(DF-DFW))/MSEW; PRINT 'ANOVA F-TEST',, FN FT FNT; ************************************; * LR-TEST (Section 4.2.4.); ************************************; BETAB=BNBETW; BETAW=BNWITHIN; PHIB=1000000; PHIW=0; DO WHILE (PHIB-PHIW>0.001); DB =Y-XRAW*BETAB; ***BETWEEN RESIDUALS ACROSS FIRM ***; DW =Y-XRAW*BETAW; ***WITHIN RESIDUALS ACROSS FIRM ***; PHIB=(DB`*PQ2*DB)/((T-1)*(DB`*Q2*DB)); PHIW=(DW`*PQ2*DW)/((T-1)*(DW`*Q2*DW)); BETAB=INV(XRAW`*(PQ2+PHIB*Q2)*XRAW)*XRAW`*(PQ2+PHIB*Q2)*Y; BETAW=INV(XRAW`*(PQ2+PHIW*Q2)*XRAW)*XRAW`*(PQ2+PHIW*Q2)*Y; END; LRUNRES=-(N*T/2)*LOG(DW`*(PQ2+PHIW*Q2)*DW)+N/2*LOG(PHIW); LRTEST=-2*(LROLS-LRUNRES); /* equation (4.39) */ PRINT 'LR-TEST ',, LRTEST; ****************************************************; * HAUSMAN TEST (Section 4.3);problem 4.15 ****************************************************; DIFFM3=BNWITHIN-BNBETW; /* equation (4.46) */ VARM3=COVBNW+COVBNB; /* equation (4.48) */ M3=DIFFM3`*INV(VARM3)*DIFFM3; **************************************************; ** CALCULATE THETA USING SWAR APPROACH; **************************************************; THETA

=1-SQRT(MSENW/MSENB);

PRINT 'THETA OF SWAR',, THETA; ********************************************; ** TRANSFORM Y, X INTO YSTAR, XSTAR ; ** FOR SWAR GLS; ********************************************; YSTAR=Y-THETA#YIBAR; XSTAR=X-THETA#XIBAR; FP=INV(XSTAR`*XSTAR);

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

6 BGLS=FP*XSTAR`*YSTAR; RGLS=YSTAR-XSTAR*BGLS; DF=N*T-K-1; MSE=RGLS`*RGLS/DF; COVBGLS=MSE*FP; Q1=BGLS(|2:K+1,|)-BNWITHIN; VARM1=COVBNW-COVBGLS(|2:K+1,2:K+1|); M1=Q1`*INV(VARM1)*Q1;

/* equation (4.41) */

Q2=BGLS(|2:K+1,|)-BNBETW; VARM2=COVBNB-COVBGLS(|2:K+1,2:K+1|); M2=Q2`*INV(VARM2)*Q2; *******************************; * AUGMENTED HAUSMAN TEST; *******************************; XTILDA=PQ2*XRAW; RHS=XSTAR||XTILDA;

/* equation (4.42) */

FP=INV(RHS`*RHS); BGLSH=FP*RHS`*YSTAR; RGLSH=YSTAR-RHS*BGLSH; DFH=N*T-2*K-1; MSEH=RGLSH`*RGLSH/DFH; FAUGHAUS=((MSE*DF-MSEH*DFH)/K)/MSEH; PRINT 'HAUSMAN TEST',, M1 M2 M3; PRINT 'AUGMENTED HAUSMAN TEST',, BGLSH FAUGHAUS; FINISH MAIN; RUN MAIN;

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

7 SAS Output for Grunfeld The SAS System RESULTS OF OLS LOOK1

PARAMETER STANDARD ERROR

T-STATISTICS

INTERCEPT FIRMV CAPITALV

-42.7144 0.11556 0.23068

9.51168 0.00584 0.02548

-4.49073 19.80259 9.05481

BREUSCH-PAGAN TEST LM1

COL1

LM2

ROW1 798.16155

COL1

LM

COL1

ROW1 6.4538816

ROW1 804.61543

B

C

HONDA TEST A

COL1

ROW1 28.251753

COL1

COL1

ROW1 -2.540449

ROW1 18.180637

B

KW

KING-WU TEST A

COL1

ROW1 28.251753

COL1

ROW1 -2.540449

COL1

ROW1 21.832209

STANDARD LAGRANGE MULTIPLIER TEST SLMA

COL1

SLMB

ROW1 32.666049

COL1

ROW1 -2.432565

GHM TEST GHM COL1 ROW1 798.16155 RESULTS OF WITHIN ESTIMATION LOOK1 FIRMV CAPITALV

PARAMETER STANDARD ERROR

T-STATISTICS

0.01375 0.02272

8.56035 15.75404

0.11772 0.35792

WITHIN ESTIMATES ACROSS FIRMS BNWITHIN ROW1 ROW2 COVBNW ROW1 ROW2

COL1 0.1101238 0.3100653 COL1

COL2

0.0001406 -0.000077 -0.000077 0.0003012

BETWEEN ESTIMATES ACROSS FIRMS

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

8 BNBETW

COL1

0.1346461 ROW1 0.0320315 ROW2 COL1 COVBNB ROW1 ROW2

COL2

0.0008263 -0.0037 -0.0037 0.0364572

ANOVA F-TEST FN

COL1

ROW1 49.176625

FT

COL1

ROW1 0.2345083

FNT

COL1

ROW1 17.403146

LR-TEST LRTEST COL1 ROW1 193.09078 THETA OF SWAR COL1 THETA ROW1 0.8612236 ********************Problem 4.15 ************************* HAUSMAN TEST M1

COL1

ROW1 2.3303669

M2

COL1

ROW1 2.1313791

M3

COL1

ROW1 2.1313662

AUGMENTED HAUSMAN TEST BGLSH

COL1

ROW1 -8.527114 ROW2 0.1346461 ROW3 0.0320315 ROW4 -0.024522 ROW5 0.2780339

FAUGHAUS ROW1

COL1 1.0656831

4.9 We also run xttest0 using Stata on Grunfeld’s data to test for zero random firm effects using the Breusch and Pagan Lagrangian multiplier test. . xttest0 Breusch and Pagan Lagrangian multiplier test for random effects: I[fn,t] = Xb + u[fn] + e[fn,t] Estimated results: Var sd = sqrt(Var) | ---------+----------------------------I | 47034.89 216.8753 e | 2784.458 52.76796 u | 7089.8 84.20095

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

9 Test:

Var(u) = 0

chi2(1) = Prob > chi2 =

798.16 0.0000

Using EViews one can also replicate the F-statistics in Table 4.1 as shown also in Table 4.3 in the text. This is done by invoking the two-way fixed effects estimation on the Grunfeld data and then running the test for redundant fixed effects. The time and firm effects are jointly significant. However, the time effects are not significant once the firm effects are included. The firm effects are significant having included the time effects.

Grunfeld’s Data. F-tests for Redundant Fixed Effects.

Redundant Fixed Effects Tests Equation: EQFE Test cross-section and period fixed effects Statist ic

Effects Test

Cross-section F Cross-section Chi-square

52.36 2355 266.3 9550 0

d.f.

(9,169 ) 9 (19,16

Period F

1.403 241 29.29

9)

Period Chi-square

7556

19 (28,16

Cross-Section/Period Cross-Section/Period F Chisquare

17.40 3146 271.3 4022 4

9)

Pro b.

0.0 00 0 0.0 00 0 0.1 30 9 0.0 61 4 0.0 00 0 0.0 00 0

28

Cross-section fixed effects test equation: Dependent Variable: I Method: Panel Least Squares Sample: 1935 1954 Cross-sections included: 10 Total panel (balanced) observations: 200

Variable

Co effi cie nt

Std. Error

tStatis tic

Pro b.

C

41.

10.44 985

3.925

0.0 00

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

10

F

K

02 25 0 0.1 16 79 8 0.2 19 70 7

653

1

18.44 767

0.0 00 0

6.802 881

0.0 00 0

Mean dependent var

145 .95 82

S.D. dependent var

216 .87 53

0.006 331 0.032 296

Effects Specification Period fixed (dummy variables)

R-squared Adjusted Rsquared S.E. of regression Sum squared resid

Log likelihood Durbin-Watson stat

0.8 16 98 9 0.7 95 39 8 98.

09 91 2 171 29 72.

11 89.

33 0 0.1 94 49 5

Akaike info criterion Schwarz criterion

F-statistic

Prob(F-statistic)

12.

11 33 0 12.

47 61 1 37.

83 90 3 0.0 00 00 0

Period fixed effects test equation: Dependent Variable: I Method: Panel Least Squares Sample: 1935 1954 Cross-sections included: 10 Total panel (balanced) observations: 200

Variable

Co effi cie

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

Std. Error

tStatis tic

Pro b.

11 nt

C

F

K

58.

74 39 4 0.1 10 12 4 0.3 10 06 5

4.716 990

0.0 00 0

9.287 901

0.0 00 0

17.86 656

0.0 00 0

Mean dependent var

145 .95 82

S.D. dependent var

216 .87 53

12.45 369 0.011 857 0.017 355

Effects Specification Cross-section fixed (dummy variables)

R-squared Adjusted Rsquared S.E. of regression Sum squared resid

Log likelihood Durbin-Watson stat

0.9 44 07 3 0.9 40 80 0 52.

76 79 7 523 47 8.1 10 70.

78 1 0.7 16 73 3

Akaike info criterion Schwarz criterion

F-statistic

Prob(F-statistic)

Cross-section and period fixed effects test equation: Dependent Variable: I Method: Panel Least Squares Sample: 1935 1954 Cross-sections included: 10 Total panel (balanced) observations: 200 © 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

10.

