ECONOMETRICS // Spring 2007
Cerebral Exercises: SET 7
1.
Consider the following regression results for mortgage debt outstanding in the United States.
ˆ
Y
=
155.7
+
0.8258 X
1

56.4393 X
2
se
=
(578.33)
(0.0635)
(31.454)
n = 16
tstat
=
(0.27)
(12.99)
(1.79)
R
2
= 0.9894
pval
=
(0.79)
(0.000)
(0.096)
AdjR
2
=
0.9878
where
Y
=
mortgage debt outstanding (billions$)
X
1
=
personal income (billions$)
X
2
=
new mortgage cost (loan interest rate %)
a)
Do the signs of the estimated coefficients make economic sense?
b)
How would you interpret the estimated regression coefficients?
c)
Does personal income have a significant effect on mortgage debt?
d)
Does new mortgage cost have a significant effect on mortgage debt?
e)
Does personal income have a significant positive effect on mortgage debt?
f)
Does new mortgage cost have a significant negative effect on mortgage debt?
g)
How much of the variation in mortgage debt outstanding is explained by this regression model with
personal income and mortgage cost as explanatory variables?
h)
How much of the variation in mortgage debt outstanding is NOT explained by this regression model
with personal income and mortgage cost as explanatory variables?
i)
How much of the variation in mortgage debt outstanding is explained by factors other than personal
income and mortgage cost?
j)
Provide a 95% CI estimate for
β
1
.
Provide a 95% CI estimate for
β
2.
a)
A priori, mortgage debt is expected to be positively related to income, i.e., the higher personal income is, the higher is a
person’s ability to borrow to finance new housing.
Since
β
1
is supposed to reflect this relationship,
it is estimate is
expected to be positive.
Moreover, based on demand theory, mortgage debt is expected to be negatively related to
mortgage cost, i.e., if the cost of owning a house goes up, then demand for new housing falls and so would demand for new
mortgages. And since
β
2
is supposed to reflect this relationship, it’s estimate is expected to be negative.
b)
According to the regression results, the partial regression coefficient of X
1
of 0.83 means that holding all other variables
constant (i.e., mortgage cost), the average amount of mortgage debt goes up by about 83 cents for every dollar increase in
income.
As expected, the relationship between the two is positive.
Likewise, the partial slope coefficient of –56.44 means that if mortgage cost goes up by 1 percentage point, the average
amount of mortgage debt outstanding goes down by about $56 billion, holding other things (i.e., income) constant.
As
expected, the relationship between the two variables is negative.
The intercept value of 155.7 means that if both income and mortgage cost variables assumed zero values, the mean , or
average, amount of mortgage debt outstanding will be about $157 billion.
This mechanical interpretation of the intercept
however, has no viable economic meaning in the present context.