An effort of mapping the income inequality in the district of Purulia, West Bengal, India

Abstract

The incidence of income inequality belongs to the core of poverty, food insecurity, malnutrition, starvation and a few hundreds of other socioeconomic problems or may be said the socioeconomic hazards. Present-day researches within the domain of socioeconomic sciences are focused to develop the ‘tools and techniques’ of demarcating the areas having a degree of vulnerability to a particular socioeconomic hazard and to examine the internal functions of the interactive variables associated with the process. The distribution of income inequality, spatially or temporally, can be expressed not by the per-capita income only but through combining the distribution of workforce, accompanied with the assorted income level within the working population; and, based on this algorithm, the present paper proposes an indicator of income inequality. The response of the indicator is validated by analyzing its synchronization with the renowned Kuznets inequality distribution model. Then, the mapping of income inequality is done for the district of Purulia, utilizing the validated indicator on GIS platform.

Introduction

The concept of development has long been debated in terms of its philosophical implications, approaches and issues of measurement; however, there is hardly any literary debate in this issue that the principal aim of the development is to reduce the inequality. The discussion of unequal development possesses a vast dimension within which the income distribution analysis has a classical concern that is largely accounted for descriptive as well as quantitative presentation of inequality on spatial or temporal perspective. The measurement of unequal distribution of development or deprivation, based on the income data from household surveys, is advantaged with its seemingly straight forward linkage with the economy, as the monetary value is conceptually linked with the GDP. However, linking income data to the economy are not self-evident in practice (Dercon 1999). Real per-capita income of a given spatial unit is an excellent measure to compare the achieved standard of socioeconomic development of the region in comparison with another spatial unit, but it does not explore the internal economic inequality of any of the regions. The major disadvantages of per-capita income (or in general sense, the mean individual income) to be used for economic inequality mapping, which is the principal concern of the present study, are: firstly, it does not reflect the difference of standard of living among the people as this is an arithmetic mean and this value of mean income may not represent the standard of living of the people, if the increased total income goes to the few rich instead depriving the many poor (see Fig. 1), and secondly, if per-capita income is taken as the base of measurement, the population problem is ignored, since population has already been divided out which unduly narrow down the socioeconomic field of enquiry. As Kuznets warns, the choice of per capita, per unit or any similar measure to gauge the economic development carries with it the danger of neglecting the denominator of the ratio (Kuznets 1955).

Fig. 1
figure1

Two different levels of unequal income distributions (i.e., a and b) result into equal mean income

Fig. 2
figure2

Location of Purulia district in the state of West Bengal in India. The blocks are indicated with colors, and Gram Panchayat boundaries are demarcated with yellow lines inside the district map (color figure online)

Mapping of income inequality of a region is the graphical representation of the ‘answers’ of each point within the given spatial extension against the question ‘How fairly the income is distributed here?’ which is completely different from that of ‘How much income is generated here?’ There are different measurement of ‘how fairly income is distributed over space,’ but in the present paper we shall try to get the ‘answer’ through analyzing the classical decision-making models whether the pattern of people’s participation to income-generating process does indicate the pattern of income inequality on a given spatial extension.

Study area

Purulia (see Fig. 2), the western-most district of West Bengal at present, making boundary with the state of Jharkhand and Bihar, was included as Manbhum district in state of undivided Bihar during independence. The district of Purulia was formed and merged with West Bengal on November 1, 1956, by separating areas under 16 police stations of the then Bihar as per the recommendation of the State Reorganization Commission. The district of Purulia has been selected as the study area for assessing and mapping of economic inequality. The Purulia district is extended between 22.70295°N to 23.71335°N latitude and 85.82007°E to 86.87508°E longitude, covering a total area of 6259 sq. km, and accommodates 2,930,115 population with an average population density of 468 persons per sq. km (Census of India 2011). This is the land of infertile lateritic tracts. The undulated landscape is characterized by the presence of a number of residual hills and hillocks, narrow river channels with the bank margins dominated by gully erosion, isolated patch of tropical dry northern deciduous forest. The climate is rough; both the summer and winter are experienced in severe form in this district (maximum temp. is 45 °C in June, and minimum temp. is 9 °C in January averagely). The soil is hardly supportive to agricultural activities; the rain-fed cultivation is confined within only one cropping session (basically July to October) in a year. About 57.53% of total land is considered as cultivable land and only 25.66% of cultivated area enjoys the opportunity of irrigation facility from different sources. But this agricultural activity is limited to the river banks and low land areas only. The district receives the lowest rainfall (1150 mm on an average) in the state where the shortage of rainfall from the normal often creates the drought situation in the district (District Statistical Handbook: Purulia 2013). Except a few urban centers like Purulia Town, Adra etc. the rest of the district is economically backward where the hunger and starvation are not a very rare incidence and poverty prevails in its extreme form at most of the distant ‘hamlets.’

