Transcript supplement13 - Ka

Supplement 13:
An example of regression analysis
A test of the relation between fertility
rate and mortality rate?
Ka-fu Wong © 2007
ECON1003: Analysis of Economic Data
Supplement13-1
Are mortality and fertility related?
 Demographers have pointed out that in many cases mortality
decline precedes fertility decline, which suggests a causal link from
falling mortality to falling fertility.
 The model of Barro and Becker (1989) implies falling mortality
rates tend to lower the cost of having a surviving child, hence
fertility actually increases, not decreases, as mortality declines.
(Instead of emphasizing mortality decline, the Barro-Becker
framework points to the quantity-quality tradeoff as an explanation
for fertility decline: parents choose to have smaller families in order
to invest more in the education of each child.)
Barro, Robert and Gary S. Becker (1989): “Fertility Choice in a Model of Economic
Growth,” Econometrica 57(2): 481-501.
Ka-fu Wong © 2007
ECON1003: Analysis of Economic Data
Supplement13-2
Are mortality and fertility related?
 Kalemli-Ozcan (2003) argues when mortality is stochastic and
parents want to avoid the possibility of ending up with very few (or
zero) surviving children, a “precautionary” demand for children
arises.
 Extending the theoretical model of Barro and Becker (1989),
Doepke (2005) predicts a negative relationship between mortality
and fertility.
Kalemli-Ozcan, Sebnem (2003) “A Stochastic Model of Mortality, Fertility, and Human
Capital Investment.” Journal of Development Economics, 70 (1): 103-118
Doepke, Matthias (2005): “Child Mortality and Fertility Decline: Does the Barro-Becker
Model Fit the Facts?” Journal of Population Economics, 18(2): 337-366.
Ka-fu Wong © 2007
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Are income and fertility related?
 Burdsall (1988) suggest the so-called Norm curve, which describes
fertility as a monotonically declining function of per capita income.
Birdsall, N. (1988): “Economic Approaches to Population Growth”, in Handbook of
Development Economics, by H. Chenery and T.N. Srinivasan, Eds, Vol. 1, Elsevier:
Amsterdam.
Ka-fu Wong © 2007
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Supplement13-4
Theme of this project
 We use fertility data across countries to estimate the relationship
between fertility and mortality and per capita income.
Ka-fu Wong © 2007
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Data sources and description
 World Development Indicator (WDI) 2002, available from the HKU
main library.
 Time: year 2000 only.
 172 countries (out of 207) with relevant variables
 GDP per capita (in 1995 US$) – a proxy for income per capita.
 Infant mortality rate (per 1,000 live births)
 Fertility rate (births per woman)
 Drop 35 countries:
 32 countries did not report GDP per capita.
 Additional 3 countries did not report fertility rate.
 Do not consider adult illiteracy rate because substantial number of
developed countries (such as UK and US) did not report this
variable.
Ka-fu Wong © 2007
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Supplement13-6
Descriptive statistics: Fertility rate
count
172
mean
3.15
Standard deviation
1.60
1st quartile
1.77
minimum
1.02
median
2.63
maximum
7.22
3rd quaritle
4.42
range
6.20
interquartile range
2.64
34.3% countries below replacement fertility rate: (=2.1).
0
1
2
3
4
5
6
7
8
Hong Kong
Ka-fu Wong © 2007
ECON1003: Analysis of Economic Data
Supplement13-7
Descriptive statistics: Mortality rate
count
172
mean
38.76
Standard deviation
35.99
1st quartile
10.01
minimum
2.90
median
23.60
maximum
153.60
3rd quaritle
60.00
range
150.70
interquartile range
50.00
0
50
100
150
200
250
Hong Kong
Ka-fu Wong © 2007
ECON1003: Analysis of Economic Data
Supplement13-8
Descriptive statistics: GDP per capita
count
172
mean
6,617.45
Standard deviation
10,809.61
1st quartile
528.212
minimum
115.88
median
1,611.19
maximum
56371.99
3rd quaritle
5,372.00
range
56256.12
interquartile range
4,843.79
0
10000
20000
30000
40000
Hong Kong
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ECON1003: Analysis of Economic Data
50000
60000
Luxembourg
Supplement13-9
Scatter plot: fertility vs. GDP per capita
y = -7E-05x + 3.6178
R2 = 0.2245
8
7
6
fertility rate
(y)
5
4
3
2
1
0
-1 0
10000
20000
30000
40000
50000
60000
GDP per capita (x)
Ka-fu Wong © 2007
ECON1003: Analysis of Economic Data
Supplement13-10
Scatter plot: fertility vs. mortality
8
7
(y)
fertility rate
6
5
4
3
2
y = 0.0382x + 1.6748
R2 = 0.739
1
0
0
50
100
150
200
mortality rate, infant (x)
Ka-fu Wong © 2007
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Regression model I:
Fertility
=
3.617
-
0.07005
Stderror
(0.1263)
(0.00998)
P-value
[5.71E-67]
[5.18E-11]
GDP
Statistically different from
zero at 1% level of
significance.