82 78 1 11.

02 57 1

288 .49 96 0.0 00 00 0

12

Variable

C

F

K

R-squared Adjusted Rsquared S.E. of regression Sum squared resid

Log likelihood Durbin-Watson stat

Co effi cie nt 42.

71 43 7 0.1 15 56 2 0.2 30 67 8 0.8 12 40 8 0.8 10 50 4 94.

40 84 0 175 58 50.

11 91.

80 2 0.2 19 59 9

Std. Error

tStatis tic

9.511 676

4.490 730

0.005 836

19.80 259

0.025 476

9.054 808

Pro b.

0.0 00 0 0.0 00 0 0.0 00 0

Mean dependent var

145 .95 82

S.D. dependent var

216 .87 53

Akaike info criterion Schwarz criterion

F-statistic

Prob(F-statistic)

11.

94 80 2 11.

99 75 0

426 .57 57 0.0 00 00 0

4.10 We also run xttest0 using Stata on the Gasoline data to test for zero random country effects using the Breusch and Pagan Lagrangian multiplier test. . xttest0 Breusch and Pagan Lagrangian multiplier test for random effects: © 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

13 c[coun,t] = Xb + u[coun] + e[coun,t] Estimated results: Var sd = sqrt(Var) | ---------+----------------------------c | .301299 .5489071 e | .0085249 .0923303 u | .0382377 .1955447 Var(u) = 0 Test: chi2(1) = 1465.55 Prob > chi2 = 0.0000

Using EViews one can also obtain the F-statistics for the Gasoline data. This is done by invoking the two-way fixed effects estimation on the Gasoline data and then running the test for redundant fixed effects. The time and country effects are jointly significant. Also, the time effects are significant once the country effects are included, and the country effects are significant having included the time effects.

Gasoline Data. F-tests for Redundant Fixed Effects.

Redundant Fixed Effects Tests Equation: EQ01 Test cross-section and period fixed effects

Statistic d.f.

Effects Test 113.35 1303 682.63 5958 6.2338 49 107.74 7064 55.955 615 687.42 9282

Cross-section F Cross-section Chi-square Period F Period Chi-square Cross-Section/Period F Cross-Section/Period Chi-

square

(17,303 ) 17 (18,303

Prob .

35

0.00 00 0.00 00 0.00 00 0.00 00 0.00 00 0.00 00

) 18 (35,303 )

Cross-section fixed effects test equation: Dependent Variable: GAS Method: Panel Least Squares Sample: 1960 1978 Periods included: 19 Cross-sections included: 18 Total panel (balanced) observations: 342

C

Coef ficie nt

Std. Error

tSt ati st i c

Prob .

2.44

0.1298

18.799

0.00

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

14

INC

PMG

063 7 0.89 989 6 -0.8 991 47 0.7 -642 40

22

80

00

0.0370 78

24.270 15

0.00 00

0.0311 87

0.00 00

39.824 20

0.00 00

0.0191 90

CAR

28.830 43

Effects Specification Period fixed (dummy variables)

R-squared Adjusted Rsquared

S.E. of regression Sum squared resid

Log likelihood F-statistic Prob(F-statistic)

0.85 695 4 0.84 756 7

Mean dependent var S.D. dependent var

0.21 430 8 14.6 969 2

4.29 624 2 0.54 890 7 0.1 -806 41

Akaike info criterion Schwarz criterion

52.8 895 5 91.2 881 0 0.00 000 0

Hannan-Quinn criter.

0.06 604 3 -0.0 823 69

Durbin-Watson stat

0.12 953 2

Std. Error

tStatisti c

Prob .

0.2253 09

10.663 87

0.00 00

0.0733 86 0.0440 99

9.0241 91 7.2949 -

0.00 00 0.00 00

Period fixed effects test equation: Dependent Variable: GAS Method: Panel Least Squares Sample: 1960 1978 Periods included: 19 Cross-sections included: 18 Total panel (balanced) observations: 342 Coef ficie nt

C INC PMG

2.40 267 0 0.66 225 0 0.3

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

15 217 02 -0.6 404 83 CAR

64 0.0296 79

21.580 45

0.00 00

Effects Specification Cross-section fixed (dummy variables)

squared

0.97 336 6 0.97 170 6

S.E. of regression

0.09 233 0

Sum squared resid

2.73 649 1

R-squared Adjusted R-

Log likelihood F-statistic Prob(F-statistic)

Mean dependent var S.D. dependent var

Akaike info criterion

4.29 624 2 0.54 890 7 1.8 -674 50 1.6 319 79 -1.7 736 45

Schwarz criterion -

340.

334 0 586.

555 6 0.00 000 0

Hannan-Quinn criter.

Durbin-Watson stat

0.32 657 8

Cross-section and period fixed effects test equation: Dependent Variable: GAS Method: Panel Least Squares Sample: 1960 1978 Periods included: 19 Cross-sections included: 18 Total panel (balanced) observations: 342 Coef ficie nt

C INC

PMG

2.39 132 6 0.88 996 2 0.8 -917 98 0.7 633 -73

Std. Error

tStatisti c

Prob .

0.1169 34

20.450 17

0.00 00

0.0358 06

24.855 23

0.00 00

0.0303 15

29.417 96

0.00 00

41.023 25

0.00 00

CAR

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

0.0186 08

16

Adjusted Rsquared

0.85 493 5 0.85 364 8

S.E. of regression

0.20 999 0

Akaike info criterion

Sum squared resid

14.9 043 6

Schwarz criterion

R-squared

Log likelihood F-statistic Prob(F-statistic)

50.4 928 9 663.

999 3 0.00 000 0

Mean dependent var S.D. dependent var

4.29 624 2 0.54 890 7 -0.2 718 88 0.2 270 37 0.2 540 21 -

Hannan-Quinn criter.

Durbin-Watson stat

0.13 746 1

4.11 We also run xttest0 using Stata on the public capital data to test for zero random state effects using the Breusch and Pagan Lagrangian multiplier test. . xttest0 Breusch and Pagan Lagrangian multiplier test for random effects: lny[stid,t] = Xb + u[stid] + e[stid,t] Estimated results: Var sd = sqrt(Var) | ---------+----------------------------lny | 1.04271 1.021132 e | .0014544 .0381371 u | .0068377 .0826905 Var(u) = 0 Test: chi2(1) = 4134.96 Prob > chi2 = 0.0000 _____________________________________________________________________________ __________________ Using EViews one can also obtain the F-statistics for the Public Capital data. This is done by invoking the two-way fixed effects estimation on the Public Capital data and then running the test for redundant fixed effects. The time and state effects are jointly significant. Also, the time effects are significant once the state effects are included, and the state effects are significant having included the time effects.

Public Capital Data. F-tests for Redundant Fixed Effects.

Redundant Fixed Effects Tests Equation: EQ01

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

17 Test cross-section and period fixed effects Statistic Effects Test

d.f.

93.801 842 1575.4 07574 12.319 268 190.85 9574 73.101 795 1605.9 58679

Cross-section F Cross-section Chi-square Period F Period Chi-square Cross-Section/Period F Cross-Section/Period Chi-

square

(47,748 )47 (16,748 )16 (63,748 ) 63

Prob .

0.00 00 0.00 00 0.00 00 0.00 00 0.00 00 0.00 00

Cross-section fixed effects test equation: Dependent Variable: LNY Method: Panel Least Squares Sample: 1970 1986 Periods included: 17 Cross-sections included: 48 Total panel (balanced) observations: 816 Coef ficie nt

C LNK1 LNK2 LNL

1.63 907 9 0.16 478 0 0.30 359 6 0.58 881 1 0.0 060 57

U

Std. Error

tStatisti c

Prob .

0.0573 37

28.586 83

0.00 00

0.0174 91

9.4207 15

0.00 00

0.0104 43

29.072 71

0.00 00

0.0137 76

42.742 87

0.00 00

0.0017 70

3.4219 44

0.00 07

Effects Specification Period fixed (dummy variables)

squared

0.99 286 6 0.99 268 6

S.E. of regression

0.08 732 8

R-squared Adjusted R-

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

Mean dependent var S.D. dependent var

Akaike info criterion

10.5 088 5 1.02 113 2 2.0 -128 87

18 Sum squared resid

Log likelihood F-statistic Prob(F-statistic)

6.06 284 7

Schwarz criterion

842.

258 0 5531 .87 4 0.00 000 0

1.8 918 18 -1.9 664 21

Hannan-Quinn criter.

Durbin-Watson stat

0.05 997 8

Std. Error

tStatisti c

Prob .

0.1748 13

13.459 38

0.00 00

Period fixed effects test equation: Dependent Variable: LNY Method: Panel Least Squares Sample: 1970 1986 Periods included: 17 Cross-sections included: 48 Total panel (balanced) observations: 816 Coef ficie nt

C

LNK1 LNK2 LNL

U

2.35 287 8 0.0 261 46 0.29 200 8 0.76 815 6 -0.0 052 98

0.0290 02

0.9015 45

0.36 76

0.0251 20

11.624 67

0.00 00

0.0300 92

25.527 08

0.00 00

0.0009 89

5.3582 96

0.00 00

Effects Specification Cross-section fixed (dummy variables)

R-squared Adjusted Rsquared

S.E. of regression Sum squared resid

0.99 869 2 0.99 860 5 0.03 813 7 1.11 118 8

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

Mean dependent var S.D. dependent var

Akaike info criterion Schwarz criterion

10.5 088 5 1.02 113 2 3.6 336 57 3.3 338 -

19 66 Log likelihood F-statistic Prob(F-statistic)

1534 .53 2 1144 1.6 5 0.00 000 0

Hannan-Quinn criter.