Data and methods

Sampling design for primary data collection

The present study is based on the primary data collected through household survey with a preprinted survey schedule. The district of Purulia is constituted with 20 C.D. Blocks and a total of 170 Gram Panchayats (GPs) within the jurisdiction of these Blocks. The survey is designed to estimate simple proportions without any cross-classifications in a large population with using the following equation to determine the size of the sample (National Statistical Service 2016):

$$n_{x} \ge \frac{{\left( {Z_{1 - \alpha } } \right)^{2} \left( {\frac{{p_{E} }}{{p_{x} }}} \right)\left( {1 - \frac{{p_{E} }}{{p_{x} }}} \right) }}{{c^{2} }}$$
(1)

where \(n_{x}\) is sample size for x set of population; \(Z_{1 - \alpha }\) is the Z value at α significance level; \(p_{x}\) is the population within set x; and \(p_{E}\) is the expected population to have the attributes those are being estimated from the survey and c is the confidence interval.

For the present study, the ratio \(\left( {\frac{{p_{E} }}{{p_{x} }}} \right)\) is assumed to be unknown and has been set to 0.5 (i.e., 50%), as this produces a conservative estimate of variance. The value of confidence interval (c) has been set as 0.05 for the present study. The required numbers of sample have been collected from each C.D. Blocks in a simple random basis, provided that the sample is distributed at least one census village in each of 170 Gram Panchayats of the districts for ensuring a better representativeness of the entire blocks. The coordinates of all the surveyed villages have been recorded for the purpose of utilizing the data representation using a GIS software platform.

Secondary sources of data

The Primary Census Abstract (PCA), Directory of Village Amenities (VDA) of the population enumeration data of Census of India for three consecutive census years, i.e., 1991, 2001 and 2011, are the principal secondary data sources for the present study. Besides, the reliable data products from other government reports are also utilized to some extent in the present study and they are mentioned at their places.

Linking income with workforce

People living on a particular space execute rational decision making in choosing field of occupation. Rationality is equated with scientific reasoning, empiricism and positivism and with the use of decision criteria of evidence, logical argument and reasoning (Huczynski and Buchanan 2001). The classical decision-making models argue that man as decision maker always consider all possible alternatives and their consequences before selecting the optimal solution and the whole process of decision making is directed toward maximizing the profit, minimizing the stress and competition, ensuring the best fit between the available and demanded skills. Heracleaous (1994) mentioned the eight strictly defined sequential processes of decision making, which can easily explain the process of decision making of population to participate in economic activities (see Fig. 3).

Fig. 3
figure3

The process of decision making of population to participate in economic activities using a generalized classical decision-making model as represented by Heracleous (1994)

Another issue in the present concern is the mode of participation of the population in income-generating process. The working population are classified into two broad categories—main and marginal workers. The two categories have been ascribed as their nature of involvement to the economy. Ministry of Statistics and Programme Implementation, Govt. of India, has defined ‘main workers’ as ‘those workers who had worked for the major part of the reference period (i.e., 6 months or 180 days) or more,’ and ‘marginal workers’ as ‘Those workers who had not worked for the major part of the reference period’ (Manual on Labour Statistics I 2012). Whatever the definition may be, the issue of marginality in involvement in the economic system is not a mere data field in the census report, rather it has a greater socioeconomic implication. The Merriam-Webster’s dictionary defines ‘marginalization’ as ‘to relegate to an unimportant or powerless position within a society or group.’ Marginalization typically involves some degree of exclusion from access to power and/or resources; it indicates a group at the periphery or at the edge of the society in virtual sense, i.e., those who are marginalized, do not get to enjoy the full or typical benefits that those who are closer to the center tend to receive (Maynard and Ferdman 2015). The presence of marginalization can be conceptualized as the existence of some degree of social exclusion within the region. Beside this, the spatial pattern of share of marginal workers within the population in a region has significant scope to provide a meaningful insight into the ongoing economic process of the region. There is hardly any debate regarding the generalization that the working population within a field of occupation always give effort toward upgrading their level of income and minimizing the risk of insecurity of the source of income. So the tendency of the population toward marginal mode of involvement in the economic process is not a voluntary decision from the end of marginal working population of a region, rather the internal functions of the economic process underlying the region have forced to deprive the group from availing permanent source of income. The inconsistent pattern of income from the occupation by the marginal workers tends to reduce the per-capita income figure of a region.

