2.2.4 Smoothing

The per capita age profiles are noisy, particularly at ages with relatively few observations, and except as noted below should be smoothed. The following guidelines should be followed:

• The per capita education profile should not be smoothed.

• Basic components should be smoothed, but not aggregations. For example, private health consumption and public health consumption profiles should be smoothed, but the sum of the two should not be smoothed.

• The objective is to reduce sampling variance but not eliminate what may be “real” features of the data. For example,

• Public health spending may increase dramatically when individuals reach an age threshold, e.g., 65. This kind of feature of the data should not be smoothed away.

• Due to unusual high health consumption by newborns, we tend not to smooth health consumption by age 0. This could be done by including estimated unsmoothed health consumption by newborns to the age profile of smoothed private health consumption by other age groups.

• Only adults (usually ages 15 and older) receive income, pay income taxes and make familial transfer outflows. Thus, when we smooth these age profiles, we begin smoothing from the adults age, excluding those younger age group who do not earn income.

• However, problem arises when some beginning age group may appear to have negative values for these variables. This could be solved by replacing the negative by the unsmoothed values for the beginning age group.

There are a couple of steps to smoothing the per capita profile. The first step is to create a spreadsheet, which contains unsmoothed age profile and the number of observations for each age. The second step is to use Friedman's SuperSmoother (supsmu function in R) to smooth the per capita profile incorporating the number of observations. The following is the R code to use the command “supsmu”. Suppose “thyl.csv” is the file name (tab delimited excel file format), yl the unsmoothed variable name, and sample is the number of observations for each age in the data. The R programming code is R code;

The alternative smoothing method is “lowess” smoothing. The procedure is found to be unreliable because it does not incorporate sample weights. We recommend that it not be used. However, some researchers may feel more comfortable using the Stata rather than the R program, and would prefer to use the lowess smoothing method. If that is the case, before smoothing the age profile using the lowess command, the survey data are should be adjusted to incorporate the sample weight of each observation. Each observation is duplicated in proportion to its sample weight to produce a representative sample. Then, the lowess command is used to smooth the representative sample.

Illustrative Examples.

After smoothed, the national population age distribution is used to the age profiles to match the macro control total, as described in Aggregate Controls. Figure 2 shows the per capita consumption profile by component for Taiwan in 1998. Most consumption is private rather than public, and in many important areas, food, housing, and clothing, for example, the private sector dominates. The public sector is also important, particularly in education and health. By and large, however, it is private consumption that shapes the consumption side of the lifecycle equation. The sharp increases among children in Taiwan reflect private spending on education.

Source: Lee, Lee, and Mason (2008).

Figure 3 presents the per capita labor income profile by component for Finland and the Philippines. Note that, for purposes of comparison, each curve is normalized by dividing it by the unweighted average labor income for ages 30-49. This age range was chosen to exclude younger ages that might be affected by educational enrollments, and older ages that might be affected by retirement. The two labor income profiles are similar, inverse U-shaped. It should come as no surprise that the share of self-employment income is much larger for the Philippines than for Finland. The share of self-employment income is 52% for the Philippines, and 5% for Finland. To the contrary, the share of fringe benefits is much larger for Finland (22%), compared with the Philippines (5%).

Source: Authors’ calculation.

More information on smoothing is available in 5.3 Other Methods section.