The name is absent



Stata Technical Bulletin

23


. sureg cl c2 c3 c4 c5

P

Equation

Obs Parms        RMSE

"R-sq"          F

—

cl

20

3    91.78166

0.9214   111.0618

0.0000

c2

20

3    13.27856

0.9136   88.06545

0.0000

c3

20

3    27.88272

0.7053   19.92612

0.0000

c4

20

3    10.21312

0.7444   25.13699

0.0000

cδ

20

3    102.3053

0.4403   6.361697

0.0027

—

I

Coef.

Std. Err.

t

p>∣t∣

[957. Conf.

—

Interval]

---------+.

—

cl          I

market1 ∣

.120493

.0234601

5.136

0.000

.0738481

.1671379

stockl I

.3827462

.0355419

10.769

0.000

.3120793

.453413

„cons I

-162.3641

97.03215

-1.673

0.098

-355.29

30.56183

—————————⅛-

—

c2          I

market2 ∣

.069S4S6

.0183279

3.795

0.000

.0331048

.1059864

stock2 I

.308S44S

.028053

10.999

0.000

.2527677

.3643213

„cons I

.5043113

12.48742

0.040

0.968

•24.32402

25.33264

—————————⅛-

—

c3          I

market3 I

.0372914

.0133012

2.804

0.006

.010845

.0637379

stock3 I

.130783

.0239163

5.468

0.000

.083231

.178335

„cons I

-22.43892

27.67879

-0.811

0.420

•77.47177

32.59393

—————————⅛-

—

c4          I

market4 ∣

.0570091

.0123241

4.626

0.000

.0325055

.0815127

stock4 I

.0415065

.0446894

0.929

0.356

-.047348

.130361

„cons I

1.088878

6.788627

0.160

0.873

•12.40873

14.58649

—————————⅛-

—

c5          I

markets I

.1014782

.0594213

1.708

0.091

∙.0166671

.2196236

stocks I

.3999914

.1386127

2.886

0.005

.1243922

.6755905

_cons I

85.42324

121.3481

0.704

0.483

•155.8493

326.6957

Here, we instead estimate a random coefficients model

. use invest, clear

. xtrchh invest market stock, !(company) t(time)
Hildreth-Houck Random coefficients regression

—

invest I

Coef.

Std. Err.

z

P>∣z∣

[957. Conf.

—

Interval]

—————————+—
market I

.0807646

.0250829

3.220

0.001

.0316031

—

.1299261

stock I

.2839885

.0677899

4.189

0.000

.1511229

.4168542

_cons I

-23.58361

34.55547

-0.682

0.495

-91.31108

44.14386

Test of parameter constancy
chi(12)   = 603.994

P(X > chi) =   0.0000

Just as subjective examination of the results of our simultaneous equation model do not support the assumption of parameter
constancy, the test included with the random coefficient model also indicates that the assumption of parameter constancy is not
valid for this data. With large panel datasets obviously we would not want to take the time to look at a simultaneous equations
model (aside from the fact that our doing so was very subjective).

References

Greene, W. H. 1993. Econometric Analysis. 2d ed. New York: Macmillan.

Grunfeld, Y. and Z. Griliches. 1960. Is aggregation necessarily bad? Review of Economics and Statistics 42: 1-13.

Hildreth, C. and C. Houck. 1968. Some estimators for a linear model with random coefficients, Journal of the American Statistical Association 63:
584-595.

Johnston, J. 1984. Econometric Methods. New York: McGraw-Hill.

Swamy, P. 1970. Efficient inference in a random coefficient model. Econometrica 38: 311-328.

----. 1971. Statistical Inference in Random Coefficient Regression Models. New York: Springer-Verlag.



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