# Calculating Sen’s Real National Income for New Zealand

<>Keywords: Distributional Economics; Growth & Innovation; Statistics;

I have just realised that we can calculate Amartya Sen’s ‘real income’ measure  for New Zealand for a 30 year period, by combining our Statistics New Zealand estimates of national income with the Ministry of Social Development estimates of household gini coefficients. This note describes how this may be done and reports the results. It demonstrates the exercise is feasible and that the gains from improved terms of trade over the last decades seem to have gone only to the rich rather than across the community as a whole.

Sen’s Measure of Real Income

The conventional measure of GDP, when interpreted in welfare terms, ignores the distributional impact of any gains (or losses) of output. Thus it gives exactly the same outcome if the all gains go to the very rich as if the gains are shared equally among everybody.

To get an insight into the issue consider two people whose joint income is 100. Richard has 70 of it; Paul 30 (this is roughly the share between the richest and poorest halves of New Zealand). Now suppose they get between them an extra 10. The GDP approach is to assess this as a 10 percent increase. But suppose it all goes to Richard. His increase is 14.28 percent while Paul’s is zero. Perhaps a better measure might be to say the increase was the average of the two or 7.14 percent. A different sharing of the income increase – say Paul got it all, a 33.3 percent increase – would give a different increase to the joint incomes – 16.67 percent as it happens. The point of the illustration is that the distribution of any gains (or losses) matters and that the GDP measure ignores this.

Sen suggested an alternative measure which he called ‘real national income’, which takes into account the distributional impact of changes. (1976; 1979) Ultimately it deducts from national income the share, measured by the gini coefficient, to reflect the degree of inequality.

Practically the gini coefficient is the average difference (in income in this case) between any two people in a population scaled by the mean of the distribution (in effect it is calibrated to one unit). A gini coefficient of zero expresses perfect equality, where everyone has exactly the same income; a gini coefficient of one expresses perfect inequality, where one person has all the income. If there is perfect equality with each person receiving the same share, Sen’s real national income corresponds to the conventional measure of national income in the system of national accounts; if there is perfect inequality Sen’s real national income is zero.

Of course, Sen has a more complicated – and rigorous – analysis (including whiy it is the gini coefficient which is used for the adjustment rather than some other index). But the exposition thus far is sufficient for these purposes. (There are other distributionally sensitive measures of income. See Jenkins 2012 and Atkinson 1970.)

Constructing Sen’s Index of Real National Income

We begin with the official GDP series. (In all of the following the aggregate measure is valued in constant prices and per capita.) This is converted to National Income in Production Prices (NIPP) by deducting consumption of capital (depreciation) and net payments to foreign factors. (As it happens the proportional deduction is broadly constant over the period; the rise in foreign ownership of New Zealand production is roughly offset by a falling share of depreciation in GDP.)

Since NIPP is measured in production prices, for income assessments it is necessary to convert it to National Income in Spending Prices (NISP) which differs by changes in the terms of trade. Generally, the terms of trade were rising in the period, so the spending price aggregate was rising faster than the production price aggregate.

The final step to get to Sen’s Real National Income (SRNI) is to multiply NISP by one minus the gini coefficient. The gini coefficient is as derived by the MSD report on Household Incomes. (Perry 2013) Years for which there is no data have been interpolated. Because income inequality has been rising, the SRNI grows more slowly that NISP (but, as we shall see, at a similar rate to NIPP).

National Income: 1982-2012

Each of the three series is scaled to an average of 1000 over the 1982 to 2012 years. (The gini coefficient series begins in-1982.) The data is shown in the Appendix Table and the Graph of the table.

Much of the story they tell is familiar. There was economic growth in the early 1980s, but from the mid 1980s there was a downturn reaching its nadir in 1992 or 1993. The turnaround led to strong growth, although income did not return to its mid-1980s level until the mid-to-late-1990s. Growth continued steadily until the mid-2000s, slowed down (or flattened out) and went into a contraction following the Global Financial Crisis. All the income series show a rebound at the end of the period, but this is mainly a statistical consequence of the treatment of insurance inflows after the Canterbury earthquakes of 2010 and 2011. (The inflows precede the write-offs of capital destroyed by the earthquake.)

To what extent do the three series tell different stories?

Over the thirty years between 1982 and 2012 the terms of trade rose about 40 percent. There was a major lift (of about 20 percent) in the period from 1986 to 1994, and further lift (again of about 20 percent) from 2003 to 2012.