Per-capita annual income (y) of a region can be represented as,

$$y = \frac{Y}{P}$$

where Y = total income generated by working population, P = total population

$${\text{or}},\quad y = \frac{{m.P.c_{M} + r.P.c_{R} }}{P}$$

where m = share of main workers to total population, r = share of marginal workers to total population, c M = mean annual income of main workers, c R = mean annual income of marginal workers

$${\text{or}},\quad y = m.c_{M} + r.c_{R}$$
$${\text{or}},\quad y = m.(c_{R} )^{x} + r.c_{R}$$

[representing mean annual income of the main workers as xth power than that of the marginal workers]

$${\text{or}},\quad x.\log \left( {c_{R} } \right) = \log \left( { y - r.c_{R} } \right) - { \log }\left( m \right)$$
$${\text{or}},\quad x = \frac{{\log \left( { y - r.c_{R} } \right) - { \log }\left( m \right)}}{{\log \left( {c_{R} } \right)}}$$
(2)

For ‘zero income inequality’ situation, in Eq. (2) above, \(x = 1\)

$${\text{Hence}},\quad \frac{{\log \left( { y - r.c_{R} } \right) - \log \left( m \right)}}{{\log \left( {c_{R} } \right)}} = 1$$
$${\text{or}},\quad \log \left( {\frac{{y - r.c_{R} }}{{m.c_{R} }}} \right) = 0$$
(3)

Again, from Eq. (3) above,

$$\frac{{y - r.c_{R} }}{{m.c_{R} }} = 1$$
$${\text{or}},\quad y = \left( {m + r} \right)c_{R}$$
$${\text{or}},\quad y = w.c_{R}$$

[working population share to total population, w = (m + r)]

$${\text{or}},\quad \log \left( y \right) = \log \left( w \right) + { \log }\left( {c_{R} } \right)$$

Differentiating the above equation, with time (t),

$$\frac{1}{y} \left( {\frac{\partial y}{\partial t}} \right) = \frac{1}{w}\left( {\frac{\partial w}{\partial t}} \right) + \frac{1}{{c_{R} }}\left( {\frac{{\partial c_{R} }}{\partial t}} \right)$$
(4)

Equation (4) states that to maintain a long-term ‘zero inequality’ condition for a region, the rate of change of income per capita should be equal with the sum of rate of change of total working population and the rate of change of average annual income of the marginal working population. The value of \(\left[ {\log \left( {\frac{{y - r.c_{R} }}{{m.c_{R} }}} \right)} \right]\) in Eq. (3) for a particular region provides ‘0’ when there is absolutely equal share in income for the main and marginal population within the area and it deviates away as the degree of inequality in income share between working classes enhanced. The value of \(c_{R}\) for a region can be easily derived from the wage rate of different wage classes of marginal workers. Hence, the proposed indicator of inequality can be written as:

$${\acute{\omega}} = \log \left({\frac{{y - r.c_{R}}}{{m.c_{R}}}} \right)$$
(5)

The response of the ratio (ώ) at different levels of welfare condition with national-level data of India will be tested in the next section to validate ώ as an indicator for measuring economic inequality of a region.

Validation of the inequality indicator

Getting the idea of inequality distribution from Kuznets’ model

The path-breaking economic model by Kuznets (1955) proposing ‘a law of motion for the distribution of income, during his address to the American Economic Association, still forms a fundamental concept regarding the explanation and analysis of economic inequality. Kuznets model is based on the assumption that the rural agricultural incomes are lower but more equally distributed than that of the urban-industrial income, and there are ample evidences from the economic history of different countries to have channelized from rural agricultural economy toward urban-industrial economy that results into a rising fraction of workers earning higher industrial wage (Gallup 2012). As a consequence, a steady rise of income inequality becomes an indispensable economic incidence for a developing economy, and this situation of enhancing inequality with growing per-capita income level tends to work up to a threshold level when the predominance of industrial worker will improve the income distribution by earning similar higher level of industrial wage (see Fig. 4). A series of empirical papers in last four decades have discussed the validity of the Kuznets hypothesis using wide level of cross-country dataset and different econometric techniques. Most of the studies, like Chenery and Syquin (1975), Ahluwalia (1976), Papanek and Kyn (1986), Randolph and Lott (1993), Bourguignon (1994), Chang and Ram (2000), Huang and Lin (2007), found robust support favoring Kuznets hypothesis. The analysis of the international income distribution data brings to fore the scenario that the middle-income countries (e.g., the Latin American countries) tend to exhibit higher level of income inequality than the low- or high-income countries.