Durbin-Watson stat

3.5 185 98 0.41 353 2

Cross-section and period fixed effects test equation: Dependent Variable: LNY Method: Panel Least Squares Sample: 1970 1986 Periods included: 17 Cross-sections included: 48 Total panel (balanced) observations: 816 Coef ficie nt

C LNK1 LNK2 LNL

1.64 330 2 0.15 500 7 0.30 919 0 0.59 393 5 0.0 -067 33

U

squared

0.99 259 3 0.99 255 7

S.E. of regression

0.08 809 6

Sum squared resid

6.29 414 3

R-squared Adjusted R-

Log likelihood F-statistic Prob(F-statistic)

826.

982 4 2717 1.7 1 0.00

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

Std. Error

tStatisti c

Prob .

0.0575 87

28.535 88

0.00 00

0.0171 54

9.0363 11

0.00 00

0.0102 72

30.100 36

0.00 00

0.0137 47

43.203 29

0.00 00

0.0014 16

4.7536 82

Mean dependent var S.D. dependent var

Akaike info criterion

0.00 00 10.5 088 5 1.02 113 2 2.0 -146 63 1.9 858 37 -2.0 036 00

Schwarz criterion Hannan-Quinn criter.

Durbin-Watson stat

0.07 926 9

20 000 0

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

21

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

22

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

23

For problem 4.15, we run xthausman using Stata on Grunfeld’s data after estimating the model with xtreg, re . xthausman Hausman specification test ---- Coefficients ---| Fixed Random I | Effects Difference Effects -------------+----------------------------------------.0003427 F | .1101238 .1097811 .0019524 C | .3100653 .308113 Test: Ho: difference in coefficients not systematic chi2( 2) = (b-B)'[S^(-1)](b-B), S = (S_fe S_re)

= Prob>chi2 =

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

2.33 0.3119

24

For problem 4.16, we run xthausman using Stata on the Gasoline data after estimating the model with xtreg, re © 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

25 . xthausman Hausman specification test ---- Coefficients ---| Fixed Random c | Effects Difference Effects -------------+----------------------------------------.107264 y | .6622498 .5549858 .0986868 p | -.3217025 -.4203893 -.0336428 car | -.6404829 -.6068402 Test: Ho: difference in coefficients not systematic chi2( 3) = (b-B)'[S^(-1)](b-B), S = (S_fe S_re)

4.17

= Prob>chi2 =

306.09 0.0000

We run xthausman using Stata on the public capital data after estimating the model with xtreg, re

. xthausman Hausman specification test ---- Coefficients ---| Fixed Random lny | Effects Effects Difference -------------+----------------------------------------lnk1 | -.0261493 .0044388 -.0305881 .2920067 .3105483 -.0185416 lnk2 | .038489 lnl | .7681595 .7296705 u | -.0052977 -.0061725 .0008747 Test: Ho: difference in coefficients not systematic chi2( 4) = (b-B)'[S^(-1)](b-B), S = (S_fe - S_re) = 10.13 Prob>chi2 = 0.0383 ---------------------------------------------------------------------------------------------------------------------------

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

1

Chapter 5 Heteroskedasticity and Serial Correlation in the Error Component Model 5.1

5.3

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

2

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

3

5.4

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

4

5.6

5.8

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

5

5.10

5.12

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

6

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

7

5.17

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

8

5.19

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

9

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

10

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

11

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

12

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

13

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

14

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

15

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

1

Chapter 6 Seemingly Unrelated Regressions with Error Components 6.1

6.3

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/copllege/baltagi

2

6.5

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/copllege/baltagi

1

Chapter 7 Simultaneous Equations with Error Components 7.1

7.2

7.4

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

2

7.5

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

3

7.8

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

4

7.11

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

5

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

6

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

7

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

8

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

9

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

10

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

11

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

12

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

13

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

14

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

15

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

16

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

1

Chapter 8 Dynamic Panel Data Models 8.1

8.3

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

2

8.4

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

3

8.6

8.8

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

4

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

5

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

6

8.8

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

7

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

8

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

9

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

10

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

11

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

12

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

13

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

14

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

15

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

16

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

17

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

18

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

19

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

20

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

21

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

22

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

23

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

24

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

25

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

26

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

27

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

28

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

29

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

30

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

31

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

32

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

33

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

1

Chapter 9 Unbalanced Panel Data Models 9.1

9.2

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

2

9.4

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

3

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

4

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

5

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

6

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

7

9.8

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

8

9.11

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

9

9.12

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

1 Chapter 10 Special Topics

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

2

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

3

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

4

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

5

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

6

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

7

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

8

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

9

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

10

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

11

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

12

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

13

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

1 Chpater 11 Limited Dependent Variables and Panel Data

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

2

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

3

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

4

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

5

11.6

This replicates some of the results in Vella and Verbeek (1998)using Stata.

(a) This replicates parts of Table I of Vella and Verbeek (1998, p.168). . tsset nr year, yearly panel variable: nr, 13 to 12548 time variable: year, 1980 to 1987 xtsum educ exper union married black hisp poorhlth rur nrtheast nrthcen south > lwage Variable

|

Mean

Std. Dev.

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

Min

Max |

Observations

6 -----------------+--------------------------------------------+---------------4360 educ overall | 11.76697 1.746181 3 16 | N = 545 between | within | | 1.747585 3 16 | n = 8 0 11.76697 11.76697 | T = 4360 2.825873 0 | N = 545 1.654918 3.5 18 | n = exper overall | 6.514679 8 2.291551 3.014679 14.5 | T = between | 4360 .4295639 0 N = 10.01468 | within | 545 .3294467 0 n = | | 8 .2759787 -.6309633 T = 1 | union overall | .2440367 4360 .4963208 0 N = 1 | between | 545 .3766116 0 n = 1.119037 | within | 8 .3236137 -.4360092 T = | 4360 .3197769 0 N = | 1 | 545 .320034 0 n = married overall | .4389908 1 | 8 0 .1155963 T = between | 4360 .3628622 0 N = 1.313991 | within | 545 .3631539 0 n = | | 8 0 .1559633 T = 1 | 4360 .129183 0 N = black overall | .1155963 1 | 545 .062947 0 n = between | .1155963 | 8 .1128374 -.7330275 T = within | 4360 .402941 0 N = | 545 .3588299 0 n = | 1 | 8 .1838732 -.6711009 T = hisp overall | .1559633 1 | 4360 .3924546 0 N = between | .1559633 | 545 .3852761 0 n = within | | 8 .0762974 -.6848624 T = | 4360 .4374725 0 N = 1 | 545 .4227381 0 n = poorhlth overall | .0169725 .75 | between | 8 .1138494 -.6172018 .8919725 | T = 4360 .4772402 0 N = within | | 545 .4644838 0 n = | 1 | 8 .1111732 -.5243119 T = 1 | rur overall | .2038991 4360 .5326094 -3.579079 1.078899 | N = between | 545 .3907468 .3333435 n = | within | 8 .3622636 -2.467201 T = 1 | | (c) This replicates column [3] of Table III of Vella1 and Verbeek (1998, | nrtheast overall | .1901376 p.171).

1.065138 | between | | within | 1 | | 1 | nrthcen overall | .2577982 1.132798 | between | | within | 1 | | 1 | south overall | .3506881 1.225688 | between | | within | 4.05186 | | 3.174173 | lwage overall | 1.649147 3.204687 | between | within |

. xtreg lwage union educ exper exper2 hisp black rur married poorhlth nrtheast > south nrthcen agric min construc manuf trad fin bus per ent pro, fe Fixed-effects (within) regression Number of obs = 4360 Group variable (i): nr Number of groups = 545 R-sq: within = 0.1898 Obs per group: min = 8 between = 0.0070 avg = 8.0 overall = 0.0753 max = 8 = 46.81 F(19,3796) = 0.0000 Prob > F -----------------------------------------------------------------------------[95% Conf. Interval] lwage | Coef.

