African Journal of Mathematics and Computer Science Research Vol. 2(8), pp. 179-183, September, 2009
Available online at http:/www.academicjournals.org/ajmcsr
2009 Academic Journals
Full Length Research Paper
Causal relationship between gross domestic pr
hypothesis that there are constant returns to scale, i.e., (2+3)=1?
b.If there are constant returns to scale, how would you interpret regression (3)?
c.Does it make any difference whether we divide (1) by Lrather than
8.6. Critical values of R2
se=(0.91) (0.32) (0.20)
whereC=cigarette consumption, packs per year
P=real price per pack
Y=real disposable income per capita
a.What is the elasticity of demand for cigarettes with respect to price?
Is it statistically significant? If so, is it
290 PART ONE: SINGLE-EQUATION REGRESSION MODELS
You are to consider the following model:
Yi =1+2X2t +3X3t +4X4t +5X5t +6X6t +ut
a.Estimate the preceding regression.
b.What are the expected signs of the coefficients of this model?
the two estimated variances in the numerator.) From the Ftables in Appendix D, we see that the 5 and 1
percent critical Fvalues for 12 and 10 df are
2.91 and 4.71, respectively. The computed Fvalue is significant at the 5 percent level and is almost
b.Is it statistically significant?
c.If so, is it significantly different from unity?
d.A priori, what are the expected signs of X3(price of carnations) and X4
(income)? Are the empirical results in accord with these expectations?
e.If the coefficients of
Multiplier Tests: An Expository Note, American Statistician,vol. 36, 1982, pp. 153157.
Russell Davidson and James G. MacKinnon, Estimation and Inference in Econometrics,
Oxford University Press, New York, 1993, p. 456.
J. MacKinnon, H. White, and R.
exceeds the critical Fvalue, we reject the hypothesis of parameter stability
and conclude that the regressions (8.8.1) and (8.8.2) are different, in which
case the pooled regression (8.8.3) is of dubious value, to say the least.
Returning to our example,
variant of the ANOVA technique.
d.How would you compute the interest-rate elasticity of demand for
e.How would you test the significance of estimated R
8.17.Consider the following wage-determination equation for the British
should not be statistically significant in Step IV, for in that case the estimated
Yvalues from the linear model and those estimated from the loglinear
model (after taking their antilog values for comparative purposes) should
not be different. The same co
hypothesis on the basis of the t test, and do not reject the other individual hypotheses on the basis of
3.Reject the joint null hypothesis on the basis of the Fstatistic, and
reject each separate null hypothesis on the basis of the individual
the true error variances, we can obtain their estimates from the RSS given
in the regressions (8.8.1a) and (8.8.2a), namely,
Notice that, since there are two par
Sample Exam and Questions for Practices
DO NOT PANIC! THE NON-MULTIPLE-CHOICE
QUESTIONS ARE NOT GOING TO BE ON THE FINAL EXAM.
THEY ARE HERE FOR YOU TO PRACTICE.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
^ iY )2= ( ^ 0+ ^1 X i Y )2= [ ^ 1( X i X ) ]2
^ 21 ( X i X
(X i X )(Y iY )
Since we know that:
^ 1= i=1
( X i X )2
( X i X )2
X i X
( X i X )( Y iY )
( i=0)=1 p
# 3.2 ( Y i=1)= p Pr
E ( Y i )=0 Pr ( Y =0 ) +1 Pr(Y =1)= p
Var ( Y i )=E [ ( Y i r )2 ]
( Y i=0 ) +(1p)2 Pr (Y i=1)
(0 p) Pr
p ( 1 p )+(1 p) p= p(1 p)
success ( Y i=1 ) i=1
E ( ^p )=E
The tstatistic is 2.13 with a pvalue of 0.03 . The null hypothesis is rejected
At the 5 level because pvalue isless than 0.05 .
b) 95 confidence interval for 1 is cfw_ 1 1.96 SE ( 1 ) .
3.2 1.96 1.5=3.2 2.94
#2.7 (a) C = M (male) + F (female)
c = M + F
C =40,000+45,000=$ 85,000 Per year.
(b) cor r ( M , F )=
cov (M , F)
cov ( M , F )=cor ( M , F ) M F =0.8 12,000 18,000=172,800,000
(c) Standard deviation of C C
+ 2F +2 cov ( M
ECO480 - Econometrics 1
Computer Assignment 1
Due date: Friday, October 14, 2016 at the beginning of class
Instructions: The objective of computer assignments are to teach you how to apply the theories you learned in the class to analyzing
follows the Fdistribution with (n1k)and(n2k)df in the numerator and
the denominator, respectively, in our example k=2, since there are only two
parameters in each subregression.
, the preceding Ftest reduces
are unbiased estimators of
the true variances in the two subperiods. As a result, it can be shown that if
that is, the variances in the two subpopulations are the same (as
assumed by the Chow test)then it can be shown that
,F, and t.)
8.8.Suppose in the regression
ln (Yi/X2i)=1+2ln X2i +3ln X3i +ui
the values of the regression coefficients and their standard errors are
From this knowledge, how would you estimate the parameters
and standard errors of the following
b.How would you decide between the two models?
c.In what situations will the quadratic model be useful?
d.Try to obtain data on automobile sales in the United States over the
past 20 years and see which of the models fits the data better.
8.2.Show that th
Now the possible differences, that is, structural changes, may be caused by
differences in the intercept or the slope coefficient or both. How do we find
that out? A visual feeling about this can be obtained as shown in Figure 8.2.
But it would be useful
(0.008) (0.007) (0.038) (4)
t =(13.2) (3.3) (5.3) R
a.Are these results supportive of the CAPM?
b.Is it worth adding the variable s
to the model? How do you know?
c.If the CAPM holds, 1 in (2)
should approximate the average value of
Equation (3) is known as the restricted log-likelihood function (RLLF)
because it is estimated with the restriction that a priori 3is zero, whereas
Eq. (1) is known as the unrestricted log LF (ULLF)because a priori there
are no restrictions put on the par
model by including total fertility rate (TFR). The data on all these variables are already given in Table 6.4.
We reproduce regression (7.6.2) and
give results of the extended regression model below:
1.CMi =263.64160.0056 PGNPi 2.2316 FLRi (7.6.2)
are independent, we may use the weaker assumption that the values of Xvariables anduare
uncorrelated contemporaneously (i.e., at the same point in time). In this case OLS estimators
may be biased but they are consistent,that is, as the sample size increas
, setting the resulting expressions to zero, and solving, we obtain
the ML estimators of these estimators. The ML estimators of1,2, and3
will be identical to OLS estimators, which are already given in Eqs. (7.4.6)
to (7.4.8), but the error varian
It is very important to note that this statement is true only if E(ui)=wfor each i. However,
, that is, a different constant for each i, the partial slope coefficients may be biased
as well as inconsistent. In this case violation of Assum