Economically, we expect fertility rate to lower
by 0.07005 per woman when the per capita
income increases by US$1000.
Or: fertility rate to lower by 7 per 100 women
Ka-fu Wong © 2007
ECON1003: Analysis of Economic Data
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Regression model I:
ANOVA
Source
SS
df
MS
F
p-value
Regression
98.05
1
98.05
49.22
5.18E-11
Residual
338.63
170
1.99
Total
436.68
171
R-square
0. 225
Rejects the hypothesis that all
coefficients are jointly zero.
The explanatory variable (per
capita income) explains
22.5% of the variation in
fertility rate.
Ka-fu Wong © 2007
ECON1003: Analysis of Economic Data
Supplement13-13
Regression model II:
Fertility
=
1.7950
-
0.00973
GDP
+
0.0367
Stderror
(0.1230)
(0.00664)
(0.0020)
P-value
[9.44E-32]
[0.1446]
[2.83E-42]
Not statistically different
from zero even at 10% level
of significance.
Economically, holding
mortality rate constant, we
expect fertility rate to lower
by 0.00973 per woman
when the per capita income
increases by US$1000.
Ka-fu Wong © 2007
mortality
Statistically different
from zero at 1% level of
significance.
Economically, holding per
capita income constant, we
expect the fertility rate to rise
by 0.0367 per woman when
mortality increases by 1 infant
death per thousand births.
ECON1003: Analysis of Economic Data
Supplement13-14
Regression model II:
ANOVA
Source
SS
df
MS
F
p-value
Regression
324.125
2
162.0623
243.34
1.76E-50
Residual
112.555
169
0.666
Total
436.677
171
R-square
0.742
Rejects the hypothesis that all
coefficients are jointly zero.
The explanatory variables
together explain 74.2% of the
variation in fertility rate.
Ka-fu Wong © 2007
ECON1003: Analysis of Economic Data
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Regression model III:
Fertility
=
1.6748
+
0.0382
Stderror
(0.0919)
(0.0017)
P-value
[7.89E-42]
[1.86E-51]
mortality
Statistically different from
zero at 1% level of
significance.
Economically, we expect
fertility rate to increase by
0.0382 per woman when
mortality increases by 1
infant death 1 per 1000
birth.
Ka-fu Wong © 2007
ECON1003: Analysis of Economic Data
Supplement13-16
Regression model III:
ANOVA
Source
SS
df
MS
F
p-value
Regression
322.69
1
322.69
481.28
1.86E-51
Residual
113.98
170
0.67
Total
436.68
171
R-square
0. 739
Rejects the hypothesis that all
coefficients are jointly zero.
The explanatory variable (per
capita income) explains
73.9% of the variation in
fertility rate.
Ka-fu Wong © 2007
ECON1003: Analysis of Economic Data
Supplement13-17
Conclusion
 Fertility rate is strongly directly related to mortality rate.
 When mortality rate is included, the explanatory power of income per
capita on fertility rate seems small.
 Cautions:
 Although the model setup seems to suggest a low mortality rate will
cause a low fertility rate. The reverse could be true. Countries with a
low fertility rate may spend more on infant survival and hence a low
mortality rate.
 The true relationship need not be linear, e.g., Strulik and Sikandar
(2002).
Strulik, Holger and Siddiqui Sikandar (2002): “Tracing the income-fertility nexus:
Nonparametric Estimates for a Panel of Countries,” Economics Bulletin, 15 (5): 1-9.
Ka-fu Wong © 2007
ECON1003: Analysis of Economic Data
Supplement13-18
Supplement 13:
An example of regression analysis
A test of the relation between fertility
rate and mortality rate?
- END -
Ka-fu Wong © 2007
ECON1003: Analysis of Economic Data
Supplement13-19