The shift is sufficiently long term to require a structural explanation. The most compelling account is that the current phase of globalisation, in which manufacturing jobs are shifting to East Asia, is raising the demand for food faster than it can be supplied and so the price of foodstuffs (and also other natural resources) is rising faster than that of manufactures, the reverse of the story of the first three-quarters of the twentieth century. (Easton 2006) The shift only affects the quarter or so of New Zealand output which is exported, so income in spending prices rose about 10 percent more than income in production prices over the three decades.

So while the annual growth in NIPP was 1.37 percent, that of NISP was 1.66 percent.  That means that the terms of trade gain added slightly more than a quarter to incomes relative to production. The graph shows them having slightly different tracks over the three decades, but the difference is small compared to their secular trends.

The gini coefficient which converts the NISP to Sen’s measure rose in the period (sharply in the first decade and subsequently level since), which means it will not have increased as much as NISP. Again the track is not too different from the NIPP and NISP. The trend annual increase is 1.31 percent, very similar to NIPP and 0.35 percentage points (or about a fifth) below the NISP.

The implication is that the gains from the improved terms of trade went to those on higher incomes rather than were shared across the whole community (as was the intention of the General Wage Order when Arbitration Court operated). However, it is not obvious that the two phenomena are directly connected.

New Zealand’s Ranking in the OECD

In 2009 the OECD ranked New Zealand 21st out of 34 (its 33 members plus Israel) in per capita Net National Income, based on current PPP (i.e common prices). This measure corresponds near enough to NISP (but in common prices so there is no need for a terms of trade adjustment). Converting the totals to Sen’s measure (by multiplying by the complement of the gini coefficient) New Zealand’s place on a SRNI ranking falls to 24th (out of 34) passed by Iceland, Slovenia, and Korea. Each has a lower NISP but their less unequal income distribution means they rate higher on Sen’s measure of SRNI.

(One may have doubts whether New Zealand NISP has such a low level or whether there is some statistical artefact depressing New Zealand’s aggregate. However the basic message – that New Zealand’s relatively high income inequality compared to those near it in rankings lowers its SRNI ranking – probably applies if the NISP is higher. It should also be noted that 2009 – the most recent year for which we have comprehensive gini coefficients for the OECD countries – is the year in which the Global Financial Crisis impacted on the world’s economies with the probability that there have been some major changes in the GDP and NISP relative levels.)

Conclusion

This note establishes that it is possible to construct Sen’s measure of Real National Income back to 1982 and that the resulting series are appear to be useful for interpreting some aspects of New Zealand’s economic performance.

References

Atkinson, A. B. (1970). ‘On the measurement of inequality’, Journal of Economic Theory, 2, 244–263.

Easton, B. H. (2006) The Globalisation of the Wealth of Nations (Auckland AUP)

Jenkins, S. J. (2012) Distributionally-sensitive Measures of National Income and Income Growth, paper to LSE Growth Commission (24 May 2012)

Perry, B. (2103) Household Incomes in New Zealand: Trends in Indicators of Inequality and Hardship 1982-2012 (Wellington, MSD)

Sen, A. (1976). ‘Real national income’, The Review of Economic Studies, 43 (1), 19–39.

Sen, A. (1979). ‘The welfare basis of real income comparisons’, Journal of Economic Literature, 17 (1), 1–45.

Appendix Table: Measures of National Income

 Year toMarch NATIONAL INCOME Production Prices (NIPP) Spending Prices  (NISP) Sen’s Real Index  (SRNI) 1982 842 811 864 1983 844 809 862 1984 859 823 874 1985 889 849 905 1986 875 831 889 1987 977 841 901 1988 901 881 946 1989 907 902 944 1990 912 916 933 1991 889 883 892 1992 868 855 857 1993 831 824 822 1994 873 868 861 1995 904 897 886 1996 937 927 911 1997 966 953 935 1998 969 954 934 1999 990 973 949 2000 1051 1032 1005 2001 1047 1043 1010 2002 1066 1069 1038 2003 1116 1106 1077 2004 1145 1146 1119 2005 1176 1193 1165 2006 1187 1205 1177 2007 1175 1198 1171 2008 1183 1236 1205 2009 1151 1206 1173 2010 1126 1166 1156 2011 1165 1238 1184 2012 1277 1365 1356 Trend 1.37 % p.a. 1.66% p.a. 1.31% p.a.