Fig. 4
figure4

a The well circulated form of Kuznets curve—the inverse ‘U’-shaped trend of relationship between income per capita and inequality when plotted with cross-country dataset; b when a very small segment of the curve from the slope of rising inequality is considered, it represents a positive linear relationship between income per capita and inequality; and embedded with the mutually opposite directions of maximizing income and equality which characterize the economy at developing stage; c similarly, a very small segment from the slope of falling inequality provides a negative linear relationship; and embedded with the unidirectional trend of maximization of income and equality that indicates the economy as developed stage

Calculating the value of ώ for states of India

The population enumeration data of Indian Census 2011 provide required dataset to calculate the share of main and marginal workers to total population (i.e., value of m and r, calculated in Table 1) statewise (see Fig. 5 also). The annual per-capita income data of different states for the year 2010–2011 have been collected from the annual report of the then Planning Commission of India. But there is hardly any dataset available regarding the statewise average income of the marginal workers in India, which necessitates a degree of interpolation in the calculation. The marginal workers in the country are almost dependent to daily wage-based income sources. On the other hand, the National Rural Employment Guarantee Act, 2005 of Govt. of India, has been enacted to provide for the enhancement of livelihood security of the households in rural areas of the country by providing at least one hundred days of guaranteed wage employment in every financial year to every household whose adult members volunteer to do unskilled manual work and for matters connected therewith or incidental thereto (The Gazette of India, December 07, 2005). Hence, the statewise hundred days average wage in public and non-public works (c #R ) has been used as a proxy to average income of the marginal workers. Though the actual dataset may vary with the interpolated dataset, the interpolated data are pretty enough to satisfy the present objective of a relative assessment of the value of ώ between states in India and correlating it with some other common indicators.

Table 1 Calculation of ώ for different states in India
Fig. 5
figure5

Statewise share of main and marginal workers to corresponding total population in India, 2011

Testing the response of ώ against GDP and income per capita

The value of ώ is the expression of the inequality of inter-working group share of income. To validate the function of ώ as an inequality indicator, its response against the income condition is required to be tested primarily. India is a country of large population, and there is a wide variation of inter-state economic characteristics and income level also. The annual per-capita income figure ranges from as low as Rs 20,708 in Bihar to as high as Rs 158,572 in Goa (see Table 1). When the statewise values of ώ are plotted along the ordinate of a Cartesian plot against the logarithmic value of per-capita income along the abscissa and the trend line is fitted, a positive trend of relationship between the two variables is clearly viewed, and simply the same trend of relationship is displayed if the value of per-capita income in replaced with annual per-capita Gross State Domestic Production (GSDP) on the x-axis (see Fig. 6).

Fig. 6
figure6

Response of ώ against the logarithm of per-capita income and GSDP of states in India

Pearson’s correlation coefficient (r) has been calculated for each of two sets of variable, and t test (at 99.9% confidence level) is applied for testing the null hypothesis that ‘there is no significant relationship between annual per-capita income/GSDP and ώ (see Table 2 for the summary of t test). The result of the t test shows that for both the independent variables, t > t 0.999(df=x) . Hence, the null hypothesis is rejected. As a summary of the above analysis, it can be stated that the states generating larger amount of domestic products and possessing higher level of income are also exhibiting an wider unequal share of income between different working classes.

Table 2 Test of the significance of correlation using t test

Testing the response of ώ with GDP originated by different sectors

Now, the careful observation on the accumulation of GDP by industry of origin within different states of India and its statistical relationship with ώ is to be tested. There is a very frequent statement fond in economic literature about India that there exists an unequal spatial distribution of population within the country. Besides, the concentration of GDP over some states at larger magnitude has made the situation more complicated. More than 60% of total GDP of the country is generated by seven states (i.e., Maharashtra, Uttar Pradesh, Andhra Pradesh, Tamil Nadu, Gujarat, West Bengal and Karnataka) covering only about 38% of the total geographical area of the country. In view of satisfying the objective of the present study, the relative concentration of GDP form different industry of origin is required to be analyzed with reference to the relative distribution of population in different states in the country. The relative concentration of GDP with reference to the population can be expressed as:

$$q_{i\left( x \right)} = {{\left( {{{G_{i(x)} } \mathord{\left/ {\vphantom {{G_{i(x)} } {\mathop \sum \limits_{i = 1}^{n} G_{i(x)} }}} \right. \kern-0pt} {\mathop \sum \limits_{i = 1}^{n} G_{i(x)} }}} \right)} \mathord{\left/ {\vphantom {{\left( {{{G_{i(x)} } \mathord{\left/ {\vphantom {{G_{i(x)} } {\mathop \sum \limits_{i = 1}^{n} G_{i(x)} }}} \right. \kern-0pt} {\mathop \sum \limits_{i = 1}^{n} G_{i(x)} }}} \right)} {\left( {{{P_{i} } \mathord{\left/ {\vphantom {{P_{i} } {\mathop \sum \limits_{i = 1}^{n} P_{i} }}} \right. \kern-0pt} {\mathop \sum \limits_{i = 1}^{n} P_{i} }}} \right)}}} \right. \kern-0pt} {\left( {{{P_{i} } \mathord{\left/ {\vphantom {{P_{i} } {\mathop \sum \limits_{i = 1}^{n} P_{i} }}} \right. \kern-0pt} {\mathop \sum \limits_{i = 1}^{n} P_{i} }}} \right)}}$$
(6)

where \(G_{i\left( x \right)}\) = GSDP from the x industry of origin in ith state, \(P_{i}\) = population of the ith state.