Std. Err. t P>|t| -------------+----------------------------------------------------------------

corr(u_i, Xb) = -0.1272

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

7 union | .0793986 .0194323 4.09 0.000 .0412998 .1174973 educ | (dropped) .0084669 13.29 0.000 .0959337 .1291341 .1125339 .0006067 -6.84 0.000 -.0053377 -.0029587 exper | exper2 | -.0041482 hisp | (dropped) black | (dropped) .0501049 rur | .0289779 1.73 0.084 -.0067088 .1069186 .0397283 married | .0182573 2.18 0.030 .0039333 .0755233 poorhlth | -.0165744 .0470585 -0.35 0.725 -.1088368 .0756879 .0774357 .0802382 0.97 0.335 -.0798784 .2347499 nrtheast | .1081117 .0623142 1.73 0.083 -.0140607 .2302842 south | nrthcen | -.0215774 .0583298 -0.37 0.711 -.1359382 .0927834 agric | -.0658778 .0503917 -1.31 0.191 -.1646753 .0329198 min | -.0258975 .0709226 -0.37 0.715 -.1649475 .1131526 construc | -.0525372 .0388689 -1.35 0.177 -.1287432 .0236687 .0191406 .0309658 0.62 0.537 -.0415706 .0798518 manuf | trad | -.0804114 .0309681 -2.60 0.009 -.1411272 -.0196957 .1330248 .0528192 2.52 0.012 .0294681 .2365816 fin | -.030849 .0351251 -0.88 0.380 -.0997149 .0380169 bus | .0246343 .0547843 0.45 0.653 -.0827752 .1320437 per | ent | -.1848436 .0603531 -3.06 0.002 -.3031711 -.066516 pro | -.0564456 .0366313 -1.54 0.123 -.1282645 .0153733 1.058114 .0581485 18.20 0.000 .9441087 1.172119 _cons | -------------+---------------------------------------------------------------sigma_u | .39852301 sigma_e | .34941634 rho | .56537415 (fraction of variance due to u_i) -----------------------------------------------------------------------------Prob > F = 0.0000 F test that all u_i=0: F(544, 3796) = 6.77

(c) This replicates column [4] of Table III of Vella and Verbeek (1998, p.171). . xtreg lwage union educ exper exper2 hisp black rur married poorhlth nrtheast > south nrthcen agric min construc manuf trad fin bus per ent pro occ1 occ2 occ > 3 occ4 occ5 occ6 occ7 occ8, fe Fixed-effects (within) regression Group variable (i): nr R-sq: within = 0.1923 between = 0.0110 overall = 0.0819

Number of obs = Number of groups = Obs per group: min = avg = max =

4360 545 8 8.0 8

= 33.40 F(27,3788) = 0.0000 Prob > F -----------------------------------------------------------------------------[95% Conf. Interval] lwage | Coef.

Std. Err. t P>|t| -------------+---------------------------------------------------------------.118632 union | .0803958 .0195024 4.12 0.000 .0421596 .1277928 .0085685 12.95 0.000 .094194 educ | (dropped) -.0028876 .0006102 -6.69 0.000 -.0052801 .1109934 exper | exper2 | -.0040838 hisp | (dropped) black | (dropped) .0478213 rur | .0290078 1.65 0.099 -.0090512 .1046937 .0382273 married | .0182872 2.09 0.037 .0023736 .074081 -.009975 poorhlth | .0471546 -0.21 0.832 -.1024259 .0824758 .0833803 nrtheast | .0803512 1.04 0.299 -.0741555 .2409161 .1093797 south | .0623713 1.75 0.080 -.0129048 .2316642 nrthcen | -.0238679 .0585818 -0.41 0.684 -.1387229 .0909871 agric | -.0658308 .0568864 -1.16 0.247 -.1773618 .0457002 min | -.0266996 .0710229 -0.38 0.707 -.1659465 .1125473 construc | -.0506548 .0391387 -1.29 0.196 -.1273897 .0260802 .0216979 .0312045 0.70 0.487 -.0394814 .0828772 manuf | trad | -.0767307 .0312452 -2.46 0.014 -.1379896 -.0154717 .1500444 .053356 2.81 0.005 .0454351 .2546537 fin |

corr(u_i, Xb) = -0.1115

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

8 bus | -.0317546 .0352842 -0.90 0.368 -.1009324 .0374232 .027005 .054955 0.49 0.623 -.0807392 .1347493 per | ent | -.1852791 .0604392 -3.07 0.002 -.3037757 -.0667826 pro | -.0590724 .0369477 -1.60 0.110 -.1315118 .013367 .0389308 .0348517 1.12 0.264 -.029399 .1072606 occ1 | .0304954 .0333217 0.92 0.360 -.0348348 .0958256 occ2 | occ3 | -.0334693 .0391471 -0.85 0.393 -.1102208 .0432821 occ4 | -.0454817 .0323055 -1.41 0.159 -.1088196 .0178563 .0001048 .0311655 0.00 0.997 -.060998 .0612076 occ5 | occ6 | -.0074731 .0308442 -0.24 0.809 -.0679459 .0529997 occ7 | -.0010076 .0333976 -0.03 0.976 -.0664865 .0644713 .002143 .0758017 0.03 0.977 -.1464731 .1507591 occ8 | 1.064028 .0628588 16.93 0.000 .940788 1.187269 _cons | -------------+---------------------------------------------------------------sigma_u | .39575702 sigma_e | .34925551 rho | .56217486 (fraction of variance due to u_i) -----------------------------------------------------------------------------Prob > F = 0.0000 F test that all u_i=0: F(544, 3788) = 6.52

11.7

This replicates the results in Table 1 of Wooldridge (2005, p.52).

. use union.dta . tsset nr year, yearly panel variable: nr, 13 to 12548 time variable: year, 1980 to 1987 . *Column 1 of Table 1 . xtprobit union married union_1 union80 marr81 marr82 marr83 marr84 marr85 marr86 marr87 d81 d82 d83 d84 d85 d86 d87, re note: d87 dropped due to collinearity Fitting comparison model: Iteration 0: Iteration 1: Iteration 2: Iteration 3: Iteration 4:

log likelihood = -2115.4174 log likelihood = -1380.244 log likelihood = -1366.1078 log likelihood = -1366.0497 log likelihood = -1366.0497

Fitting full model: rho = 0.0 rho = 0.1 rho = 0.2 rho = 0.3 Iteration 0: Iteration 1: Iteration 2: Iteration 3: Iteration 4: Iteration 5:

log likelihood = -1366.0497 log likelihood = -1346.9419 log likelihood = -1342.4578 log likelihood = -1345.9175 log likelihood = -1342.4579 log likelihood = -1308.5098 log likelihood = -1291.6826 log likelihood = -1291.2598 log likelihood = -1291.2555 log likelihood = -1291.2555

Random-effects probit regression Group variable (i): nr Random effects u_i ~ Gaussian

Number of obs = Number of groups = Obs per group: min = avg = max =

3815 545 7 7.0 7

= 403.30 Wald chi2(16) = 0.0000 Prob > chi2 ------------------------------------------------------------------------------

Log likelihood = -1291.2555

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

9 union | Coef.

Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------.3775373 married .1645174| .1086856 1.51 0.130 -.0485024 1.143565 union_1 .9778509| .0845496 11.57 0.000 .8121366 1.611331 union80 1.342638| .1370911 9.79 0.000 1.073944 .4335321 .0557457 marr81 | .1927517 0.29 0.772 -.3220408 .3404939 marr82 | -.1061208 .2278688 -0.47 0.641 -.5527355 .3781455 marr83 | -.0740984 .2307409 -0.32 0.748 -.5263423 .4896174 .0019333 .248823 0.01 0.994 -.4857507 marr84 | .8171854 .3572686 .2346558 1.52 0.128 -.1026483 marr85 | .5607392 .1000752 .235037 0.43 0.670 -.3605888 marr86 | -.0272087 marr87 | -.3870529 .1835973 -2.11 0.035 -.7468971 .1521039 d81 | -.0765441 .1166593 -0.66 0.512 -.3051922 .1763065 d82 | -.0489836 .1149461 -0.43 0.670 -.2742738 .0629241 d83 | -.1634238 .1154857 -1.42 0.157 -.3897717 .1002319 d84 | -.1246027 .1147137 -1.09 0.277 -.3494374 -.105163 d85 | -.3350622 .1172977 -2.86 0.004 -.5649614 -.1476579 d86 | -.3777447 .1173934 -3.22 0.001 -.6078316 -1.394519 _cons | -1.644473 .1275296 -12.89 0.000 -1.894426 -------------+---------------------------------------------------------------.1532389 /lnsig2u | -.0889939 .1235904 -.3312267 -------------+---------------------------------------------------------------1.079631 sigma_u | .9564785 .0591058 .8473738 .5382349 rho | .4777662 .0308365 .4179422 -----------------------------------------------------------------------------149.59 Prob >= chibar2 = 0.000 Likelihood-ratio test of rho=0: chibar2(01) = . *Column 2 of Table 1 . xtprobit union married union_1 union80 marr81 marr82 marr83 marr84 marr85 marr86 marr87 educ black d81 d82 d83 d84 d85 d86 d87, re note: d87 dropped due to collinearity Fitting comparison model: Iteration 0: Iteration 1: Iteration 2: Iteration 3: Iteration 4:

log likelihood = -2115.4174 log likelihood = -1373.8345 log likelihood = -1358.5405 log likelihood = -1358.4666 log likelihood = -1358.4666

Fitting full model: rho = 0.0 rho = 0.1 rho = 0.2 rho = 0.3 Iteration 0: Iteration 1: Iteration 2: Iteration 3: Iteration 4: Iteration 5:

log likelihood = -1358.4666 log likelihood = -1340.0864 log likelihood = -1336.1705 log likelihood = -1340.1285 log likelihood = -1336.1705 log likelihood = -1327.2927 log likelihood = -1289.632 log likelihood = -1286.589 log likelihood = -1286.5635 log likelihood = -1286.5635

Random-effects probit regression Group variable (i): nr Random effects u_i ~ Gaussian

Number of obs = Number of groups = Obs per group: min = avg = max =

3815 545 7 7.0 7

= 413.52 Wald chi2(18) = 0.0000 Prob > chi2 -----------------------------------------------------------------------------[95% Conf. Interval] union | Coef.

