Regression method
(basic level)
Joze Sambt
NTA Hands-On Workshop
Berkeley, CA
January 14, 2009
Why do we need
a regression method?
Education and health care expenditures
are usually reported at the household
level, but in NTA context everything has
to be assigned to individuals
Example of the linear relation
between two variables
2500
Consumption
2000
1500
y = 0.4998x + 678.93
R2 = 0.8269
1000
500
0
0
1000
2000
Income
3000
The idea of the regression analysis
yi   0  1 x1i   2 x2i  ... k xki   i
For example:
CONSUMPTION '  678.93  0.4998 * INCOMEi
◦ The slope coefficient is about 0.50, suggesting that an
increase in real income of 1 dollar is leading, on average,
to an increase of about 50 cents in real consumption
expenditure.
◦ Constant: about 679 dollars is the level of autonomous
consumption (in the case that person receives no income,
i.e. if the value of the independent variable is 0).
Allocating health expenditure
Private health expenditure of household j is regressed on
the number of household members in each age group x

CFH j    ( x) M j ( x)
x 0
To use broader age groups could be a good idea (because
of degrees of freedom, small number of observations in
some age groups). Don’t worry, your age profile will
most likely not look like stairs because of that.
CFH j  1 ( M j ,04 )   2 ( M j ,59 )  ...  19 ( M j ,90 )
STATA code

Grouping into 5-year age groups:
gen agegrp=age
recode agegrp (0/4=2.5) (5/9=7.5)
(10/14=12.5) (15/19=17.5) … (90/max=90)

Calculating the number of individuals in each
age group (by households):
by
by
by
by
by
…
by
hhid:
hhid:
hhid:
hhid:
hhid:
egen
egen
egen
egen
egen
p4=sum(agegrp==2.5)
p9=sum(agegrp==7.5)
p14=sum(agegrp==12.5)
p19=sum(agegrp==17.5)
p24=sum(agegrp==22.5)
hhid: egen p90=sum(agegrp==90)
Household health expenditures are regressed on
the number of individuals in each age group
within a household (without an intercept),
reg cfhc p4 p9 p14 p19 p24 p29 p34 p39 p44
p49
p54 p59 p64 p69 p74 p79 p84 p89 p90
[w=weight], robust noconstant
intercept
supressed!
… and coefficients are stored for a future use
gen
gen
gen
…
gen
bp4=_b[p4]
bp9=_b[p9]
bp14=_b[p14]
bp90=_b[p90]
However,
◦ summing up obtained values for all members
of the household results in different amount
of health expenditures than reported in the
survey (at the household level).
◦ Therefore: we need further adjustment
whereby we use only relative size of those
coefficients between household members, i.e.
we consider them as within household shares
(weights).
For example:
Assume a household with three individuals:
◦ child, aged 6 years
◦ mother, aged 33 years
◦ father, aged 36 years
Let’s further assume that the obtained (from the regression)
coefficient for the age group 5-9 years is 20, for the age group of
30-34 years it is 80, and for the age group of 35-39 years is 100.
This would sum up to 200. However, in the survey household has
reported 300 dollars for health expenditures. This means, we have
to rescale those values, so they will match 300:
Regression
coefficients
Share
Rescaled
values
Child
20
10%

30
10%
Mother
80
40%

120
40%
Father
100
50%

150
50%
SUM
200
300
Share
(remains the
same)
STATA code
Coefficients are assigned corresponding age groups
(coefficients by age groups are multiplied with the
number of household members by age groups):
gen hp4=bp4*(agegrp==2.5)
gen hp9=bp9*(agegrp==7.5)
gen hp14=bp14*(agegrp==12.5)
…
gen hp90=bp90*(agegrp==90)
egen sum=rsum(hp4 hp9 hp14 hp19 hp24 hp29 hp34
hp39 hp44 hp49 hp54 hp59 hp64 hp69 hp74 hp79 hp84
hp89 hp90)
Sum of weights by households are calculated (i.e.
household estimated expenditures on health) :
by hhid:egen total=sum(sum)
Relative shares of weights (of individuals) in
total sum of household weights are used to
distribute reported health expenditures
(CFHj) among household members
CFH ij 
CFH j  ( x)
  ( x) M
j
( x)
… rewritten as STATA code:

Relative share for each household member is calculated (by
dividing individuals’ coefficients with a total sum of coefficients
of all household members):
gen rhp4=hp4/total
replace rhp4=0 if rhp4==.
gen rhp9=hp9/total
replace rhp9=0 if rhp9==.
…
gen rhp90=hp90/total
replace rhp90=0 if rhp90==.

Finally, relative shares of household members of each
household are multiplied with reported health expenditures of
that household to obtain health expenditures by individuals:
gen th4=cfhc*rhp4
gen th9=cfhc*rhp9
…
gen th90=cfhc*rhp90
It has already been said during the
workshop: if you have information…

about the subcategories of the expenditures (for example
information on household members using inpatient care
(IN) or out-patient (OUT) services), use that information:


x 0
x 0
CFH j    ( x) IN j ( x)    ( x)OUT j ( x)

about household members being enrolled (E) and nonenrolled (NE) into the educational process, use that
information:


x 0
x 0
CFE j    ( x) E j ( x)    ( x) NE j ( x)
… or if you…

have external profile of per capita utilization by age
(U) and number of household members by age (M),
use that information:

CFH j    ( x)U ( x) M j ( x)
x 0

have detailed data available (for example separately
reported expenditures on primary, secondary and tertiary
education level), use them: limit the analysis only to
those age groups, for which the expenditures are
relevant. This is especially relevant for education
expenditures.
Some final details

There is no constant term (i.e. estimated in
homogeneous form), so the household consumption
is fully allocated.

Constrain negative values of the coefficients to zero.

In the case of education – do not apply smoothing.

You might want to have two age groups (age 0 and
age 1-4) instead of the 0-4 age group, to capture
higher health expenditures in the first year of age,
reported in countries where such detailed data is
available.