Observation on the calculated value of q (a) , q (m) and q (s) for different states in India at Table 3 exhibits an unequal distribution of GDPs of varying industry of origin (see Fig. 7). The distribution of GSDP from agriculture shows that there is no state having an exceptionally high degree of concentration; ‘seven sisters’ states of northeast India except Assam show higher concentration of agricultural GDP, leaded by the state of Nagaland. In the rest of India, Andhra Pradesh, Haryana, Himachal Pradesh, Punjab and Andaman and Nicobar Islands possess higher concentration of GDP originated from agriculture. In case of manufacturing GDP, the states of Goa and Sikkim boast for generating an exceptionally high degree (q (m)  ≥ 5.0) of manufacturing GDP, but this is to be kept under consideration that the states of Sikkim and Goa share only 0.19% and 0.09% of land and 0.05% 0.12% of population of the country, respectively; hence, this very high level of concentration of manufacturing GDP has no significant impression on the interpretation of national-level economic phenomena. The states of Maharashtra, Gujarat, Haryana and Uttarakhand concentrate relatively higher manufacturing GDP (2.0 ≤ q (m)  ≤ 3.0), followed by the states of Himachal Pradesh, Punjab and Tamil Nadu with a moderate level of concentration (1.5 ≤ q (m)  ≤ 2.0). The concentration of GDP from services reflects a trend similar with the case of manufacturing—the very high concentration (q (s)  ≥ 3.0) in the smaller states of Delhi, Chandigarh and Goa. The states of Puducherry and Andaman and Nicobar Islands have high concentration of GDP from services (2.0 ≤ q (s)  ≤ 3.0) followed by the states of Haryana, Karnataka, Maharashtra and Tamil Nadu with a moderate level of concentration (1.5 ≤ q (s)  ≤ 2.0).

Table 3 Relative concentration of GDP with reference to population in different states of India
Fig. 7
figure7

Statewise relative concentration of GSDP from different industry of origin in India; a GSDP from agricultural sources; b manufacturing; c service; d distribution of ώ index (not normalized) in different states of India

The statewise values of ώ when plotted along y-axis against the values of q (a) , q (m) and q (s) along x-axis as independent variable, a distinct trend of relationship is viewed. The states having higher concentration of GDP from agricultural origin exhibit a lower value of ώ, whereas the states are responded with higher values of ώ with the higher value of q (m) and q (s) (see Fig. 8). The value of Pearson’s correlation coefficient (r) and the test of significance using Students t test bring to fore a more specific understanding of the relationship between GDP concentration and inequality in share of income. Assuming the null hypothesis that ‘there is no significant relationship between \(q_{i\left( x \right)}\) and ώ’ the t test is applied at 99.9% level of confidence.

Fig. 8
figure8

Response of ώ against relative concentration GDP originated from agriculture, manufacturing and services in different states of India

The summary of the t test, as displayed in Table 4, shows that the relative concentration of GDP from manufacturing and services has remarkably significant positive relationship with the inter-working class income inequality at as high as 99.9% confidence level as for both the cases, t > t 0.99(df=x) . On the other hand, there is a ‘mild’ negative relationship between relative concentration of GDP from agriculture and allied processes, and, for this case, at the specified confidence level of 99.9%, t < t 0.99(df=x) ; which indicates that the relationship between q (a) and ώ is insignificant at the said precision level. In developing economy like India, this is hardly possible to expect for any economic sector where the growth would assure the minimization of inequality. Rather, this insignificant negative relationship between q (a) and ώ is, itself, a notable support favoring the statement that the rural agricultural system possesses more equal distribution of personal incomes than that of the manufacturing.

Table 4 Test of the significance of correlation using t test

How far the ώ follows Kuznets?

Now, return to the Kuznets’ economic inequality model which addresses two generalized conclusion for developing economies—(1) the magnitude of economic inequality is directly proportional to the per-capita income and (2) growth of manufacturing sector results in increasing the economic inequality, i.e., the magnitude of economic inequality is inversely proportional to the GDP generated from agricultural sources. The economy which has dominant source of GDP from agricultural origin would show comparatively well distributive welfare process than that of the manufacturing or higher sector dominated economy. The economy possessing greater concentration of GDP from the manufacturing and service sectors witness the accumulation of the profit of the production of goods and services within a narrower part of the population, keeping a larger part excluded from the benefit of the economic process.