Std. Err. z P>|z| -------------+---------------------------------------------------------------.3801168 married | .1666075 .1089353 1.53 0.126 -.0469017

Log likelihood = -1286.5635

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

10 union_1 .976652| .0849498 11.50 0.000 .8101534 1.143151 union80 1.310118| .1370362 9.56 0.000 1.041532 1.578704 .038103 marr81 | .1932175 0.20 0.844 -.3405963 .4168022 marr82 | -.0688345 .2275028 -0.30 0.762 -.5147318 .3770627 marr83 | -.0880275 .2300634 -0.38 0.702 -.5389434 .3628884 .0258623 .2491106 0.10 0.917 -.4623855 .5141102 marr84 | .3708715 .2350619 1.58 0.115 -.0898414 .8315844 marr85 | .1068035 .2348234 0.45 0.649 -.3534419 .5670489 marr86 | -.359518 .1836126 -1.96 0.050 -.719392 .0003561 marr87 | educ | -.0156374 .0326283 -0.48 0.632 -.0795877 .0483128 .4961749 .1641641 3.02 0.003 .1744193 .8179305 black | -.075501 .1168569 -0.65 0.518 -.3045363 .1535344 d81 | d82 | -.0476582 .1150923 -0.41 0.679 -.2732349 .1779185 d83 | -.1630849 .1156522 -1.41 0.159 -.3897591 .0635893 d84 | -.1242375 .1148798 -1.08 0.279 -.3493978 .1009229 d85 | -.3350009 .1174665 -2.85 0.004 -.565231 -.1047709 d86 | -.3778186 .1175724 -3.21 0.001 -.6082563 -.1473808 _cons | -1.558261 .400001 -3.90 0.000 -2.342249 -.7742735 -------------+---------------------------------------------------------------.1433462 /lnsig2u | -.1033883 .1258873 -.3501229 -------------+---------------------------------------------------------------1.074304 sigma_u | .9496192 .0597725 .8394054 .5357753 rho | .4741759 .0313879 .4133526 -----------------------------------------------------------------------------143.81 Prob >= chibar2 = 0.000 Likelihood-ratio test of rho=0: chibar2(01) =

11.8

This replicates some of the results in Table 2 of Ruhm (1996, p.444). Note that some of the variables used in Ruhm’s article were missing from the Stock and Watson data set posted on their web site.

(b) The first set of results replicate column (a) of Table 2, p.444 of Ruhm (1996) with time effects but no state effects. This differs from the results in that Table perhaps because we did not use weighted least squares as Ruhm suggests, but rather the robust White cross-section option in EViews:

Dependent Variable: LVFR Method: Panel Least Squares Sample: 1982 1988 Cross-sections included: 48 Total panel (balanced) observations: 336 White cross-section standard errors & covariance (d.f. corrected) Variable

Coefficient Std. Error

t-Statistic

Prob.

C BEERTAX MLDA DRY VMILES YNGDRV

-9.055212 0.298995 0.117725 0.029004 -0.029707 0.005629 0.004234 0.000807 7.35E-05 3.79E-05 2.525457 0.469029

-30.28546 4.058978 -5.277340 5.244790 1.938560 5.384433

0.0000 0.0001 0.0000 0.0000 0.0534 0.0000

Effects Specification Period fixed (dummy variables) R-squared

0.324035

Mean dependent var

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

-8.534862

11 Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

0.301086 0.230792 17.25784 22.00254 0.351357

S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic)

0.276063 -0.059539 0.076786 14.11955 0.000000

The second set of results replicate column (b) of Table 2, p.444 of Ruhm (1996) with both time effects and state effects. This differs from the results in that Table perhaps because we did not use weighted least squares as Ruhm suggests, but rather the robust White cross-section option in EViews:

Dependent Variable: LVFR Method: Panel Least Squares Sample: 1982 1988 Cross-sections included: 48 Total panel (balanced) observations: 336 White cross-section standard errors & covariance (d.f. corrected) Variable

Coefficient Std. Error

t-Statistic

Prob.

C BEERTAX MLDA DRY VMILES YNGDRV

-8.789914 -0.203998 0.002290 0.008846 8.64E-06 1.113314

-69.12403 -2.405499 0.390778 4.055527 1.742469 2.151167

0.0000 0.0168 0.6963 0.0001 0.0825 0.0323

0.127161 0.084805 0.005860 0.002181 4.96E-06 0.517540

Effects Specification Cross-section fixed (dummy variables) Period fixed (dummy variables) R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

0.922077 0.905762 0.084747 1.989416 384.9540 1.304337

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic)

-8.534862 0.276063 -1.940203 -1.269936 56.51402 0.000000

Note how the results change by including the state dummies, making beer tax negative and significant rather than positive and significant. Also, minimum legal drinking age changes from negative and significant to positive and insignificant.

The last set of results replicate column (d) of Table 2, p.444 of Ruhm (1996) with both time effects and state effects. This does not include test law, dram shop law, administrative, per se law, and implied consent law since these variables were not in the data set. Also, here we have a separate dummy variable for jail and community service. We did not use weighted least squares as Ruhm suggests, but rather the robust White cross-section option in EViews:

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

12

Dependent Variable: LVFR Method: Panel Least Squares Sample: 1982 1988 Cross-sections included: 48 Total panel (unbalanced) observations: 335 White cross-section standard errors & covariance (d.f. corrected) Variable

Coefficient Std. Error

t-Statistic

Prob.

C BEERTAX MLDA DRY YNGDRV VMILES BREATH JAILD COMSERD PERINC

-9.361589 0.132383 -0.183533 0.077658 -0.004465 0.007814 0.008677 0.002611 0.493472 0.450802 6.91E-06 4.23E-06 -0.015930 0.027952 -0.012623 0.038973 0.020238 0.024505 0.060305 0.010275

-70.71570 -2.363344 -0.571427 3.323523 1.094651 1.632849 -0.569893 -0.323888 0.825867 5.868945

0.0000 0.0188 0.5682 0.0010 0.2746 0.1037 0.5692 0.7463 0.4096 0.0000

Effects Specification Cross-section fixed (dummy variables) Period fixed (dummy variables) R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

0.931852 0.916318 0.079977 1.739808 405.7652 1.433777

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic)

-8.534768 0.276471 -2.046359 -1.329075 59.98854 0.000000

The results on beer tax and breath and minimum drinking age are robust as far as their significance is concerned. (c) This reports the F-tests for the significance of state and year dummies: Redundant Fixed Effects Tests Equation: EQ01 Test cross-section and period fixed effects Effects Test

Statistic

d.f.

Prob.

Cross-section F Cross-section Chi-square Period F Period Chi-square Cross-Section/Period F Cross-Section/Period Chi-square

34.901652 653.350674 2.967741 21.242751 31.866945 661.752731

(47,272) 47 (6,272) 6 (53,272) 53

0.0000 0.0000 0.0080 0.0017 0.0000 0.0000

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

13

We conclude that state and time dummies are jointly significant and that ignoring either set of dummies would bias the results.

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

1 Chapter 12 Nonstationary Panels 12.3 This performs the panel unit root tests on real exchange rates from 18 OECD countries over the period 1975:1- 2002:4, using EViews.

Pool unit root test: Summary Sample: 1975Q1 2002Q4 Series: RER_AUSTRIA, RER_BELGIUM, RER_CANADA, RER_DENMARK, RER_FINLAND, RER_FRANCE, RER_GREECE, RER_ITALY, RER_JAPAN, RER_KOREA, RER_NETHERLANDS, RER_NORWAY, RER_PORTUGAL, RER_SPAIN, RER_SWEDEN, RER_SWITZ, RER_UK, RER_US Exogenous variables: Individual effects Automatic selection of maximum lags Automatic selection of lags based on SIC: 0 to 8 Newey-West bandwidth selection using Bartlett kernel

Crosssections

Obs

18 18

1970 1952

Null: Unit root (assumes individual unit root process) Im, Pesaran and Shin W-stat -3.42675 0.0003 ADF - Fisher Chi-square 63.6336 0.0030 PP - Fisher Chi-square 58.1178 0.0112

18 18 18

1970 1970 1998

Null: No unit root (assumes common unit root process) Hadri Z-stat 9.43149 0.0000

18

2016

Method Statistic Prob.** Null: Unit root (assumes common unit root process) Levin, Lin & Chu t* -1.83839 0.0330 Breitung t-stat -3.06048 0.0011

** Probabilities for Fisher tests are computed using an asympotic Chi -square distribution. All other tests assume asymptotic normality.

Pool unit root test: Summary Sample: 1975Q1 2002Q4 Series: RER_AUSTRIA, RER_BELGIUM, RER_CANADA, RER_DENMARK, RER_FINLAND, RER_FRANCE, RER_GREECE, RER_ITALY, RER_JAPAN, RER_KOREA,

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

2 RER_NETHERLANDS, RER_NORWAY, RER_PORTUGAL, RER_SPAIN, RER_SWEDEN, RER_SWITZ, RER_UK, RER_US Exogenous variables: Individual effects User specified lags at: 4 Newey-West bandwidth selection using Bartlett kernel Balanced observations for each test

Crosssections

Obs

18 18

1926 1908

Null: Unit root (assumes individual unit root process) Im, Pesaran and Shin W-stat -4.27437 0.0000 ADF - Fisher Chi-square 73.0933 0.0003 PP - Fisher Chi-square 58.1178 0.0112

18 18 18

1926 1926 1998

Null: No unit root (assumes common unit root process) Hadri Z-stat 9.43149 0.0000

18

2016

Method Statistic Prob.** Null: Unit root (assumes common unit root process) Levin, Lin & Chu t* -2.42052 0.0077 Breitung t-stat -3.79789 0.0001

** Probabilities for Fisher tests are computed using an asympotic Chi -square distribution. All other tests assume asymptotic normality.

