Economics as Classical Mechanics: Income distribution: cross country comparison

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.