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Social Indicators Research

Erschienen in:

01.11.2010

Negative and Positive Partial Mobility: A Study of the Relative Changes in Human Development

verfasst von: Atanu Sengupta, Abhijit Ghosh

Erschienen in: Social Indicators Research | Ausgabe 2/2010

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Abstract

In this paper, we have considered the issues concerning dynamic changes in HDI and its various components from a relative standpoint. The analysis of HDI mobility should entail directional movement introduced by Fields (in Distribution and development: a new look at the developing world. MIT Press, Cambridge, 2001). However, Fields’ analysis was in the space of absolute values. Here, we will try to extend this exercise to the positional mobility index by considering the question of improvement and deterioration in relative positions. This requires the concept of partial mobility where mobility is judged from the viewpoint of a particular group. We then try to introduce directional changes in partial mobility through axiomatic framework. Finally, we provide an illustrative example from the Indian data.

Vorheriger Artikel Measuring Capacities for Community Resilience

Nächster Artikel A Comparison of Affect Ratings Obtained with Ecological Momentary Assessment and the Day Reconstruction Method

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In fact formulation process of HDI draws several criticisms.

One can argue for absolutist position only in the very limited case where everybody is symmetrically affected by the overall change in social welfare so that the original relative position is maintained. This case is very close to the classical Pareto optimality where everybody in the society is well-off with none worse-off. Even in this case a status quo (in the relative position) may be quite unpalatable to those at the lowest end of the situation. However, once asymmetry is introduced the complicated questions of compensation and distribution do creep up.

Several types of scaling factors have been used in the literature. For example some authors have tried to represent individual values as proportion of the group mean (Quah 1993; Ray 1998). An alternative suggestion is the use of efficiency indices a la ^/Farrell (1957). The method attempts to maximize the ratio (1) given some constraints imposed by the production structure assumed. The technique has been extended to the analysis of HDI using the capability production function approach. Sengupta and Ghosh (2008) used the maximum value of the relevant parameter as the appropriate scaling factor. If we define \( \delta_{0}^{t} = {\frac{1}{{x_{i}^{t} }}} \times {\frac{{x_{i}^{t} - \min \left( {x_{i}^{t} } \right)}}{{\max \left( {x_{i}^{t} } \right) - \min \left( {x_{i}^{t} } \right)}}} \) for \( x_{i}^{t} \ne 0 \) and \( \delta_{0}^{t} = 0 \) for \( x_{i}^{t} = 0 \), we get the traditional UNDP formulation. However, the axiomatic structure developed in the paper is independent of the type of scaling factor used.

In fact, the “perfectly immobile” mobility matrix becomes an identity matrix.

According to Shorrocks (1978), “Stricter versions of these last two properties are available. The index could be said to satisfy the strong immobility (SI) condition when M(P) = 0 if and only if P = I; and that of strong perfect mobility (SPM) when M(P) = 1 if and only if P has identical rows. These stronger versions rule out the possibility that other types of matrices can take the extreme values.”.

Quah (1993) pioneers the use of income mobility matrix for evaluation of social purposes in his study of global inequality.

Aggregating individual viewpoints to get an overall picture will bring forth the traditional social choice problem that is beyond the scope of this paper.

Here, we are discussing only positive mobility indices-that is a natural extension of Shorrock’s measures. The discussion of negative mobility is done later.

In certain cases the lowest feasible category may not exist at time point t. In this case we may move onto the least observable category. Similarly argument may be extended for the highest feasible category k.

This certainly means that EPM seems to imply total indifference to what happens to the various probabilities of upward mobility. An introduction of such a preference pattern will necessitate the concept of weighted partial mobility indices. We refrain from such an exercise in this paper.

Strictly speaking this is a consequence of strong immobility axiom.

Again this is a consequence of a stronger version of the axom.

The adjective positive will be cleared in the next section.

The proof is trivial.

EPM is satisfied only if α = 1.