Pool unit root test: Summary Sample: 1975Q1 2002Q4 Series: RER_AUSTRIA, RER_BELGIUM, RER_CANADA, RER_DENMARK, RER_FINLAND, RER_FRANCE, RER_GREECE, RER_ITALY, RER_JAPAN, RER_KOREA, RER_NETHERLANDS, RER_NORWAY, RER_PORTUGAL, RER_SPAIN, RER_SWEDEN, RER_SWITZ, RER_UK, RER_US Exogenous variables: Individual effects User specified lags at: 3 Newey-West bandwidth selection using Bartlett kernel Balanced observations for each test

Method

Statistic

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

Prob.**

Crosssections

Obs

3 Null: Unit root (assumes common unit root process) Levin, Lin & Chu t* -1.92561 0.0271 Breitung t-stat -3.47943 0.0003

18 18

1944 1926

Null: Unit root (assumes individual unit root process) Im, Pesaran and Shin W-stat -3.59767 0.0002 ADF - Fisher Chi-square 66.9646 0.0013 PP - Fisher Chi-square 58.1178 0.0112

18 18 18

1944 1944 1998

Null: No unit root (assumes common unit root process) Hadri Z-stat 9.43149 0.0000

18

2016

** Probabilities for Fisher tests are computed using an asympotic Chi -square distribution. All other tests assume asymptotic normality.

Pool unit root test: Summary Sample: 1975Q1 2002Q4 Series: RER_AUSTRIA, RER_BELGIUM, RER_CANADA, RER_DENMARK, RER_FINLAND, RER_FRANCE, RER_GREECE, RER_ITALY, RER_JAPAN, RER_KOREA, RER_NETHERLANDS, RER_NORWAY, RER_PORTUGAL, RER_SPAIN, RER_SWEDEN, RER_SWITZ, RER_UK, RER_US Exogenous variables: Individual effects User specified lags at: 2 Newey-West bandwidth selection using Bartlett kernel Balanced observations for each test

Method Statistic Prob.** Null: Unit root (assumes common unit root process) Levin, Lin & Chu t* -0.74558 0.2280 Breitung t-stat -3.15355 0.0008 Null: Unit root (assumes individual unit root process) Im, Pesaran and Shin W-stat -2.44631 0.0072 ADF - Fisher Chi-square 50.5343 0.0547 PP - Fisher Chi-square 58.1178 0.0112

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

Crosssections

Obs

18 18

1962 1944

18 18 18

1962 1962 1998

4 Null: No unit root (assumes common unit root process) Hadri Z-stat 9.43149 0.0000

18

2016

** Probabilities for Fisher tests are computed using an asympotic Chi -square distribution. All other tests assume asymptotic normality.

Pool unit root test: Summary Sample: 1975Q1 2002Q4 Series: RER_AUSTRIA, RER_BELGIUM, RER_CANADA, RER_DENMARK, RER_FINLAND, RER_FRANCE, RER_GREECE, RER_ITALY, RER_JAPAN, RER_KOREA, RER_NETHERLANDS, RER_NORWAY, RER_PORTUGAL, RER_SPAIN, RER_SWEDEN, RER_SWITZ, RER_UK, RER_US Exogenous variables: Individual effects User specified lags at: 1 Newey-West bandwidth selection using Bartlett kernel Balanced observations for each test

Crosssections

Obs

18 18

1980 1962

Null: Unit root (assumes individual unit root process) Im, Pesaran and Shin W-stat -3.04702 0.0012 ADF - Fisher Chi-square 59.3350 0.0085 PP - Fisher Chi-square 58.1178 0.0112

18 18 18

1980 1980 1998

Null: No unit root (assumes common unit root process) Hadri Z-stat 9.43149 0.0000

18

2016

Method Statistic Prob.** Null: Unit root (assumes common unit root process) Levin, Lin & Chu t* -1.71432 0.0432 Breitung t-stat -2.86966 0.0021

** Probabilities for Fisher tests are computed using an asympotic Chi -square distribution. All other tests assume asymptotic normality.

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

5 12.4 This reproduces EViews output for the panel unit root tests for GDP of G7 countries.

Group unit root test: Summary Sample: 1950 1992 Series: GDP_CAN, GDP_FRA, GDP_GER, GDP_ITA, GDP_JPN, GDP_UK, GDP_US Exogenous variables: Individual effects Automatic selection of maximum lags Automatic selection of lags based on SIC: 0 to 1 Newey-West bandwidth selection using Bartlett kernel

Crosssections

Obs

7 7

292 285

Null: Unit root (assumes individual unit root process) Im, Pesaran and Shin W-stat 4.83525 1.0000 ADF - Fisher Chi-square 0.80568 1.0000 PP - Fisher Chi-square 0.66842 1.0000

7 7 7

292 292 294

Null: No unit root (assumes common unit root process) Hadri Z-stat 11.5443 0.0000

7

301

Method Statistic Prob.** Null: Unit root (assumes common unit root process) Levin, Lin & Chu t* 1.36042 0.9132 Breitung t-stat 1.28607 0.9008

** Probabilities for Fisher tests are computed using an asympotic Chi

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

6 Group unit root test: Summary Sample: 1950 1992 Series: GDP_CAN, GDP_FRA, GDP_GER, GDP_ITA, GDP_JPN, GDP_UK, GDP_US Exogenous variables: Individual effects, individual linear trends Automatic selection of maximum lags Automatic selection of lags based on SIC: 0 to 1 Newey-West bandwidth selection using Bartlett kernel

Crosssections

Obs

7 7

289 282

Null: Unit root (assumes individual unit root process) Im, Pesaran and Shin W-stat -1.56421 0.0589 ADF - Fisher Chi-square 21.5070 0.0893 PP - Fisher Chi-square 12.3071 0.5817

7 7 7

289 289 294

Null: No unit root (assumes common unit root process) Hadri Z-stat 3.96309 0.0000

7

301

Method Statistic Prob.** Null: Unit root (assumes common unit root process) Levin, Lin & Chu t* -0.92186 0.1783 Breitung t-stat -1.61499 0.0532

** Probabilities for Fisher tests are computed using an asympotic Chi -square distribution. All other tests assume asymptotic normality.

-square distribution. All other tests assume asymptotic normality.

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

7 GDP of 7 countries, lag specified at 1 Pool unit root test: Summary Sample: 1950 1992 Series: GDP_CAN, GDP_FRA, GDP_GER, GDP_ITA, GDP_JPN, GDP_UK, GDP_US Exogenous variables: Individual effects User specified lags at: 1 Newey-West bandwidth selection using Bartlett kernel Balanced observations for each test

Crosssections

Obs

7 7

287 280

Null: Unit root (assumes individual unit root process) Im, Pesaran and Shin W-stat 4.49059 1.0000 ADF - Fisher Chi-square 0.99039 1.0000 PP - Fisher Chi-square 0.66842 1.0000

7 7 7

287 287 294

Null: No unit root (assumes common unit root process) Hadri Z-stat 11.5443 0.0000

7

301

Method Statistic Prob.** Null: Unit root (assumes common unit root process) Levin, Lin & Chu t* 1.04498 0.8520 Breitung t-stat 1.12018 0.8687

** Probabilities for Fisher tests are computed using an asympotic Chi -square distribution. All other tests assume asymptotic normality.

12.5 This performs the panel unit root tests and cointegration tests on inventories and shipments for 8 sectors over the period 1968M01 1995M12, using EViews. (a) Panel unit roots for inventories allowing for individual sector effects Panel unit root test: Summary Series: IVM Sample: 1968M01 1995M12 Exogenous variables: Individual effects Automatic selection of maximum lags Automatic selection of lags based on SIC: 0 to 7 Newey-West bandwidth selection using Bartlett kernel

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

8

Crosssections

Obs

0.0137

8

2551

Null: Unit root (assumes individual unit root process) Im, Pesaran and Shin W-stat 1.49452 0.9325 ADF - Fisher Chi-square 6.28297 0.9847 PP - Fisher Chi-square 5.08532 0.9953

8 8 8

2551 2551 2568

Method Statistic Prob.** Null: Unit root (assumes common unit root process) Levin, Lin & Chu t*

-2.20538

** Probabilities for Fisher tests are computed using an asymptotic Chi -square distribution. All other tests assume asymptotic normality.

Panel unit roots for inventories allowing for individual sector effects and individual linear trends Panel unit root test: Summary Series: IVM Sample: 1968M01 1995M12 Exogenous variables: Individual effects, individual linear trends Automatic selection of maximum lags Automatic selection of lags based on SIC: 0 to 7 Newey-West bandwidth selection using Bartlett kernel Crosssections

Obs

0.8544 0.7594

8 8

2551 2543

Null: Unit root (assumes individual unit root process) Im, Pesaran and Shin W-stat 2.66094 0.9961 ADF - Fisher Chi-square 8.95375 0.9153 PP - Fisher Chi-square 4.40319 0.9980

8 8 8

2551 2551 2568

Method Statistic Prob.** Null: Unit root (assumes common unit root process) Levin, Lin & Chu t* Breitung t-stat

1.05537 0.70433

** Probabilities for Fisher tests are computed using an asymptotic Chi -square distribution. All other tests assume asymptotic normality.

