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 these two
regressions.
TABLE 11.4
ILLUSTRATION OF WEIGH
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 Economic Performance,
International Economic Review, 19, 289
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
Research.
Sylos-Labini, P. (1974) Trade Unions, Inflation
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. (1960) A Generalization of Causal Chain Models, Econome
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 legal or
constructive obligation to pay further contribu
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 equation is used for prediction. In this case, yis ter
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
FINANCIAL ACCOUNTING III
Stocks at 30 September 19 1 were as f
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 1,289,800
Opening accumulated fund as at (July 2004) 7,64
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 Publishing Co.
Klein, L. R. and Y. Shinkai (1963) An Econo
(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, 213248.
Shapiro, H. T. and L. Halabuk (1976) Macro-Econom
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 the following facts.
Between 1 January 1995 and 31 Oct
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 Simultaneous,
Nonlinear, Implicit Equations in the Conte
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 amortise goodwill arising on consolidation. However in the
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 more than
one
study variables, the regression is termed
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 to provide numerical values to the parameters
of
economi
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 the two regressions?
b.What is the author assuming in
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 exercise 11.16, but this time regress the logarithm of expe
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 feature of the transformed model: It has no intercept
term.
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
of (11.3.8) can also be expressed as
*
2=
wiy
*
i
x
*
i
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 variable X(see Figure 11.10), one may transform
the orig
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, under the null hypothesis of
no heteroscedasticity, has a
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
i=1
f
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 (see Figure 11.11):
Yi
Xi
=
1
Xi
+2 Xi +
ui
Xi
=1
1
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 transform the original equation as follows,
Yi
E(Yi)
=
1
E(Yi)
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 relationship between var ( 2)under heteroscedasticity and
under
=
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=
gross national product in year t, and D=national defense e