To understand the response of ώ, with two independent variables, i.e., agricultural share to state GDP (GSDPa) and income per-capita (y), a three-dimensional scatter diagram has been plotted (Fig. 9) with GSDPa along x-axis, log(y) along y-axis and ώ along z-axis. When the data from all the provinces in India are plotted, the diagram shows clearly that the states possess comparatively higher per-capita income, having their GSDP originated mainly from non-agricultural sources show higher value of ώ (e.g.,, Goa, Puducherry, Haryana and Gujarat get ώ > 1.4). Alternatively, increasing dependency of the GSDP on agriculture lowers the per-capita income figure and simultaneously reduces the value of ώ also (e.g., Uttar Pradesh, Madhya Pradesh and all NE Indian states except Meghalaya).

Fig. 9
figure9

The complex relationship between income per capita (log y), GSDP share to agriculture (GSDPa) and the value of ώ with the help of three-dimensional scatter plots. The figure also represents the trend of relationship between log(y) and ώ as well as GSDPa and ώ on the corresponding planes. (The graphical operation has been done utilizing VBA macro-codes in Excel 3D scatter plot, v2.1, designed by Gabor Doka, Switzerland.)

The multiple regression analysis gives a deep insight into the internal function of interacting variables. The variables GSDP a and log y are fed as independent variables and ώ as dependent variable to the SPSS 17 software (see Table 5) which clearly state that both the independent variables significantly influence the dependent variable, depicting \({\acute{\omega}} \propto \left({\frac{1}{{GSDP_{A}}}} \right)\) and \({\acute{\omega}} \propto { \log }\left(y \right)\) which is synchronous with the Kuznets inequality distribution. This relationships are excellently reflected by the trend line drawn in the scatter diagram where the points (GSDP a , log y, ώ) are seen arranged around the PQRS plain, standing vertically over (GSDP a x log y) plane touching it diagonally. The overall discussion in this section approves the eligibility of ώ to be used as an indicator of assessing and mapping the economic inequality of a region under developing economy.

Table 5 The result of multiple regression analysis between GSDPa (independent var.), log y (independent var.) and ώ (dependent var.)

Income inequality mapping in Purulia district using ώ

The rationale of income inequality mapping for the district

Before proceeding toward the assessment and mapping of economic inequality in the district, this is necessary to get a brief introduction with the background of the present socioeconomic backwardness of the district. The district of Manbhum (presently Purulia) was included in the province of Bihar during the independence of India. As a consequence of the movement of Bengali-speaking peoples at the major portion of the district, the areas under 16 police stations were included with West Bengal as the district of Purulia vide the Transfer of Territory Act of Govt. of India on November 1, 1956 (Mahato 2007). Purulia got the recognition of new district, separated from Manbhum; however, the mineral resource affluent and mine-based industry prospective areas were excluded from it which starts a new economic challenge for the peoples of Purulia.

Post-independent Purulia experiences a rapid growth of population. The data from the Census of India (1991, 2001 and 2011) show the fact that there is around 15% decadal growth rate of population for the decades of 1951–1961 (16.33%), 1961–1971 (17.86%), 1971–1981 (15.65%), 1981–1991 (20%), 1991–2001 (14.02%) and 2001–2011 (15.52%). This addition of a high volume of population adds surplus pressure on land and forests in the districts. Forests were cleared rapidly to remit the growing demand of agricultural land and establishing settlement. As a result, the extensive forest coverage has been gradually transforming into isolated forest patches, dissected by human settlement and agricultural tracts. 1159 km2 of forest covered area (i.e., 18.51% of total area) of the district in 1991 (West Bengal State Forest Report 2008) has been reduced to 750.48 km2 (i.e., 11.99% of total area) in the year of 2011 (Economic Review 2011). Most part of the agricultural fields is characterized by shallow to moderately deep loamy red lateritic soil (including the very shallow gravely loamy red lateritic soil at hill slopes) with least water holding capability and insufficient humus content. Under this soil condition, the agricultural output has limited scope to be increased through enhancing the productivity of the soil with proper management. Moreover, only 711.3 km2 area (11.37% of total area) of the district is facilitated with irrigation (District Statistical Handbook 2013); hence, in most part of the district the agriculture is a seasonal activity which is almost dependent to the ‘whimsical’ monsoon rainfall.

The detailed information about the change of workforce is readily available in the population enumeration report of the Census of India. The total population of the district has increased by 15.52% between 2001 and 2011, where the main worker volume has interestingly reduced by 4.97%, and again, the marginal worker volume has increased by 32.01% (which is more than double of the figure of decadal change of total population) and non-worker population has increased by 19.28% (greater than decadal change of total population by 3.76% or as more as 121,884 in numbers). There is a spatial variation of this changing pattern of the workforce all over the district. The relative growth of x counterpart of total population p for the time frame t can be given as:

$$\left[ {\gamma_{rX} } \right]_{0}^{t} = \left( {\frac{{p_{0} }}{{x_{0} }}} \right)\frac{{\left( {x_{t} - x_{0} } \right)}}{{\left( {p_{t} - p_{0} } \right)}}$$
(7)

Figure 10 shows that there is the negative growth of main workers relative to the growth of total population at all the blocks in the district, and positive growth of marginal workers and main workers all over the area; besides, one more distinct feature is visible, the areas experiencing greater decrease in proportion of main workers also showing a greater magnitude of the relative growth of the marginal workers. This trend of partial marginalization of workforce has an immense implication on the income figure of the corresponding areas.

