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] |
|
—————————+— |
.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.