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ASSIGNMENT #2
Economics 4F03 2022 Section 3 Paul Contoyannis
SUBMIT TO THE DROPBOX IN A2L. Due OCT 24
th
@7.00pm
1.
T h e f o l l o w i n g r e g r e s s i o n h a s b e e n e s ti m a t e d :
Dependent Variable:
disability1
Independent Variables:
(1) Constant, (2) Person's age (ecage26), (3) male1
“male1” is equal to 1 for males and 0 for females;
disability1 is equal to 1 for disabled and 0 for not disabled
. regress disability1 ecage26 male1
Source |
SS
df
MS
Number of obs =
47705
-------------+------------------------------
F(
2, 47702) = 2979.42
Model | 1137.25995
2 568.629974
Prob > F
= 0.0000
Residual | 9104.04738 47702 .19085253
R-squared
=
0.1110
-------------+------------------------------
Adj R-squared = 0.1110
Total | 10241.3073 47704 .214684457
Root MSE
= .43687
------------------------------------------------------------------------------
disability1 |
Coef. Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
ecage26 |
.0084218
.0001093
77.04
0.000
.0082076
.0086361
male1 |
-.0084567
.0040058
-2.11
0.035
-.0163082
-.0006052
_cons |
-.0891858
.0060068
-14.85
0.000
-.1009592
-.0774125
------------------------------------------------------------------------------
1.1 Interpret the estimated values (including the constant) in the following two senses:
a) What do the estimated coefficients mean mathematically? Use the estimated values in your
answer.
Cons – the predicted probability that a zero-year-old female would have a disability is -0.089;
2 marks
male1 – at any age the predicted probability of being disabled is less for a male than a female;
the difference is -0.008
2 marks
ecage26 – each additional year of age is associated with an increase of 0.008 in the predicted
probability of having a disability.
2 marks
b) What are some economic
reasons
why the estimated coefficients might take on the values
that they do?
Cons- such a value is, of course, impossible since probabilities must be within the range from 0 to
1.
2 marks
Disabilities (physical frailty) generally increase with age (our bodies wear out) and also reflect
the accumulated impact of any unhealthy lifestyle choices, so a positve coefficient would be
expected;
2 marks
males, on average, have fewer disabilities that females, due to higher income or to other
reasons, so the coefficient would be expected to be negatve
2 marks
1.2 You can use your estimated coefficients to form a linear function predicting the probability of a disability
for either sex at any age.
Solve this equation to find the age at which the predicted probability of a
disability for a female is equal to 0. Remember that for a female, the variable male1 = 0. For what age range
is the predicted probability of a disability < 0 for a female?
Solve 0 = -0.0891858 + 0.0084218*ecage26 for ecage26; the answer is
10.6
;
4 marks
hence the predicted probability would be negatve for
all ages younger than 10.
4 marks
1.3 Solve this same equation to find the age at which the predicted probability of a disability for a female=1.
For what age range is the predicted probability of a disability >1 for a female?
Solve 1 = -0.0891858 + 0.0084218*ecage26 for ecage26; the answer is
129.3
;
4 marks
hence the predicted probability would be greater than 1 for
all ages older than 129
.
4 marks
1.4 Briefly explain what both of these findings tell you about the problem of estimating a linear regression
when the dependent variable is a binary variable (i.e., either 1 or 0)
Because the estmated relatonship is
linear
, predicted values are not restricted to the 0-1 interval,
as they must logically be if interpreted as probabilities. Predicted probabilities outside the 0-1
range do not make sense
.
4 marks
N.B However, we note in this instance that a linear approximaton may provide a reasonable
representation over the relevant (in this case) age range. That is not always the case, and should
be checked. Alternatvely a probit or logit model can be used.
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Table 3
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