Canada vs. USA
We finish our country analysis with
Canada, which provides an extended set of income data. These
data cover all persons who completed specific tax return forms for the year of
reference. Therefore, the data are related to tax purposes only and some
non-taxable income sources are missing from the dataset. In 2013, about
74.9% of Canadians (of all ages) filed tax returns. Most children do not file
tax return as well some elder people. That may
introduce age-specific bias in the estimates for children and pensioners.
Unlike the CPS survey, all data are extracted from administrative files. The
sample includes 100% of individuals who filed an individual tax return but not
all population. Depending on age, from 89% to 96% of the population is covered
by administrative records [8]. Overall, the population and income source
coverage is good for the purposes of our research.
Figure 19 depicts the evolution of real
mean income since 1976 [9]. Three years age shown for comparison – 1976, 1993 and 2011, i.e. with
approximately a 17 year step. The real mean income estimates are given in 2011
constant Canadian dollars and calculated in 10-year bins except the two
youngest age groups: under 20 years – the average age of 17 years is used, and
between 20 and 24 years of age. The curve for 2012 presents real mean incomes only
in 10-year bins; it was obtained from a different table provided by Statistics
Canada.
Figure 19. The evolution of age-dependent real mean
income (in 2011 constant Canadian dollars) in Canada from 1976 to 2012. All
estimates are given in 10-year bins except the two youngest age groups (below
20, and between 20 and 24). The curve for 2012 presents mean incomes only in
10-year bins and was obtained from a different table provided by Statistics
Canada. The highly unusual feature is the 1976 curve above the 1993 curve.
The first and highly unusual observation is that the 1976 curve is above
the 1993 curve. The real GDP per capita curve in Figure 5 gives $18,138 (1990
US$) in 1992 and $14,902 in 1976. For comparison, the mean income for the whole
population with income in Canada is presented in Figure 20. In fact, the average
income in 1976 was $35,700 and only $33,300 in 1993. The contradiction between
real GDP per capita and mean income is likely related to the difference between
domestic currency and that converted at Geary Khamis PPPs. In our quantitative
analysis, this discrepancy may introduce large errors in theoretical estimates
of the peak age.
Following the
procedure developed in two previous paragraphs, we normalize the curves in
Figure 19 to their respective peak value and present the central segments of
the obtained curves in Figure 21. The 1976 curve peaks between 41 and 42 years
of age (27 to 28 years of work experience). In 1992, the peak age is about 45
years, and then it reaches 49 to 50 years in 2012. Overall, the increase in the
age of peak mean income increases by about 8 years. Theoretically, the change
in real GDP per capita from $14,902 to $25,629 should change by a factor of
1.31, i.e. the peak working age experience rises from 27.5 years to 36.1 years
(50 years of age). This is an extremely accurate prediction, especially taking
into account the problems with real GDP per capita estimates. The proportion of
working age population does not change much in the USA since the mid-70s. It is
likely not a big error if we assume that the share of working age population in
three studied countries does not change since 1976. Then the correction for
population does not affect the relative change in real GDP per capita and the
estimates of the peak age increase in Canada, New Zealand and the UK are not
biased.
Figure 20. The evolution of mean income (2011 CAD) in
Canada between 1976 and 2011.
Figure 22 is
similar to Figures 10 and 16 and displays the evolution of peak-normalized mean
income in various age groups. The peak age resides in the bin from 35 to 44
years of age before 1990. Then the peak jumps into the elder group and will
likely stay below 54 years before the group between 55 and 64 overtakes the
lead. As in other three countries, the proportion of mean income has been
increasing in all elder groups and decreasing in the younger groups. In Canada,
fluctuation of the curves in Figure 22 is much lower than that for New Zealand
and likely at the same level as in the UK. This is a consequence of income data
quality – better coverage of population is directly translated into the
accuracy of mean income estimates.
Figure 21. Three curves in Figure 19 normalized to
their respective peak values. The age of peak mean income value increases with
time from 42 years in 1976 to 49 years in 2012.
Figure 22. The evolution of mean income in
all 10-year age groups normalized to the peak value in the same year. In the
younger age groups (“18”, “22”, and ”30”) the proportion of mean income has
been falling since 1976.
