**New Zealand vs. USA**

Statistics New Zealand provides
information on individual and household income, including wages and salaries,
self-employment, government transfers, and investment income. Here, we analyse only
the age dependence of mean income. All income estimates are collected in the New Zealand
Income Surveys
(NZIS), which is an annual supplement to the Household Labour Force Survey
(HLFS), conducted during the June quarter (1 April to 30 June). Based on NZIS data
a comprehensive range of income statistics is produced. The corresponding tables
for the years between 1998 and 2014 were downloaded from the NZIS website. They
cover almost the same period as in the UK. Among other estimates, these tables
contain individual weekly mean incomes in relatively narrow (5-year-wide) age
groups.

There exists one potentially significant problem with the
NZ income survey. The HLFS includes only 15,000 households, randomly selected
throughout New Zealand, and the final NZIS personal income dataset consists of
approximately 28,000 records. This is definitely not enough to cover the whole
diversity of incomes depending on age, gender, and ethnicity. In the USA, the
CPS includes more than 80,000 households and more than 200,000 individual
records. Nevertheless, the CPS PIDs demonstrate measurable problems with the
higher income estimates, which are subject to larger fluctuations between
adjacent income bins and with time. Therefore, one may suggest that the New Zealand
data demonstrate even larger fluctuations in the aggregate income estimates between
adjacent age bins than we have observed in the CPS data. In this context, we consider
the term “fluctuations” as the deviations from smooth curves described by
function 1-exp(-a/

*t*), where*t*is the work experience and a>0, before the critical age and by exponential fall above this age [1].
Figure 13
displays seventeen (nominal) mean income curves expressed in NZD, which
illustrate the evolution of the age-dependent mean income in New Zealand from
1998 to 2014. Since we use nominal incomes, the earliest (1998) curve (black
dotted line) is below all other curves almost everywhere, except may be the
smallest work experience. The midpoints of all 5-year bins are shown by
circles. The 2014 curve is above others almost everywhere. As was discussed
above, the deviation from theoretically predicted smooth lines, similar to
those in Figure 3, is relatively high and thus may introduce significant bias
in the comparison with the U.S. The largest problem may arise for work
experience above 40 years, where some curves (e.g. 2002, 2007, 2010, and 2013)
demonstrate the largest deviation from the adjacent curves. We leave the
explanation of these unexpected features with Statistics New Zealand.

Figure 13. The evolution of the
age-dependent mean income in New Zealand from 1998 to 2014. The 1998 curve
(black dotted line) is below all other lines almost everywhere. The midpoints
of all 5-year bins are shown by circles. The 2014 curve is above others almost
everywhere. The deviation from the expected smooth lines, like those in Figure
3, is relatively high and may introduce some bias in the comparison with the US.

As discussed in
paragraph 2.2, one way to carry out a cross country comparison of mean incomes
is to represent them in normalized form. In Figure 14, we display the curves
from Figure 13, but all divided by their respective peak values. As for the UK,
there are two important observations – the work experience corresponding to the
peak mean income increases with real GDP per capita and the 2014 curve now lies
below all other curves before the peak value and above almost all curves,
except few, after the peak work experience. In other words, the critical age
increases with time while the relative mean income of the younger population
decreases.

Using
the central segments of the dimensionless curves shown in Figure 15 we estimate
the age of peak mean incomes. For the 1998 curve, we find the peak slightly
above 32 years of work experience. Similar estimates are made for the years between
1999 and 2001. Unexpectedly, the 2002 curve peaks at 35 years. Neglecting this
and other years of anomalous behaviour, we observe that the peak gradually
shifts from 32 years to 36-37 years of work experience in the period from 2009
to 2014. Therefore, the observed change
in the age of peak mean income is about 5 years.

Figure 14. Same curves as in
Figure 12 with all mean income estimates normalized to the peak mean incomes
for the respective years.

Figure 15. The central segments
of the curves in Figure 14 are used to estimate the change in the age (work experience)
of peak mean income.

The
estimates of real GDP per capita in New Zealand are $15,404 and $20,526 for
1998 and 2014, respectively. Theoretically, the working experience should
increase from 32 years to 32√(20526/15404)=36.9 years. The difference between
theoretical estimates for 1998 and 2014 is ~5
years. It is in excellent agreement with the observed change. The square root
dependence of the peak age on GDP per capita is well confirmed by the evolution
of mean income in New Zealand.

Despite
the theoretically predicted change in the critical age confirms the observed
change, there is a significant discrepancy with the UK peak age estimates. The
level of real GDP per capita in New Zealand lags behind that in the UK by a few
thousand USD. In 1998, this difference was $3,623 and then slightly fell to
$3,273 in 2014. Under our framework, the peak age in the UK has to be larger
than that in New Zealand by several years, but we observe an opposite
situation. This contradiction needs detailed investigation, but here we just
refer to the accuracy of GDP estimates based on PPP conversion. There are some
controversial estimates, which indicate significant problems for some
countries. In 2014, TED provides the following estimates (in 1990 US$) of real
GDP per capita: Spain - $16,217, Portugal - $13,429, Estonia - $22,665,
Belorussia - $15,144. Hence, there are some doubts in the accuracy of TED
readings for some countries.