Fig. 10
figure10

Block wise change of a main, b marginal and c non-workers population relative to the change of total population in Purulia district (1991–2011)

The labour surplus theory of Lewis, Ranis and Fei (Lewis 1958; Ranis and Fei 1961) still forms the fundamental concept to explain the internal functions within a traditional subsistence agricultural sector. Increasing trend of population results in gradual overcrowding at the rural agricultural fields of occupation which leads to gradual declination of per-capita food production due to natural constraints in the productivity and spatial limitation of the land. As a result, the marginal productivity of labours in this sector declines ultimately falling to zero. The existence of such excess labours signifies disguised unemployment. It can be identified by the more rapid growth of non-working population volume than that of the total population volume. The district of Purulia, on its wide part, exhibits this scenario of existing subsistence agriculture-dependent economy striving for newer options of employment and income. Admittedly, the underdevelopment is rather a better condition than that of the unequal development at its extreme mode. The income inequality mapping, under this circumstance, may lead to demarcate the comparatively more vulnerable areas for providing due attention during decentralized planning and policy formulation.

Primary datasets for inequality mapping

The primary data for the analysis of income inequality have been collected from 170 villages (20 sample households from each villages), one from each of 170 Gram Panchayats all over the districts of Purulia; the coordinate of the each point has been collected using the GPS during field visit. Figure 11 shows the location of the sample sites in the district of Purulia.

Fig. 11
figure11

Primary data collection sites in Purulia district (digits in red color indicating the site identification code nos.; darker black colored lines are the boundary of blocks, and light black colored narrower lines are boundary of Gram Panchayats) (color figure online)

Calculating the value of ώ and standardizing it

The primary data from all the sample villages are processed, and the variables for calculating the values of ώ, i.e., per-capita income (y), share of main workers to total population (m), share of marginal workers to total population (r), and annual average income of marginal workers (C R ), are tabulated. The value of ώ has been determined following Equation No(4), and the calculated value of ώ has been standardized, using the following rule:

$$\acute{\omega}_{\text{std}} = \frac{{(\acute{\omega}_{\text{calculated}} - \mu_{\acute{\omega}})}}{{\sigma_{{\acute{\omega}}}}}$$
(8)

The values of \(\acute{\omega}_{\text{std}}\) have been fed to the open-source GIS software QGIS 2.8 against the respective data points attributed with specific coordinate collected by GPS for the purpose of analysis of spatial trend of income inequality. The calculation table is given in Appendix (Table 6).

Analyzing the trend

The demarcation of different income inequality zones on the spatial extension of Purulia district primarily requires categorizing the calculated indicator values through their natural clustering. Jenks natural break optimization algorithm separates the calculated and standardized values of ώ into required numbers of classes on the basis of existence of natural breaks in the distribution of the given dataset. The value of \(\acute{\omega}_{\text{std}}\) for all points is considered for the input dataset of Jenks algorithm, and all the datasets are classified into 2, 3, 4 and 5 classes consecutively through a simple Python programming using Jenks algorithm. The respective isolines, limiting the classes, are drawn on the map (see Fig. 12) via QGIS 2.8. It is found that 5 classes on the map shows a reliable spatial differentiation of the income inequality and rational explanation can be given for the classification; hence, the final inequality map has been drawn with displaying five classes (see Fig. 13) of natural breaks of the value of \(\acute{\omega}_{\text{std}}\).

Fig. 12
figure12

Demarcations of different levels of income inequality zones with the distribution of \(\acute{\omega}_{\text{std}}\)

Fig. 13
figure13

Income inequality map of Purulia district (using \(\acute{\omega}_{\text{std}}\))

