PANEL.RPF

PANEL.RPF estimates a panel data model using several different methods. It demonstrates the PREGRESS instruction plus several different uses of the PANEL instruction and how the equivalent estimators to fixed and random effects can be done using least squares with dummy variables and with panel data transformations.

This uses the grunfeld.dat data file, with $N=10$, $T=20$.

cal(panelobs=20) 1935

all 10//1954:1

open data grunfeld.dat

data(format=prn,org=cols)

Do fixed and random effects. The intercept in the fixed effects estimator gets zeroed out as a time-invariant variable, but we include it to maintain the same form as the other regressions.

preg(method=fixed) invest

# constant firmvalue cstock

preg(method=random) invest

# constant firmvalue cstock

This does a first-difference regression:

preg(method=fd) invest

# firmvalue cstock

And this does a SUR estimation. (This data set is barely adequate for that, with T relatively small relative to N).

preg(method=sur) invest

# constant firmvalue cstock

This does fixed effects as least squares with dummy variables (omitting the CONSTANT, since it is redundant with a full set of dummies).

panel(dummies=idummies)

linreg invest

# firmvalue cstock idummies

Random effects done using transformed data. We first need estimates of the component variances. The simplest (though not most accurate) can be computed using PSTATS with the residuals from a linear regression. PSTATS does a Wallace-Hussain variance calculation treating the input information as data (rather than residuals), so it will give a somewhat different values for the component variances from the one you get from PREGRESS (even with VCOMP=WH) since the latter uses information about the regression being run.

One other difference between the filtered regression and PREGRESS with METHOD=RANDOM is that the latter (in effect) uses the computed random variance component in calculating the covariance matrix, while the filtered least squares estimator uses the standard OLS estimator on the filtered data, thus recomputing the residual variance based upon the results.

linreg invest

# constant firmvalue cstock

pstats(effects=indiv) %resids

set ones = 1.0

panel(gls=standard,effects=indiv,$

vrandom=%vrandom,vindiv=%vindiv) invest / ifix

panel(gls=standard,effects=indiv,$

vrandom=%vrandom,vindiv=%vindiv) firmvalue / ffix

panel(gls=standard,effects=indiv,$

vrandom=%vrandom,vindiv=%vindiv) cstock / cfix

panel(gls=standard,effects=indiv,$

vrandom=%vrandom,vindiv=%vindiv) ones / constfix

linreg(title="Random Effects using Transformed Data") ifix

# constfix ffix cfix

preg(method=random,vcomp=wh) invest

# constant firmvalue cstock

Full Program

cal(panelobs=20) 1935
all 10//1954:1
open data grunfeld.dat
data(format=prn,org=cols)
*
* Do fixed and random effects. The intercept in the fixed effects
* estimator gets zeroed out as a time-invariant variable, but we include
* it to maintain the same form as the other regressions.
*
preg(method=fixed) invest
# constant firmvalue cstock
preg(method=random) invest
# constant firmvalue cstock
*
* First difference regression
*
preg(method=fd) invest
# firmvalue cstock
*
* SUR
*
preg(method=sur) invest
# constant firmvalue cstock
*
* Do fixed effects as least squares with dummy variables
*
panel(dummies=idummies)
linreg invest
# firmvalue cstock idummies
*
* Random effects done using transformed data. We first need estimates of the
* component variances. The simplest (though not most accurate) can be computed
* using PSTATS with the residuals from a linear regression. PSTATS does a
* Wallace-Hussain variance calculation treating the input information as data
* (rather than residuals), so it will give a somewhat different values for the
* component variances from the one you get from PREGRESS (even with VCOMP=WH)
* since the latter uses information about the regression being run.
*
* One other difference between the filtered regression and PREGRESS with
* METHOD=RANDOM is that the latter (in effect) uses the computed random variance
* component in calculating the covariance matrix, while the filtered least squares
* estimator uses the standard OLS estimator on the filtered data, thus recomputing
* the residual variance based upon the results.
*
linreg invest
# constant firmvalue cstock
pstats(effects=indiv) %resids
*
set ones = 1.0
panel(gls=standard,effects=indiv,$
   vrandom=%vrandom,vindiv=%vindiv) invest / ifix
panel(gls=standard,effects=indiv,$
   vrandom=%vrandom,vindiv=%vindiv) firmvalue / ffix
panel(gls=standard,effects=indiv,$
   vrandom=%vrandom,vindiv=%vindiv) cstock / cfix
panel(gls=standard,effects=indiv,$
   vrandom=%vrandom,vindiv=%vindiv) ones / constfix
linreg(title="Random Effects using Transformed Data") ifix
# constfix ffix cfix
*
preg(method=random,vcomp=wh) invest
# constant firmvalue cstock