Figure 23
depicts two panels where the normalized mean income curves observed Canada in
2011 ($22,994) and 1980 ($12,931) are matched by U.S. curves for 1987 ($21,788)
and 1962 ($11,904), respectively. The excellent match between Canada2011 and
USA1987 curves well corresponds to GDP estimates, while the GDP levels for 1980
in Canada and 1960 in the USA differ more in relative terms. As we discussed
above, the GDP values for the USA before 1975 have to be corrected for the
effect of changing working age population. Between 1987 and 1962 the correction
is approximately 7%. This makes the 1962 estimate to increase to $12,708. So, Canada
provides the longest time series of mean income among three studied countries
with the largest factor of peak age increase - 1.31. This makes our
measurements more precise and allows better fir between observed and predicted
change in the peak mean income.
Figure 23. The evolution of mean
income in Canada in 2011 and 1980 is matched by the curves measured in the USA
in 1987 and 1962, respectively. Age bins are 10 years for Canada. For the USA,
we use microeconomic data with annual mean income smoothed with a MA(9).
Canada
is the only country from the studied trio reporting age-dependent PIDs for the
higher incomes. Figure 24 displays the number of people with income above a
given income threshold as a function of age. We have selected different thresholds
to retain the portion of population: $100,000 in 2000, $100,000 in 2006, and
$150,000 in 2013. All age bins are 10 years, except the youngest between 0 and
24 years of age. The youngest bin is prone to strong bias because it includes children
with incomes. The 2006 curve is higher than the 2000 curve because they have
the same threshold but the total nominal income in 2006 is much larger than in
2000, and thus, more people have larger incomes. Moreover, the population
pyramid changing with time may introduce a significant bias into the number of
people of a given age. In Figure 24, three curves peak at different ages. To
suppress the population effect we have scaled the portion of people with the
highest income to the total population with income in the same age bin. Figure
25 shows three normalized curves. As one can see, the age pyramid effect is removed
and all curves peak at the same age. Summing the number of people above the
threshold in all age groups and dividing it by the total population with income,
we calculate the total portion of people with incomes above the threshold. For
the thresholds in Figure 24, this portion is 2.5% in 2000, 4.5% in 2006, and
2.8% in 2013.
Figure 24. The number of people
with income above a given income threshold as a function of age. Thresholds are
$100,000 in 2000, $100,000 in 2006 and $150,000 in 2013. Age bins are 10 years,
except the youngest between 0 and 24 years of age. The number of people depends
on threshold and population in each bin.
Figure 25. The portion of people with
income above a given income threshold as a function of age: the number of
people above the threshold in a given age bin is divided by the total number of
people in the same bin. The age pyramid effect is suppressed. The cumulative portion
of people above the threshold is 2.5% in 2000, 4.5% in 2006, and 2.8% in 2013. Notice
the same bin and threshold settings as in Figure 24.
When total
income and population are subject to significant changes with time the best way
to compare age-dependent income distributions in different years is to
normalize them to their respective peak values. Then direct comparison is
possible which shows the relative rate of income/population change with age.
Figure 26 depicts three peak-normalized curves from Figure 25. These normalized
curves practically coincide with just small differences in the age groups 25 to
34 years and 55 to 64 years. The age of the largest portion of people with the
highest incomes resides in the bin between 45 and 54 years. Because of the
width of this bin, which includes the true peak year for all curves, it is
difficult to resolve any change.
Figure 26. The curves in Figure
25 are normalized to their respective peak values. The age of largest portion
of people with the highest incomes resides in the bin between 45 and 54 years.
It is difficult to estimate the change in peak age. Notice the same bin and
threshold settings as in Figure 24.
One problem in
Figure 26 is that the 2006 curve lies above the 2000 curve, while our model and
experience suggest the opposite situation. This controversy is actually related
to the difference in the total portion of people with the highest incomes: 2.5%
in 2000 and 4.5% in 2006. All PIDs available for Canada between 2000 and 2013
are characterized by $50,000 income bins above $100,000. The choice of
threshold is limited to the boundaries of these bins. The year of 2000 is
characterized by the lowermost number of people and gross nominal income, and
thus, by the lowermost threshold of the Pareto distribution. We use it to
illustrate the change in the age-dependent portion of people with the highest
incomes for several thresholds between $50,000 and $250,000. Figure 27
illustrates the change in the age-dependent curve. The peak age grows with the
threshold, i.e. more and more time is needed to reach higher incomes. This
observation puts an important constraint on the direct cross comparison of the
age-dependent portion of people with the highest incomes. One should use
thresholds, which retain the total portion of people at the same level.
