Download Econ 302 - EN / Bilkent University

Econ 301
Econometrics
Bilkent University
Department of Economics
Berument
The estimation of a demand function:
Data, reported below, is the observations on the consumption of chicken. The objective of
the research is to analyze chicken demand for the US is reported for the period, 19601982. Economic theory indicates that the quantity demanded for a good depends on its on
price, income, and the prices of alternative goods which might be substitute or
complementary commodities for the good in question. Regression equation representing
the demand relationship is:
Yt  1   2 X 2t  3 X 3t   4 X 4t  5 X 5t  ut
(1)
where Yt - per capita consumption of chicken, lb.
X 2t - real disposable income per capita $,
X 3t - real retail price of chicken per lb, cents,
X 4t - real retail price of pork per lb, cents,
X 5t - real retail price of beef per lb, cents,
a) Plot the data as scatter diagram for Yt and X2t. What can you say about the
relationship between Yt and X2t?
b) What are the signs do you expect for  2 and  3 ? Why?
c) What are the estimated coefficients? What are the economic interpretations of
these coefficients?
d) Write the fitted equation for Yˆi and compute the fitted values of the dependent
variable Yˆ using EVIEWS,
i
e) If you estimated the following specification, then how could you interpret α2 and
α3 estimates?
Yt  1   2 X 2t   3 X 3t  ut
(2)
f) What is wrong with equation (2)?
Let’s continue with the equation (1)
What is the overall significance of equation (1)?
Test Ho: β2 = 0 vs H1 β2≠0 if variance is known
Test Ho: β2 = 0 vs H1 β2≠0 if variance is not known
Test Ho: β2 = 1 vs H1 β2≠1 if variance is known
Test Ho: β2 = 1 vs H1 β2≠1 if variance is not known
a. Test with t-test
b. Test this with F-test
l) Test Ho: β2 + β3 = 0 vs H1: not Ho if variance is known
m) Test Ho: β2 + β3 = 0 vs H1: not Ho if variance is not known
a. Test with t-test
b. Test with F-test
Assume that the variance is not known and estimated
n) Test Ho: 3β2 + 2β3 = 0 vs H1: not Ho
o) Test Ho: 3β2 + 2β3 = 4 vs H1: not Ho
p) Test Ho: β2 = β3 = 0 vs H1: not Ho
q) Test Ho: β2 = β3 = β4 = β5 =0 vs H1: not Ho
r) Test Ho: β2 = β3 = 1 vs H1: not Ho
s) Test Ho: β2 = 2*β3 = 1 vs H1: not Ho
t) Test Ho: 3β2 + 2β3 = 4, β4 = 1/3, 2β5 =β1 vs H1: not Ho
g)
h)
i)
j)
k)
u)
v)
w)
x)
Compute the residual values.
Verify that  uˆi is equal to zero.
Verify that
;
;
and
If we consider take the means of independent variable and get the its fitted values
(
;
;
and
) then prove that
.
y) Prove that
.
z) What is
?
aa) What signs do you expect for  4 and  5 ? What signs do you estimate? What are
the economic interpretations?
bb) Which are the coefficients that are statistically significant?
cc) What problems do you foresee in equation (1), answer this after estimating the
correlation coefficient between the variables?
dd) If X 6 t is a composite variable of price of pork and beef, constructed by weighted
average, used in regression to avoid the problem of multicollinearity, how is the
estimation of demand equation in the following form and its results differ from
eq. (1)?
Yt  1   2 X 2t  3 X 3t   6 X 6t  ut
(2)
ee) For alternative formulations of the model with different number of explanatory
variables and compare the residuals and sum of squared residuals.
ff) What are the R2’s of model (1) and model (2)? Which is better? Can you compare
the R2’s? What is an alternative statistic that you can use?
gg)
Obs
Y
X2
X3
X4
X5
X6
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
27.80000
29.90000
29.80000
30.80000
31.20000
33.30000
35.60000
36.40000
36.70000
38.40000
40.40000
40.30000
41.80000
40.40000
40.70000
40.10000
42.70000
44.10000
46.70000
50.60000
50.10000
51.70000
52.90000
397.5000
413.3000
439.2000
459.7000
492.9000
528.6000
560.3000
624.6000
666.4000
717.8000
768.2000
843.3000
911.6000
931.1000
1021.500
1165.900
1349.600
1449.400
1575.500
1759.100
1994.200
2258.100
2478.700
42.20000
38.10000
40.30000
39.50000
37.30000
38.10000
39.30000
37.80000
38.40000
40.10000
38.60000
39.80000
39.70000
52.10000
48.90000
58.30000
57.90000
56.50000
63.70000
61.60000
58.90000
66.40000
70.40000
50.70000
52.00000
54.00000
55.30000
54.70000
63.70000
69.80000
65.90000
64.50000
70.00000
73.20000
67.80000
79.10000
95.40000
94.20000
123.5000
129.9000
117.6000
130.9000
129.8000
128.0000
141.0000
168.2000
78.30000
79.20000
79.20000
79.20000
77.40000
80.20000
80.40000
83.90000
85.50000
93.70000
106.1000
104.8000
114.0000
124.1000
127.6000
142.9000
143.6000
139.2000
165.5000
203.3000
219.6000
221.6000
232.6000
65.80000
66.90000
67.80000
69.60000
68.70000
73.60000
76.30000
77.20000
78.10000
84.70000
93.30000
89.70000
100.7000
113.5000
115.3000
136.7000
139.2000
132.0000
132.1000
154.4000
174.9000
180.8000
189.4000