International income mobility

Economics Letters 76 (2002) 179–187 www.elsevier.com / locate / econbase

International income mobility Simon C. Parker*, Sam Gardner Department of Economics and Finance, University of Durham, 23 – 26 Old Elvet, Durham DH1 3 HY, UK Received 8 April 2001; received in revised form 2 January 2002; accepted 7 January 2002

Abstract We perform a novel analysis of the international mobility of per capita GNP. We find general but not unambiguous support for the notion that world income mobility increased between 1972 and 1992, counterpointing the increased inequality over this period.  2002 Elsevier Science B.V. All rights reserved. Keywords: Mobility; International; Income JEL classification: D30; F02; J60; R12

1. Introduction There is now a large literature on the international inequality of real per capita income (referred to as ‘income’ henceforth).1 Despite widespread recognition that inequality ‘snapshots’ do not capture the dynamics of income changes, little is known about international income mobility. International income mobility is of intrinsic interest because it describes how entrenched cross-country income differences are. It is related to the concept of ‘convergence’ between nations’ incomes, but is distinct from it, because while convergence implies mobility, the reverse does not follow. This paper uses World Bank data to gauge the extent of income mobility in 106 countries between 1972, 1982 and

* Corresponding author. Tel.: 144-191-374-7271; fax: 144-191-374-7289. E-mail addresses: [email protected] (S.C. Parker), http: / / www.dur.ac.uk / s.c.parker (S.C. Parker). 1 See, among others, Ram (1979, 1984, 1987, 1992a,b), Theil (1979, 1989), Berry et al. (1983), Maasoumi and Jeong (1985), Theil and Deepak (1994), Theil and Seale (1994), Duro and Esteban (1998), and Schultz (1998). 0165-1765 / 02 / $ – see front matter PII: S0165-1765( 02 )00044-7

 2002 Elsevier Science B.V. All rights reserved.

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1992. We use several different measures that are designed to capture different aspects of mobility. This reveals several illuminating aspects of dynamic changes in cross-national incomes.

2. Mobility measures There are several different ways of measuring mobility. One is to group income data into quantiles and to construct transition matrices spanning some time interval (e.g. Jarvis and Jenkins, 1998). While informative and of interest in its own right, researchers often supplement this information with summary mobility measures. A second approach measures changes in the vector of raw incomes over the time interval. A third approach measures income mobility as the reduction in income inequality as the accounting period is extended.

2.1. Transition matrices and measures Consider an initial vector of incomes x 5 (x 1 ,x 2 , . . . ,x n ) [ R n1 . Here x k is the income of the kth country ranked in ascending order of income, k 5 1,2, . . . ,n, and n . 1 is the population. After t periods, x becomes y [ R n1 , where the countries are ordered the same in y as in x. Let mx and my denote the arithmetic mean incomes corresponding to x and y, respectively. Suppose each country in x is allocated to one of m equally populated ranked income groups indexed by i (e.g. if m 5 10 the income groups are deciles). The countries in y are grouped in deciles based on y incomes. Let pij $ 0 be the probability that a country in group i will be in group j t periods later, and define the m 3 m transition matrix P[[ pij ], with o j pij 5 o i pij 5 1. As well as being informative in its own right, P also serves as the basis for summary measures of mobility. Two popular measures due to Bartholomew (1982) and Shorrocks (1978a) are, respectively

Op Op ui 2 ju m

B5

i51

m

i

ij

(1)

j51

m 2 tr(P) S 5 ]]] m21

(2)

where pi are the elements of the fixed point of P (i.e. p 5 p P)2 and where tr denotes the trace. B measures mobility as the movement of countries across groups, and can be interpreted as the mean number of class boundaries crossed per country. In contrast, S focuses on countries that are immobile. A different notion of mobility as unpredictability has been proposed by Parker and Rougier (2001):

OO m

m

m2 p ij2 i 51j51 U 5 ]]]] m21

(3)

The main difference between U and hB,Sj is that U does not count as mobile structures where transitions are predictable. As with B and S, higher values of U are associated with greater mobility. 2

The steady-state distribution can be taken as 1 /m.