Panel unit roots for shipments allowing for individual sector effects Panel unit root test: Summary Series: MM Sample: 1968M01 1995M12 Exogenous variables: Individual effects Automatic selection of maximum lags

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

9 Automatic selection of lags based on SIC: 1 to 6 Newey-West bandwidth selection using Bartlett kernel

Method Statistic Prob.** Null: Unit root (assumes common unit root process) Levin, Lin & Chu t*

3.02873

Crosssections

Obs

8

2548

8 8 8

2548 2548 2568

0.9988

Null: Unit root (assumes individual unit root process) Im, Pesaran and Shin W-stat ADF - Fisher Chi-square PP - Fisher Chi-square

6.66735 0.57400 0.56812

1.0000 1.0000 1.0000

** Probabilities for Fisher tests are computed using an asymptotic Chi -square distribution. All other tests assume asymptotic normality.

Panel unit roots for shipments allowing for individual sector effects and individual linear trends

Panel unit root test: Summary Series: MM Sample: 1968M01 1995M12 Exogenous variables: Individual effects, individual linear trends Automatic selection of maximum lags Automatic selection of lags based on SIC: 0 to 6 Newey-West bandwidth selection using Bartlett kernel

Method Statistic Prob.** Null: Unit root (assumes common unit root process) Levin, Lin & Chu t* Breitung t-stat

0.58341 1.58036

0.7202 0.9430

Crosssections

Obs

8 8

2545 2537

8 8 8

2545 2545 2568

Null: Unit root (assumes individual unit root process) Im, Pesaran and Shin W-stat ADF - Fisher Chi-square PP - Fisher Chi-square

0.31767 14.2524 23.9473

0.6246 0.5799 0.0907

** Probabilities for Fisher tests are computed using an asymptotic Chi -square distribution. All other tests assume asymptotic normality.

All results (except for the LLC test for inventories) do not reject the null of a common panel unit root. Of course these are all first generation panel unit roots not allowing for cross-section dependence among the sectors. (b) Kao Residual Cointegration Test allowing for individual sector effects Kao Residual Cointegration Test

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

10 Series: IVM MM Sample: 1968M01 1995M12 Included observations: 2688 Null Hypothesis: No cointegration Trend assumption: No deterministic trend Lag selection: Automatic 3 lags by SIC with a max lag of 16 Newey-West bandwidth selection using Bartlett kernel t-Statistic -1.388782

ADF Residual variance HAC variance

Prob.

0.0824

257852.7 730764.3

Augmented Dickey-Fuller Test Equation Dependent Variable: D(RESID) Method: Least Squares Sample (adjusted): 1968M05 1994M10 Included observations: 2544 after adjustments Coefficient

Std. Error

t-Statistic

Prob.

RESID(-1) D(RESID(-1)) D(RESID(-2)) D(RESID(-3))

-0.010083 -0.145755 0.084274 0.193649

0.002894 0.019585 0.019744 0.019885

-3.484199 -7.442085 4.268423 9.738481

0.0005 0.0000 0.0000 0.0000

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

0.062195 0.061087 877.6001 1.96E+09 -20848.95 2.009245

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter.

Pedroni Residual Cointegration Test allowing for individual sector effects

Pedroni Residual Cointegration Test Series: IVM MM Sample: 1968M01 1995M12 Included observations: 2688 Cross-sections included: 8

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

-16.46197 905.6992 16.39383 16.40301 16.39716

11 Null Hypothesis: No cointegration Trend assumption: No deterministic trend Lag selection: Automatic SIC with a max lag of 16 Newey-West bandwidth selection with Bartlett kernel Alternative hypothesis: common AR coefs. (within-dimension) Weighted Statistic Statistic Prob.

Panel v-Statistic Panel rho-Statistic Panel PP-Statistic Panel ADF-Statistic

4.219500 -0.400152 0.671083 -0.216806

0.0001 0.3682 0.3185 0.3897

4.119485 -2.543473 -1.254923 0.172158

Prob.

0.0001 0.0157 0.1815 0.3931

Alternative hypothesis: individual AR coefs. (between-dimension) Statistic -1.776207 -0.824320 0.538943

Group rho-Statistic Group PP-Statistic Group ADF-Statistic

Prob.

0.0824 0.2840 0.3450

Cross section specific results Phillips-Peron results (non-parametric) Cross ID AUT BUS CON CST DEP HOA MAE MIS

AR(1) 0.959 0.959 0.966 0.933 0.908 0.941 0.975 0.991

Variance 54057.16 98387.47 144092.9 579515.0 896700.4 146702.7 2996615.

2775962.

46699.67 98024.05 125609.0 468780.9 572964.8 165065.5 2018633.

3950850.

HAC

Bandwidth 23.00 7.00 4.00 6.00 7.00 6.00 3.00 7.00

Obs 321 321 321 321 321 321 321 321

Lag 5 1 0 1 2 0 6 3

Max lag 16 16 16 16 16 16 16 16

Obs 316 320 321 320 319 321 315 318

Augmented Dickey-Fuller results (parametric) Cross ID AUT BUS CON CST DEP HOA MAE MIS

AR(1) 0.983 0.971 0.966 0.949 0.974 0.941 0.976 0.977

Variance 48285.07 95843.74 144092.9 556149.1 647340.5 146702.7 2459970.

2605046.

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

12

(c)Johansen Fisher Panel Cointegration Test allowing for individual sector effects Johansen Fisher Panel Cointegration Test Series: IVM MM Date: 11/12/07 Time: 21:15 Sample: 1968M01 1995M12 Included observations: 2688 Trend assumption: No deterministic trend (restricted constant) Lags interval (in first differences): 1 1 Unrestricted Cointegration Rank Test (Trace and Maximum Eigenvalue) Hypothesized No. of CE(s)

Fisher Stat.* (from trace test)

Prob.

Fisher Stat.* (from max-eigen test)

Prob.

None At most 1

204.7 12.07

0.0000 0.7390

211.0 12.07

0.0000 0.7390

Trace Test Statistics

Prob.**

Max-Eign Test Statistics

Prob.**

Hypothesis of no cointegration AUT 22.1873 BUS 43.1638 CON 56.9099 CST 48.6846 DEP 15.5639 HOA 76.6530 MAE 54.7226 MIS 60.8672

0.0268 0.0000 0.0000 0.0000 0.1958 0.0000 0.0000 0.0000

19.8088 39.8985 53.2483 42.9905 12.4301 70.5817 52.5119 59.1997

0.0115 0.0000 0.0000 0.0000 0.1624 0.0000 0.0000 0.0000

Hypothesis of at most 1 cointegration relationship AUT 2.3785 0.7018 BUS 3.2653 0.5323 CON 3.6616 0.4648

2.3785 3.2653 3.6616

0.7018 0.5323 0.4648

* Probabilities are computed using asymptotic Chisquare distribution.

Individual cross section results

Cross Section

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

13 CST DEP HOA MAE MIS

5.6942 3.1338 6.0714 2.2107 1.6675

0.2157 0.5560 0.1853 0.7355 0.8425

5.6942 3.1338 6.0714 2.2107 1.6675

0.2157 0.5560 0.1853 0.7355 0.8425

**MacKinnon-Haug-Michelis (1999) p-values (d) sensitivity to fixing the lag at 1

Kao Residual Cointegration Test Series: IVM MM Sample: 1968M01 1995M12 Included observations: 2688 Null Hypothesis: No cointegration Trend assumption: No deterministic trend Lag selection: fixed at 1 Newey-West bandwidth selection using Bartlett kernel t-Statistic -0.603443

ADF Residual variance HAC variance

Prob.

0.2731

257852.7 730764.3

Augmented Dickey-Fuller Test Equation Dependent Variable: D(RESID) Method: Least Squares Date: 11/12/07 Time: 21:20 Sample (adjusted): 1968M03 1994M10 Included observations: 2560 after adjustments Coefficient

Std. Error

t-Statistic

Prob.

RESID(-1) D(RESID(-1))

-0.007315 -0.144238

0.002909 0.019629

-2.515054 -7.348100

0.0120 0.0000

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

0.024125 0.023744 892.1474 2.04E+09 -21023.18 1.986464

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter.

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

-16.11315 902.9312 16.42592 16.43049 16.42758

14

Pedroni Residual Cointegration Test Series: IVM MM Sample: 1968M01 1995M12 Included observations: 2688 Cross-sections included: 8 Null Hypothesis: No cointegration Trend assumption: No deterministic trend Lag selection: fixed at 1 Newey-West bandwidth selection with Bartlett kernel Alternative hypothesis: common AR coefs. (within-dimension) Weighted Statistic Statistic Prob.

Panel v-Statistic Panel rho-Statistic Panel PP-Statistic Panel ADF-Statistic

4.219500 -0.400152 0.671083 2.177869

0.0001 0.3682 0.3185 0.0372

4.119485 -2.543473 -1.254923 0.153330

Prob.

0.0001 0.0157 0.1815 0.3943

Alternative hypothesis: individual AR coefs. (between-dimension) Statistic -1.776207 -0.824320 0.987833

Group rho-Statistic Group PP-Statistic Group ADF-Statistic

Prob.

0.0824 0.2840 0.2449

Cross section specific results Phillips-Peron results (non-parametric) Cross ID AUT BUS CON CST DEP HOA MAE MIS

AR(1) 0.959 0.959 0.966 0.933 0.908 0.941 0.975 0.991

Variance 54057.16 98387.47 144092.9 579515.0 896700.4 146702.7 2996615.

2775962.

HAC 46699.67 98024.05 125609.0 468780.9 572964.8 165065.5 2018633.

3950850.

Bandwidth 23.00 7.00 4.00 6.00 7.00 6.00 3.00 7.00

Obs 321 321 321 321 321 321 321 321

Lag 1 1

Max lag ---

Obs 320 320

Augmented Dickey-Fuller results (parametric) Cross ID AUT BUS

AR(1) 0.971 0.971

Variance 51730.31 95843.74

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

15 CON CST DEP HOA MAE MIS

0.971 0.949 0.952 0.946 0.989 0.991

142612.1 556149.1 732640.9 146673.5 2737915.

