31
For comparison, we give the usual or unweighted
OLS regression results:
Yi =3417.833+148.767Xi
(81.136) (14.418) (11.6.3)
t= (42.125) (10.318) R
2=0.9383
In exercise 11.7 you are asked to compare
Fair, R. C. (1976) A Model of Macroeconomic Activity, Volume ZZ: The Empirical Model.
Cambridge:
Ballinger Publishing Company.
Fair. R. C. (1978) The Use of Optimal Control Techniques to Measure Econo
Suits, D. B. (1963) The Theory and Application of Econometric Models. Athens: Center of
Economic
Research.
Suits, D. B. (1964) An Econometric Model of the Greek Economy. Athens: Center of Economic
Res
l-66.
Walters, A. A. (1968) Econometric Studies of Production and Cost Functions, Encyclopedia of
the
Social Sciences.
Wold, H. (1954) Causality and Econometrics, Econometrica, 22, 162- 177.
Wold, H.
201,250 124,750
QUESTION FIVE
(a) (i) Defined contribution plans are post-employment benefits plans under which an
enterprise pays fixed contribution into a separate entity (a fund) and will have no l
k which gives the fitted model as
12 12 ( , ,., , , ,., ).
kk yfXX X
11
When the value of yis obtained for the given values of
12, ,., ,
k XX Xit is denoted as yand called as
fitted value.
The fitted
The following information is relevant to the preparation of the Head Office, Branch and whole
businessTrading and Profit and Loss Accounts for the
year ended 30 September 19 1:
Lesson Nine 538
FINANCI
Withdrawals from scheme (15,000)
Net additions by members 656,800
Return on investments:
Interest on investments 640,000 640,000
Other expenses:
Management expenses (7,000)
Net change in net assets 1,
Studies of the U.S. Economy. Philadelphia: University of Pennsylvania Press.
Klein, L. R. and A. S. Goldberger (1955) An Econometric Model of the United States, 1929-1952.
Amsterdam: North-Holland Pub
(eds.), The Brookings Model: Perspective and Recent Developments. Amsterdam: North-Holland
Publishing Co.
Sargent, T. J. (1981), Interpreting Economic Time Series, Journal of Political Economy, 8Y, 21
10,000
3,500
Value of net estate 1,500
Current Liabilities
Bank overdraft
(secured on plant)
3,000
Creditors 5,000
8,000 2,000
11,000
Capital 7,500
Finance lease on vehicles 3,500
11,000
You establish
Fromm, G. and P. Taubman (1968) Policy Simulations with an Econometric Model. Washington,
D.C.:
Brookings Institution.
Gallant, A. R. and D. W. Jorgenson (1979) Statistical Inference for a System of S
cost of sales.
(vi) On 31 March 200 all the inter company balances are in agreement with Afro Ltd owing Piki Ltd
sh. 24 million and Ademo Ltd owing Afro Ltd sh.18 million.
(vii) The group does not amo
there are more than one independent variables, then it is called as multiple regression model. When
there
is only one study variable, the regression is termed as univariate regression. When there are
1
Chapter 1
Introduction to Econometrics
Econometrics deals with the measurement of economic relationships. It is an integration of economics,
mathematical economics and statistics with an objective t
for a random sample of 30 firms, the following regression results were
obtained
*
:
W=7.5+ 0.009N
(1)
t=n.a. (16.10) R
2=0.90
W/N= 0.008+ 7.8(1/N)
(2)
t=(14.43) (76.58) R
2=0.99
a.How do you interpret
d.Obtain Whites heteroscedasticity-consistent standard errors and
compare those with the OLS standard errors. Decide if it is worth
correcting for heteroscedasticity in this example.
11.17.Repeat exer
Given assumption 2, one can readily verify that E(v
2
i
)=
2
, a homoscedastic situation. Therefore, one may proceed to apply OLS to (11.6.8),
regressingYi/
Xi on1/
Xi and
Xi
.
Note an important featu
a.If lnui is to have zero expectation, what must be the distribution
ofui?
b.IfE(ui)=1, will E(lnui)=0? Why or why not?
c.IfE(lnui) is not zero, what can be done to make it zero?
11.5.Show that
*
2
o
u
2
i
=
2
X
2
i
(11.6.5)
36
If, as a matter of speculation, graphical methods, or Park and Glejser
approaches, it is believed that the variance of ui is proportional to the
square of the explanatory v
u
2
i =6,219,665 +229.3508 Salesi 0.000537Sales
2
i
se=(6,459,809) (126.2197) (0.0004)
(11.7.6)
t= (0.9628) (1.8170) (1.3425)
R
2=0.2895
Using the R
2
value and n=18, we obtain nR
2=5.2124, which, und
k
i=1
f
is
2
i
f
i
=
f
is
2
i
f
provides an estimate of the common (pooled) estimate of the population
variance
2
, wheref
i =(ni 1),ni being the number of observations in
theith group and where f =
k
u
2
i
=
2
Xi (11.6.7)
If it is believed that the variance of ui, instead of being proportional to the
squaredXi
, is proportional to Xi itself, then the original model can be transformed as follows (s
u
2
i
=
2
[E(Yi
)]
2
(11.6.9)
Equation (11.6.9) postulates that the variance of ui is proportional to the
square of the expected value of Y(see Figure 11.8e). Now
E(Yi)=1+2Xi
Therefore, if we transfor
var ( 2)=
2
x
2
i
x
2
i
ki
x
2
i
The first term on the right side is the variance formula given in (11.2.3),
that is, var ( 2) under homoscedasticity. What can you say about the
nature of the relation
=
wiYi
wi
X
*
=
wiXi
wi
11.6.For pedagogic purposes Hanushek and Jackson estimate the following
model:
Ct =1+2GNPt +3Dt +ui (1)
whereCt =aggregate private consumption expenditure in year t, GNP
t=
gro