Output

Panel Regression - Estimation by Fixed Effects

Dependent Variable INVEST

Panel(20) of Annual Data From 1//1935:01 To 10//1954:01

Usable Observations 200

Degrees of Freedom 188

Centered R^2 0.9440725

R-Bar^2 0.9408002

Uncentered R^2 0.9615675

Mean of Dependent Variable 145.95825000

Std Error of Dependent Variable 216.87529623

Standard Error of Estimate 52.76796595

Sum of Squared Residuals 523478.14739

Regression F(11,188) 288.4996

Significance Level of F 0.0000000

Log Likelihood -1070.7810

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. Constant 0.0000000000 0.0000000000 0.00000 0.00000000

2. FIRMVALUE 0.1101238041 0.0118566942 9.28790 0.00000000

3. CSTOCK 0.3100653413 0.0173545028 17.86656 0.00000000

Panel Regression - Estimation by Random Effects-Wansbeek-Kapteyn

Dependent Variable INVEST

Panel(20) of Annual Data From 1//1935:01 To 10//1954:01

Usable Observations 200

Degrees of Freedom 197

Mean of Dependent Variable 145.95825000

Std Error of Dependent Variable 216.87529623

Standard Error of Estimate 51.57596760

Sum of Squared Residuals 524035.84543

Log Likelihood -1095.2767

S.D. (eta_it) 52.7680

S.D. (mu_i) 83.5235

Hausman Test(2) 2.165099

Significance Level 0.3387309

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. Constant -57.82187368 28.68561577 -2.01571 0.04383034

2. FIRMVALUE 0.10977763 0.01047110 10.48387 0.00000000

3. CSTOCK 0.30808136 0.01717229 17.94062 0.00000000

Panel Regression - Estimation by First Difference

Dependent Variable INVEST

Panel(20) of Annual Data From 1//1935:01 To 10//1954:01

Usable Observations 190

Degrees of Freedom 188

Skipped/Missing (from 200) 10

Centered R^2 0.4080548

R-Bar^2 0.4049061

Uncentered R^2 0.4288436

Mean of Dependent Variable 10.580789474

Std Error of Dependent Variable 55.606632649

Standard Error of Estimate 42.896251341

Sum of Squared Residuals 345936.61527

Log Likelihood -982.7621

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. FIRMVALUE 0.0890628288 0.0082341070 10.81633 0.00000000

2. CSTOCK 0.2786940167 0.0471564164 5.90999 0.00000002

Panel Regression - Estimation by Cross Individual SUR

Dependent Variable INVEST

Panel(20) of Annual Data From 1//1935:01 To 10//1954:01

Usable Observations 200

Degrees of Freedom 197

Log Likelihood -799.3006

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. Constant -1.896858713 0.184802520 -10.26425 0.00000000

2. FIRMVALUE 0.040795066 0.001827778 22.31949 0.00000000

3. CSTOCK 0.084165394 0.002110682 39.87591 0.00000000

Linear Regression - Estimation by Least Squares

Dependent Variable INVEST

Panel(20) of Annual Data From 1//1935:01 To 10//1954:01

Usable Observations 200

Degrees of Freedom 188

Centered R^2 0.9440725

R-Bar^2 0.9408002

Uncentered R^2 0.9615675

Mean of Dependent Variable 145.95825000

Std Error of Dependent Variable 216.87529623

Standard Error of Estimate 52.76796595

Sum of Squared Residuals 523478.14739

Regression F(11,188) 288.4996

Significance Level of F 0.0000000

Log Likelihood -1070.7810

Durbin-Watson Statistic 1.0789

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. FIRMVALUE 0.1101238 0.0118567 9.28790 0.00000000