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2.2. Measures based on changes in raw incomes Let y˜ k be the kth largest income in the vector y, with y k being the kth element of the y vector arranged in ascending order of the xs, as above. Only if no re-ranking takes place between x and y will 21 s k 5 m y uy k 2 y˜ k u

be zero for all k, and King’s (1983) mobility index

O (y˜ exphgs j)  ]]]]] K(x,y;g,l) 5  Og y˜ expH 2 ]n O s J n

3

l

k

k

k51

n

l k

k51

21 / l

4

l ±0 (4)

n

k

l50

k 51

will also be zero, where g and l are immobility aversion and constant relative risk aversion parameters, respectively. Otherwise, the index will be positive, indicating the existence of income re-ranking and hence mobility. Fields and Ok (1996) proposed an alternative measure of income mobility based on changes in levels rather than ranks. Their percentage measure of income movement is:

O uy 2 x u p (x,y) 5 ]]]] Ox n

k

0 n

k

k 51

n

(5)

k

k 51

This is the absolute sum of income changes over the period as a proportion of total initial income. A higher value of p 0n (x,y) implies greater mobility. Subsequently, Fields and Ok (1999) proposed the additional measure

O

1 n m *n (x,y) 5 ] ulog y k 2 log x k u n k51

(6)

which can be interpreted as the change in individual social utility experienced during the process x → y, if utility is taken to be the log of income.

2.3. A measure based on the inequality reduction principle Income mobility can also be regarded as the extent to which income inequality is reduced as the accounting period is extended. Let I( ? ) denote a scale invariant inequality index. In the context of a one period transition, Shorrocks (1978b) proposed the following measure:

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( mx 1 my )I(x,y) M 5 1 2 ]]]]] mx I(x) 1 my I( y)

(7)

As with all the preceding measures, higher values of M imply greater mobility.

3. Data and results Data on GNP per capita (in constant 1987 dollars) for 106 countries were taken from the 1994 World Bank World Tables for the years 1972, 1982 and 1992.3 Following Theil (1989), the countries were split into five regions: North, South, Tropical America (TAm) Tropical Asia (TAs), and Tropical Africa (TAf). Appendix A lists the countries by region.

3.1. International mobility Transition matrices and all the summary measures Eqs. (1) to (7) were computed for the transitions 1972–82, 1982–92, and 1972–92.4 Figs. 1–3 illustrate the transition matrices for all 106 countries. They show that most countries are likely to remain in the same class or only move a short distance from one period to the next. Interestingly, the diagonal in Fig. 3 (the 1972–92 transition) is broader with lower peaks than in the other two figures, indicating greater mobility. The same can be said of Fig. 2 (the 1982–92 transition) compared with Fig. 1 (1972–82). A common property of all three matrices is that countries in the highest and lowest deciles have higher probabilities of remaining in the same decile than countries in the middle deciles. Thus the richest countries tend to remain the richest and the poorest tend to remain the poorest. This can be seen from the fact that the main diagonals are U-shaped.5 The U-shape is most pronounced in Fig. 1, indicating that the poorest and richest countries were less mobile over 1972–82 than they were over the 1982–92 and 1972–92 periods. The results for the transition matrix summary measures are given in panel A of Table 1. Both B and S indicate greater mobility over 1982–92 than over 1972–82. But whereas B reports that mobility is greatest over 1972–92, S does not. The difference is attributable to S discarding all the information in the transition matrix except the principal diagonal, whose sum of probabilities marginally increased over 1972–92. B captures the off-diagonal transitions whose importance is evident from Fig. 3. According to U, transitions over 1982–92 were less predictable than over 1972–82, also suggesting that mobility of this type has increased. Values of the King and the two Fields–Ok measures appear in Panel B of Table 1. These findings differ from those based on the matrix-based measures. The King measure reveals similar amounts of 3

An alternative and widely used source of data is the Penn World Tables. Not surprisingly, the two data sets yield very similar results. 4 Analogous to most international income inequality studies, we ignore income mobility within countries. 5 One reason for limited mobility at the top of the distribution is the open-ended nature of the top income group combined with positive skew of the income distribution. It is less clear what underlies the limited mobility at the bottom of the income distribution.

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Fig. 1. Transition map 1972–1982.

re-ranking within each of the two 10-year periods, but rather less between 1972 and 1992. The ‘social utility’ measure m *n (x,y) also suggests that mobility over both 10-year periods was similar; whereas the ‘percentage’ measure p 0n (x,y) actually suggests that mobility over 1982–92 was lower than over 1972–82. Part of the reason for the latter result is that ‘initial’ mean income was twice as high in 1982 than in 1972, but was only 20% higher in 1992 than in 1982—hence the denominator of p 0n (x,y) was greater in the second sub-period.6 Both m *n (x,y) and p n0 (x,y) suggest that greater mobility occurred over the entire period than over either of the two sub-periods. Of course, greater mobility is to be expected as the transition period is extended; that this is not evident using King’s measure is attributable to the reversal over 1982–1992 of some of the re-rankings observed over 1972–82. Panel C presents the values of the M measure based on the inequality reduction principle. The variance of logarithms was used as the inequality measure I( ? ): in accordance with previous studies noting a trend increase in world income inequality since the 1970s, this measure is found to increase from 1.573 in 1972 to 1.919 in 1982 and to 2.675 in 1992. According to M, and consistent with all the measures above except p 0n (x,y), there was greater mobility over 1982–92 than over 1972–82.