On
the other hand, the evolution of mean income with GDP provides an excellent
tool to measure the level of GDP. If to consider the US GDP as a reference, New
Zealand peak age of 36 years in 2014 corresponds to real GDP per capita observed
in the USA in 1996. This makes ~$25,000. In turn, the level in the UK in 2011
(32 years of work experience) corresponds to 1983/1984 - ~$19,500. These are only
crude estimates obtained from the peak age, but they definitely highlight some
problems with the GDP estimated reported by TED. Much more accurate estimates
are obtained by matching the whole mean income curves.

Figure 16 is
similar to Figure 10 for the UK and displays the evolution of peak-normalized
mean income in various age groups. In line with the observations in Figure 15
and the above discussion, the peak work experience resides in the bin from 30
to 34 years. The peak jumps into the elder group in 2012, and then in 2014. The
mean income in the group “32” started to fall relative to that in the group
“37”. The proportion of mean income has been increasing in all elder groups and
decreasing in the younger groups. Figure 16 elaborates on the trends observed
in the age bins around the peak value. From this Figure, the peak age will
likely move into the next age group at a horizon of 10 to15 years. Overall, in
the USA, UK and New Zealand we observed gradual increase in the age of peak
mean income, which shifts from younger age bins to elder bins. This is a
consequence of increasing GDP per capita.

Figure 16. The evolution of mean
income in all 5-year age groups normalized to the peak value in the same year.
In three youngest age groups (0 to 4, 5 to 9, 10 to 14, and 15 to 19 years of
work experience), the proportion of mean income has been falling since 1999. The
peak work experience shifted from the 30 to 34 years bin to the 35 to 39 years
bin in 2014.

Now, we have
come to the most sensitive method of cross country comparison – fitting the
normalized mean income curves with time delays of decades. The results of this
method best illustrate the level of match in income distribution between the
studied countries. As suggested in paragraph 2.1, the NZ curve for 2014 has to
match the U.S. curve for 1985. However, the peak mean income for the NZ2014
curve better corresponds to 1996. So, the best fit between the U.S. and NZ
curves should be the decider. As for the UK, we use the set of income microdata
published by the IPUMS. The original mean income estimates in one year age
intervals are smoothed with a centred MA(9).

Figure 17. Trends in the evolution of the relative mean
income in three age groups.

Figure 18
presents three panels with New Zealand and matching U.S. curves for 2014, 2006
(the midpoint of the 1998-2014 interval) and 1998. The best-fit curves in the
U.S. are 1988 ($20,525 in NZ vs. $22,500 in the U.S.), 1980 ($19,028 vs.
$18,577) and ($15,403 vs. $15,304). Overall, the fit between the NZ2014 and
US1988 is excellent except the period between 25 and 39 years of work
experience. This deviation might be the reason of the overestimated critical
age in Figure 15. One of possible causes for the observed fluctuations near the
peak mean income is the underrepresentation of the very high-income individuals
in the NZIS. They could be just missing from the survey because the sample is
sparse. A similar effect is observed
with the youngest black women in the USA. For the NZ2006 curve, the overall fit
by the US1980 curve is even better than that for the NZ2014. In 2006, real GDP
per capita in New Zealand was by $500 larger than that in the USA in 1980. This
might indicate some problems in the related GDP estimates in New Zealand as
well as larger fluctuations in the shape of mean income curves measured in the
U.S. and New Zealand. For the NZ1998,
the overall fit is the worst, as might be expected from lower accuracy of
income measurements in the past. Taking into account all fluctuations in GDP
and income measurements in New Zealand and U.S. the overall match and the
evolution of shape both support the universal character of the mean income
dependence on real GDP per capita.

New Zealand
provides a slightly longer time series of mean income, which covers a wider
range of real GDP per capita than in the UK. For New Zealand, the ratio of GDP
per capita in 2014 and 1998 is 1.33. For the UK, the ratio of GDP estimates in
2011 and 1999 is only 1.18. For the total growth in the critical age during the
corresponding periods these estimates give factors 1.15 and 1.08, respectively.
The set of income data provided by New Zealand might be superior if not the
observed level of fluctuations in income estimates and the doubts in the PPP
conversion of NZD into USD. The lesson learned with the NZ data is that income
measurements have to be carefully conducted and all problems should be resolved
before reporting them to the broader scientific community. It is difficult to
believe that the observed fluctuations are real.

Figure 18. Comparison of the normalized
mean income (weekly income from all sources) curves measured in New Zealand
USA.

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