2. CSTOCK 0.3100653 0.0173545 17.86656 0.00000000

3. IDUMMIES(1) -70.2967175 49.7079588 -1.41419 0.15895875

4. IDUMMIES(2) 101.9058137 24.9383232 4.08631 0.00006485

5. IDUMMIES(3) -235.5718410 24.4316165 -9.64209 0.00000000

6. IDUMMIES(4) -27.8092946 14.0777538 -1.97541 0.04968535

7. IDUMMIES(5) -114.6168128 14.1654333 -8.09130 0.00000000

8. IDUMMIES(6) -23.1612951 12.6687393 -1.82822 0.06910077

9. IDUMMIES(7) -66.5534735 12.8429734 -5.18209 0.00000056

10. IDUMMIES(8) -57.5456573 13.9931464 -4.11242 0.00005848

11. IDUMMIES(9) -87.2222724 12.8918932 -6.76567 0.00000000

12. IDUMMIES(10) -6.5678435 11.8268910 -0.55533 0.57932822

Linear Regression - Estimation by Least Squares

Dependent Variable INVEST

Panel(20) of Annual Data From 1//1935:01 To 10//1954:01

Usable Observations 200

Degrees of Freedom 197

Centered R^2 0.8124080

R-Bar^2 0.8105035

Uncentered R^2 0.8710896

Mean of Dependent Variable 145.95825000

Std Error of Dependent Variable 216.87529623

Standard Error of Estimate 94.40840333

Sum of Squared Residuals 1755850.4841

Regression F(2,197) 426.5757

Significance Level of F 0.0000000

Log Likelihood -1191.8024

Durbin-Watson Statistic 0.3582

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. Constant -42.71436944 9.51167603 -4.49073 0.00001207

2. FIRMVALUE 0.11556216 0.00583571 19.80259 0.00000000

3. CSTOCK 0.23067849 0.02547580 9.05481 0.00000000

Linear Regression - Estimation by Random Effects using Transformed Data

Dependent Variable IFIX

Panel(20) of Annual Data From 1//1935:01 To 10//1954:01

Usable Observations 200

Degrees of Freedom 197

Centered R^2 0.7701087

R-Bar^2 0.7677747

Uncentered R^2 0.7793720

Mean of Dependent Variable 22.50972149

Std Error of Dependent Variable 110.12986275

Standard Error of Estimate 53.07131291

Sum of Squared Residuals 554863.15798

Regression F(2,197) 329.9633

Significance Level of F 0.0000000

Log Likelihood -1076.6036

Durbin-Watson Statistic 0.9831

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. CONSTFIX -57.65456985 26.45569335 -2.17929 0.03049659

2. FFIX 0.10973383 0.01029150 10.66257 0.00000000

3. CFIX 0.30764686 0.01723808 17.84694 0.00000000

Panel Regression - Estimation by Random Effects-Wallace-Hussain

Dependent Variable INVEST

Panel(20) of Annual Data From 1//1935:01 To 10//1954:01

Usable Observations 200

Degrees of Freedom 197

Mean of Dependent Variable 145.95825000

Std Error of Dependent Variable 216.87529623

Standard Error of Estimate 51.57326630

Sum of Squared Residuals 523980.95397

Log Likelihood -1095.4262

S.D. (eta_it) 53.7452

S.D. (mu_i) 87.3580

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. Constant -57.86252975 29.90491885 -1.93488 0.05300461

2. FIRMVALUE 0.10978918 0.01072476 10.23698 0.00000000

3. CSTOCK 0.30818339 0.01749842 17.61207 0.00000000