6

This can be seen by scaling up p 0n (x,y) by o nk 51 x k : the scaled measure now increases by 9% over 1982–92 relative to 1972–82.

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Fig. 2. Transition map 1982–1992.

3.2. Decomposing international mobility by region An attractive feature of m *n (x,y) is its decomposability by sub-group (Fields and Ok, 1999). Table 2 summarises income mobility within each of the five broad world regions. The final column describes the contribution of each region to international income mobility between 1972 and 1992. It is noteworthy that the North is responsible for most of the movement of log dollar incomes, despite comprising fewer countries than Tropical Africa (the region with the next largest contribution). This is because countries in the North have the highest income growth rates. The lowest income mobility occurred in the South; Tropical America and Tropical Asia have intermediate levels of income mobility.

4. Conclusions This paper contains several findings. First, six of the seven mobility measures examined find the 1982–92 period to be more mobile in terms of international real per capita incomes than the 1972–82 period. This provides general but not unambiguous support for the claim that international mobility increased between these two periods. Increasing mobility counterpoints the well-documented rise in international income inequality, further evidence of which was also found here. Second, five of the

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Fig. 3. Transition map 1972–1992.

Table 1 Mobility measures Measure

Transition period 1972–1982

1982–1992

1972–1992

0.640 0.598 0.673

0.753 0.579 0.713

B. Raw income-based measures K(x,y;g,l) 0.800 0.801 p 0n (x,y) 0.528 0.384 m n* (x,y) 0.396 0.405

0.746 0.868 0.535

C. Inequality reduction measure M 0.010 0.017

0.069

A. Matrix-based measures B 0.509 S 0.463 U 0.574

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Table 2 Log-dollar movement of international incomes Level of log-dollar movement

Decomposition

1972–1982

1982–1992

1972–1992

Entire sample

0.396

0.405

0.535

Region North South TAm TAs TAf

0.397 0.422 0.358 0.576 0.316

0.355 0.304 0.459 0.353 0.459

0.751 0.365 0.443 0.622 0.448

1972–1992

0.163 0.031 0.096 0.105 0.140

seven measures agree that there was more mobility over the entire period than over either of the sub-periods. Third, it is clear from inspection of the decile transition matrices that world income mobility is characterised by many small transitory movements, with relatively few countries experiencing large leaps in real per capita income. Most mobility takes place in the middle deciles with relatively little movement in the bottom or top deciles. Fourth, income mobility is greatest in the North and lowest in the South. After the North, Tropical Africa is the next most mobile region, but unlike the North most of the observed income changes there were negative. Extensions of the work performed here might apply the same methods to different indicators of living standards, for example comprehensive measures of well being that combine income and wealth holdings (Parker and Siddiq, 1997), or basic-needs measures which are of particular interest in developing countries (Ram, 1992a,b).

Appendix A List of sample countries • North (n 5 23): Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Japan, South Korea, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, Turkey, UK, USA. • South (n 5 9): Argentina, Australia, Botswana, Chile, Lesotho, New Zealand, South Africa, Swaziland, Uruguay. • Tropical America (n 5 23): Bahamas, Barbados, Belize, Bolivia, Brazil, Colombia, Costa Rica, Dominica, Dominican Republic, Ecuador, El Salvador, Guatemala, Guyana, Honduras, Jamaica, Mexico, Nicaragua, Panama, Paraguay, Peru, Surinam, Trinidad and Tobago, Venezuela. • Tropical Asia (n 5 18): Bangladesh, Fiji, Hong Kong, India, Indonesia, Israel, Malaysia, Maldives, Nepal, Oman, Pakistan, Papua New Guinea, Philippines, Saudi Arabia, Seychelles, Singapore, Sri Lanka, Thailand. • Tropical Africa (n 5 33): Algeria, Benin, Burkina Faso, Burundi, Cameroon, Cape Verde, Central African Republic, Chad, Comoros, Congo, Egypt, Ethiopia, Gabon, Gambia, Ghana, Guinea, Ivory

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Coast, Kenya, Madagascar, Malawi, Mali, Mauritania, Mauritius, Morocco, Niger, Nigeria, Rwanda, Senegal, Sierra Leone, Tanzania, Togo, Tunisia, Zimbabwe.

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