This certainly means that EPNM seems to imply total indifference to what happens to the various probabilities of downward mobility. An introduction of such a preference pattern will necessitate the concept of weighted partial mobility indices. We refrain from such an exercise in this paper.

The adjective positive is cleared now.

The formulation assumes weak positive and strong negative mobility. It could be appropriately modified for strong positive and weak negative mobility.

This specific form follows from the form of M-MO. Changing it will change it.

We cannot explicitly state perfect mobility or immobility here. Since it is a net measure, the effect depends on the relative strength of the positive and negative components of the measure.

See our arguments as given before.

Bandyopadhyay (2005) argues that one of the basic criticism of these mobility matrices is the “arbitrariness in the selection of income classes”. We agree with this criticism. However, as Sen noted in his noble lecture, “It is easy enough to pick holes in each of these methodologies and to criticize the relative merits of inter-personal comparisons. ……….Each of these methodologies clearly has some limitations as well as virtues, and our evaluation of their relative merits may well diverge, depending on our respective priorities.” Sen (2003).

In the Indian case we are considering, Kerala is the only member belonging to the best performing category in the non-SDP issues.

In many recent discussions, Sen (2003) stresses on ELB to be the most important indicator of well-being.

Bandyopadhyay, S. (2005). Economic growth across Indian states. In A. Shorrocks & R. Hoeven (Eds.), Growth, inequality and poverty: Prospects for pro-poor economic development. New York: Oxford University Press.

Bhattacharya, K. (1995). Employment fluctuations in rural India: A statistical analysis. Unpublished Ph.D. Thesis, Indian Statistical Institute, Kolkata.

Chandhok, H. L., & the Policy Group. (1990). Indian database: The economy (Vol. 1). New Delhi: Living Media India.

Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the Royal Statistical Society, Series A, 120(3), 253–290.CrossRef

Fields, G. S. (2001). Distribution and development: A new look at the developing world. Cambridge: MIT Press.

Ghosh, M. (2006). Economic growth and human development in Indian states. Economic and Political Weekly, 41(30), 3321–3329.

GOI (Government of India). (2002). National Human Development Report 2001. Planning Commission, New Delhi.

GOI (Government of India). (2003). National account statistics. Central Statistical Organisation, Department of Statistics, Ministry of Planning, Government of India.

Quah, D. (1993). Empirical cross-section dynamics in economic growth. European Economic Review, 37, 426–437.CrossRef

Ramirez, A., Ranis, G., & Stewart, F. (1998). Economic growth and human development. Working Paper 18, Queen Elizabeth House, Oxford.

Ranis, G., & Stewart, F. (2000). Strategies for success in human development. Working Paper 32, Queen Elizabeth House, Oxford.

Ranis, G., & Stewart, F. (2001). Growth and human development: Comparative Latin American experience, Discussion Paper No. 826, Economic Growth Centre, Yale University, New Haven.

Ray, D. (1998). Development economics. Delhi: Oxford University Press.

Sen, A. (2003). Rationality and freedom. India: Oxford University Press.

Sengupta, A., & Ghosh, A. (2008). Urbanization and human welfare in the era of globalization: A case Study in Burdwan District of West Bengal. Arthavijnana, 1(2), 129–150.

Shorrocks, A. F. (1976). Income mobility and Markov assumption. Economic Journal, 86, 566–578.CrossRef

Shorrocks, A. F. (1978). The measurement of mobility. Econometrica, 46, 1013–1024.CrossRef

UNDP. (1990). Human Development Report. New York: Oxford University Press.

Titel: Negative and Positive Partial Mobility: A Study of the Relative Changes in Human Development
verfasst von: Atanu Sengupta
Abhijit Ghosh
Publikationsdatum: 01.11.2010
Verlag: Springer Netherlands
Erschienen in: Social Indicators Research / Ausgabe 2/2010
Print ISSN: 0303-8300
Elektronische ISSN: 1573-0921
DOI: https://doi.org/10.1007/s11205-010-9577-8

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