Discussion and conclusion

The district of Purulia shows a degree of disparity within itself in terms of the income. The income inequality map drawn on the basis of the proposed indicator ώ brings to fore the spatial variation of economic inequality with some noticeable features there in. The entire district is subdivided into 5 classes of economic inequality on the basis of natural clustering of the calculated value of \(\acute{\omega}_{\text{std}}\) through Jenks algorithm. However, a clear observation on the map would reveal that the entire area has three distinct inequality zones. Firstly, the areas with the criteria \(0 \le \acute{\omega}_{\text{std}} \le 0.378\) are the areas with low level of income inequality. Almost all the blocks at south and southeastern part of the district, i.e., Bagmundi, Balarampur, Barabazar, Bandowan, Manbazar I and II and Puncha, are included in this category. These blocks are marked with low level of per-capita income, higher concentration of forest area to the total geographical area, greater dependency to agriculture, minimum scope of income from non-agricultural sources. Besides, one more important social characteristics of these blocks is that they accommodate the greater share of scheduled tribe population within the district. Lower income level and maximum share of GDP originated from agricultural and forestry results in a lower standard of living but leading to a low level of inequality of income within the region. Secondly, the areas with the criteria \(0.568 \le \acute{\omega}_{\text{std}} \le 1\) which is the zone of high to very high level of income inequality, having two subclasses: (i) the areas with ‘\(0.822 \le \acute{\omega}_{\text{std}} \le 1\)’ which is the zone of highest level of income inequality—the ‘core of inequality,’ enclosed by (ii) the areas with ‘\(0.568 \le \acute{\omega}_{\text{std}} \le 0.822\)’, which is the second highest level of inequality areas. These areas are clustering around the three municipalities (i.e., sub-district level urban headquarters), namely Purulia (23.3321° N, 86.3652° E), Jhalda (23.3650° N, 85.9752° E) and Raghunathpur (23.5344° N, 86.6687° E). Besides, almost all the small- to medium-scale industrial units of the districts are located within this zone. The higher per-capita income zone in the district has also appeared as the zone of higher-income inequality. Thirdly, areas with the criteria \(0.368 \le \acute{\omega}_{\text{std}} \le 0.568\) which posses the moderate level of inequality, may be considered as the ‘transition zone, stretched between lower and higher level of inequality areas. A close observation on the inequality map also reveals that there is a coarse color texture, indicating a contrasting higher and lower value of \(\acute{\omega}_{\text{std}}\) persisting side by side. Basically, the development initiatives, sponsored by the government have an immense role for these areas. The long-term planning policies, befitted with the sociocultural-economic characteristics of the area, targeting for alternative options of livelihood and employment may transform this wide ‘transitional’ zone to the zone of low income inequality. The process of development in India has long been equated with the agricultural growth, and the generalization of this idea may have misleaded the planning procedure, especially the vast rural areas of the country where agriculture has a degree of environmental and functional limitations (like the present study area). Now, development is required to be conceptualized as a strategy, designed to improve economic and social life of a specific group of people, necessarily sticking to a ‘pro-poor’ approach. Hence, the essence of future development lies in spontaneous people’s participation in the development process and creating the capacity of the people through the empowerment of the community for sustained development with the rational utilization of ambient natural and social resources.

The income inequality is an indispensible part of the economy of a region, and the magnitude varies at different stages of economy. As an indicator of expressing this inequality, ώ uses a very simple algorithm, i.e., the level of disproportion of income shared by the members of different classes of workers is the expression of the income inequality of a region. The four variables used for the calculation, i.e., income per capita, average income of the marginal workers and share of main and marginal workers to total population are commonly available dataset; and moreover, the link of those variables with the ambient economy is easily perceivable across academic disciplines. All of the above, the value of ώ, when used as an inequality indicator for the national-level data of India, has successfully followed the Kuznets inequality distribution which is still recognized as a benchmark in the discussion of economic inequality. It is obvious to examine the response of ώ with cross-country dataset as well as temporal data also for the more precise justification of its validity to be used as an inequality indicator. Besides, the function of ώ is advantaged with its flexibility, i.e., the function can efficiently be used with required modification in the variable settings to assess the income inequality between multiple discrete subgroups within the population (e.g., genders, religion classes, ethnic classes) provided that the income and population enumeration data remain available subgroup wise. Analysis from the standpoint of a spatial science essentially tries to link the process with the space and also concentrates on interpreting the change of the magnitude of processes over space with reference to time. The distribution of population of certain criteria over space is exhibited here clearly, and it is possible to enumerate with a satisfactory level of precision. This study has proposed to identify the variation of magnitude of development process, i.e., inequality through analyzing the distribution pattern of different classes of workers and corresponding income pattern in view of assembling the analytical tools for the researchers in the domain of economic inequality toward better understanding of the inequality over space as well as time.

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Correspondence to Mukunda Mishra.

Appendix

Appendix

See Table 6.

Table 6 The brief primary dataset to calculate ώ

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Mishra, M., Chatterjee, S. An effort of mapping the income inequality in the district of Purulia, West Bengal, India. J. Soc. Econ. Dev. 19, 111–142 (2017). https://doi.org/10.1007/s40847-017-0035-1

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Keywords

  • Working class
  • Income per capita
  • Development
  • Deprivation
  • Marginal workers
  • Non-workers