In Figure 28 we
match the 2013 Canada curve and the 1995 US curve. The coincidence between the
portions of total population with incomes above $150,000 (CAD) in Canada and
$82,500 (USD) in the USA, both in current dollars, is striking. We retain the
total portion of population above these thresholds at approximately 2.7%. That
eliminates the threshold dependent bias. Total Economy Database reports $26,000
(1990 US$) for Canada in 2013 and $24,712 for the USA in 1995. The difference
is not large and a 4% correction for the change in working age population makes
the 1995 U.S. estimate to rise to $25,643. Hence, the fit between two curves
proves that the portion of people with the highest incomes is likely a
country-independent variable. In other words, it is likely a universal variable
which depends only of real GDP per capita. It is important to extend the set of
countries in order to support this finding.
Figure 27. Canada 2000. The
age-dependent portion of people with incomes above five thresholds - from
$50,000 to $250,000. The peak age depends of threshold. Therefore, one has to
compare curves with thresholds giving the same portion of people.
Figure 28. Comparison of the
age-dependent portion of people with incomes above given threshold. The 2013
Canada curve (>$150,000, current CAD) is best fit by the 1995 US curve
(>$82,500, current US$). TED reports for Canada $26,000 (1990 US$) in 2013
and $24,712 for the USA in 1995. The total portion of population above the
thresholds in both cases is approximately 2.7%.
Conclusion
We have studied two specific features of personal
income distribution in three countries: Canada, New Zealand, and the UK, and
compared them with the USA. The dependence of mean income and the portion of
people with the highest incomes on age are both characterized by varying length
of the involved time series and their accuracy. Canada provides a set of mean income
data covering practically the whole population and the period since 1976, but
the data on personal income evolution with age are limited to the period between
2000 and 2013. Statistics New Zealand also reports tax-related income as obtained
from a survey covering a small portion of the whole population. Higher
amplitude fluctuations, likely induced by underrepresentation of the highest
incomes, limit the usefulness of these estimates for the purposed of our study.
In addition, there is some controversy between real GDP and income estimates
reported by New Zealand and the Conference Board. The UK provides the shortest
but useful time series collected by HMRC.
All data corroborate our main assumption – the
evolution of income distribution is universal, follows a unique trajectory, and
depends only on real GDP per capita converted at PPP exchange rates. We have
proved quantitatively that the dependence of mean income on age in Canada, New
Zealand and the UK as well as the age-dependent portion of people with the
highest incomes in Canada do reproduce similar dependencies observed in the USA,
but many years before, when the level of real GDP per capita was the same.
Since the U.S. outpaces three studied countries by several thousand dollars per
head, the lag reaches 20 to 25 years. For example, the mean income dependence
measured in the UK in 2012-2013 one-to-one repeats that observed in the USA in
1992. The age-dependent portion of rich people in Canada in 2013 reproduces
that measured in the USA in 1995. The time dependence of the studied
characteristics is just parametric, however.
We have proven that the growth of work experience corresponding to the
peak mean income is accurately described by the square-root function of real
GDP per capita. This feature corresponds to the key assumption of our model,
which predicts both studied features precisely. The coherence of theoretical
predictions and long-term observations in four countries proves that the
evolution of personal income (at least in these four countries) is a physical
process described by a simple relationship.
The results of measurements carried out in this study well match the
prediction of our microeconomic model. A unified quantitative description in four
countries is useful not only from theoretical point of view as a possibility to
mathematically describe the process of personal income distribution as the evolution
of a physical system. The universal character of personal income evolution as a
unique function of real GDP per capita allows accurate forecasting of very
specific income characteristics related to fiscal, monetary and other types of
socio-economic policies. Extending
the observed linear trends of real GDP growth into the future (see Figure 5),
one can be use the past U.S. PIDs as templates for the future PIDs in three
countries at a time horizon from 15 year (Canada) to 50 years (New Zealand).