2784387.

1 1 1 1 1 1

-------

320 320 320 320 320 320

Similar results are obtained when we fix the lag at 2,3, and 4. (e) sensitivity to inclusion of linear trends Pedroni Residual Cointegration Test Series: IVM MM Date: 11/12/07 Time: 21:27 Sample: 1968M01 1995M12 Included observations: 2688 Cross-sections included: 8 Null Hypothesis: No cointegration Trend assumption: Deterministic intercept and trend Lag selection: Automatic SIC with a max lag of 16 Newey-West bandwidth selection with Bartlett kernel Alternative hypothesis: common AR coefs. (within-dimension) Weighted Statistic Statistic Prob.

Panel v-Statistic 1.165075 0.2024 2.309719 Panel rho-Statistic 1.618195 0.1077 0.133578 Panel PP-Statistic 2.515132 0.0169 0.637212 Panel ADF-Statistic 2.058160 0.0480 1.734333

Prob.

0.0277 0.3954 0.3256 0.0887

Alternative hypothesis: individual AR coefs. (between-dimension) Statistic 0.093508 0.829095 1.721656

Group rho-Statistic Group PP-Statistic Group ADF-Statistic

Prob.

0.3972 0.2829 0.0906

Cross section specific results Phillips-Peron results (non-parametric) Cross ID AUT BUS CON CST

AR(1) 0.989 0.939 0.988 0.925

Variance 8423.300 120754.3 52006.85 628659.8

HAC 13323.32 120199.0 55901.93 505527.4

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

Bandwidth 9.00 7.00 7.00 6.00

Obs 321 321 321 321

16 DEP HOA MAE MIS

0.882 0.967 0.996 0.994

1051048.

53736.13 571075.3 2275925.

768151.5 94599.15 1637287.

3332654.

8.00 9.00 12.00 7.00

321 321 321 321

Lag 3 1 0 1 2 3 4 3

Max lag 16 16 16 16 16 16 16 16

Obs 318 320 321 320 319 318 317 318

Augmented Dickey-Fuller results (parametric) Cross ID AUT BUS CON CST DEP HOA MAE MIS

AR(1) 0.984 0.955 0.988 0.943 0.960 0.947 0.986 0.982

Variance 7919.828 116950.2 52006.85 600470.3 752106.3 50410.74 491973.2 2142136.

Johansen Fisher Panel Cointegration Test Series: IVM MM Sample: 1968M01 1995M12 Included observations: 2688 Trend assumption: Linear deterministic trend (restricted) Lags interval (in first differences): 1 1 Unrestricted Cointegration Rank Test (Trace and Maximum Eigenvalue) Hypothesized No. of CE(s)

Fisher Stat.* (from trace test)

None At most 1

106.3 17.70

Prob.

Fisher Stat.* (from max-eigen test)

Prob.

0.0000 0.3420

104.1 17.70

0.0000 0.3420

Prob.**

Max-Eign Test Statistics

Prob.**

* Probabilities are computed using asymptotic Chisquare distribution.

Individual cross section results

Cross Section

Trace Test Statistics

Hypothesis of no cointegration

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

17 AUT 36.6831 0.0015 BUS 23.3549 0.0997 CON 29.4446 0.0172 CST 26.3215 0.0440 DEP 24.8826 0.0660 HOA 45.5352 0.0001 MAE 37.4411 0.0012 MIS 58.0008 0.0000 Hypothesis of at most 1 cointegration relationship AUT 3.9555 0.7486 BUS 4.0694 0.7320 CON 4.2479 0.7060 CST 6.0317 0.4563 DEP 0.5797 1.0000 HOA 9.2359 0.1663 MAE 11.8819 0.0637 MIS 11.3813 0.0768 **MacKinnon-Haug-Michelis (1999) p-values

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

32.7276 19.2855 25.1968 20.2897 24.3029 36.2994 25.5592 46.6195

0.0003 0.0517 0.0064 0.0369 0.0089 0.0001 0.0056 0.0000

3.9555 4.0694 4.2479 6.0317 0.5797 9.2359 11.8819 11.3813

0.7486 0.7320 0.7060 0.4563 1.0000 0.1663 0.0637 0.0768

1 Problems and Solutions References Baltagi, B.H., 1988a, Prediction with a two-way error component regression model, Problem 88.1.1, Econometric Theory 4, 171.

Baltagi, B.H., 1988b, An alternative heteroscedastic error components model, Problem 88.2.2, Econometric Theory 4, 349–350.

Baltagi, B.H., 1989a, The equivalence of the Boothe–MacKinnon and the Hausman specification tests in the context of panel data, Problem 89.3.3, Econometric Theory 5, 454.

Baltagi, B.H., 1993a, Nested effects, Problem 93.4.2, Econometric Theory 9, 687–688.

Baltagi, B.H., 1995c, Testing for correlated effects in panels, Problem 95.2.5, Econometric Theory 11, 401–402.

Baltagi, B.H., 1995d, Testing for fixed effects in logit and probit models using an artificial regression, Problem 95.5.4, Econometric Theory 11, 1179.

Baltagi, B.H., 1996b, Heteroskedastic fixed effects models, Problem 96.5.1, Econometric Theory 12, 867.

Baltagi, B.H., 1997b, A joint test for functional form and random individual effects, Problem 97.1.3, Econometric Theory 13, 307–308.

Baltagi, B.H., 1997c, Hausman’s specification test as a Gauss–Newton regression, Problem 97.4.1, Econometric Theory 13, 757.

Baltagi, B.H., 1998, Within two way is equivalent to two withins one way, Problem 98.5.2, Econometric Theory 14, 687.

Baltagi, B.H., 1999b, The relative efficiency of the between estimator with respect to the within estimator, Problem 99.4.3, Econometric Theory 15, 630–631.

Baltagi, B.H., 2004, A Hausman Test Based on the Difference Between Fixed Effects Two-Stage Least Squares and Error Components Two-Stage Least Squares, Problem 04.1.1, Econometric Theory 20, 223-224.

Baltagi, B.H. and W. Krämer, 1995, A mixed error component model, Problem 95.1.4, Econometric Theory 11, 192–193.

Baltagi, B.H. and W. Krämer, 1997, A simple linear trend model with error components, Problem 97.2.1, Econometric Theory 13, 463.

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

2 Baltagi, B.H. and Q. Li, 1990a, A comparison of variance components estimators using balanced versus unbalanced data, Problem 90.2.3, Econometric Theory 6, 283–285.

Baltagi, B.H. and Q. Li, 1991c, Variance component estimation under misspecification, Problem 91.3.3, Econometric Theory 7, 418–419.

Baltagi, B.H. and Q. Li, 1992a, Variance component estimation under misspecification, Solution 91.3.3, Econometric Theory 8, 430–433.

Baltagi, B.H. and Q. Li, 1992e, An approximate transformation for the error component model with MA (q) disturbances, Problem 92.4.3, Econometric Theory 8, 582–583.

Baltagi, B.H. and Q. Li, 1993, An approximate transformation for the error component model with MA (q) disturbances, Solution 92.4.3, Econometric Theory 9, 692–694.

Baltagi, B.H. and D. Li, 1999, Prediction in the spatially autocorrelated error component model, Problem 99.2.4, Econometric Theory 15, 259.

Gurmu, S., 1996, Testing for fixed effects in logit and probit models using an artificial regression, Solution 95.5.4, Econometric Theory 12, 872–874.

Gurmu, S., 2000, The relative efficiency of the between-estimator with respect to the within-estimator, Solution 99.4.3, Econometric Theory 16, 454–456.

Kleiber, C., 1997, Heteroskedastic fixed effects models, Solution 96.5.1, Econometric Theory 13, 891–893.

Koning, R.H., 1989, Prediction with a two-way error component regression model, Solution 88.1.1, Econometric Theory 5, 175.

Koning, R.H., 1990, The equivalence of the Boothe–MacKinnon and the Hausman specification tests in the context of panel data, Solution 89.3.3, Econometric Theory 6, 409.

Koning, R.H., 1991, A comparison of variance components estimators using balanced versus unbalanced data, Solution 90.2.3, Econometric Theory 6, 425–427.

Li, D., 1998, A joint test for functional form and random individual effects, Solution 97.1.3, Econometric Theory 14, 154–156.

Li, D., 1999, Within two way is equivalent to two withins one-way, Solution 98.5.2, Econometric Theory 15, 781–783.

Song, S.H. and B.C. Jung, 1998, A simple linear trend model with error components, Solution 97.2.1, Econometric Theory 14, 286–289.

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi

3 Song, S.H. and B.C. Jung, 2000, Prediction in the spatially autocorrelated error component model, Solution 99.2.4, Econometric Theory 16, 149–150.

Wansbeek, T.J., 1989, An alternative heteroscedastic error components model, Solution 88.1.1, Econometric Theory 5, 326.

Xiong, W., 1995, Nested effects, Solution 93.4.2, Econometric Theory 11, 658–659.

Xiong, W., 1996a, A mixed-error component model, Solution 95.1.4, Econometric Theory 12, 401–402.

Xiong, W., 1996b, Testing for correlated effects in panels, Solution 95.2.5, Econometric Theory 12, 405–406.

© 2008 John Wiley & Sons Ltd. www.wileyeurope.com/college/baltagi