In the evolution of spatial economies, it may so happen that regions may converge at one “spatial scale” but can diverge at another scale, or there may be marked presence of “convergence clubs”. This paper analyses sectoral and aggregate per capita incomes in Maharashtra over the period 1993-94 to 2002-03. In contrast to the trend of divergence at the interstate level, the regional economies in Maharashtra are converging, though with significant differences in the rates of convergence across various sectors and regions. Marathwada and Vidarbha, with weak industrial sectors, have been the most underdeveloped regions in the state over the years. The study also highlights the impact of “spatial spillovers” on regional patterns of economic development in the state and its policy implications.

ABDUL SHABAN

M

Notwithstanding the overall higher economic growth and development in the state, all is not well with its economy as obsession with economic growth and generation of wealth has led to the relative neglect of distributional aspects. It has frequently been stated that if Greater Mumbai, and Pune division are taken out, the rest of Maharashtra would not be better than the ‘BIMARU’ states. Demand for a separate state of Vidarbha on the basis of its low development and the demand for more allocation of financial resources for the development of Marathwada can be seen in the above context.

The present paper attempts to examine the trends in regional inequality in sectoral as well as aggregate per capita income in Maharashtra. More specifically, it attempts, (1) to discern the regional structures of income and the composition of regional income in the state of Maharashtra (regions being defined in terms of districts and groups of districts), (2) to examine inter-regional and inter-sectoral differences in the growth rate of income, (3) to analyse the level and trends in regional income inequality, (4) to explore the relationship between trends in spatial associations and regional inequality, and (5) to throwlight on regional convergence and the spatial spillover process in the state.

The paper is divided into six sections. Section II deals with data and methodology used in the study. It also briefly discusses the limitation of conventional econometric methods in analysing spatial data and how spatial econometric methods have an advantage over the conventional methods. Sectoral composition of regional incomes and their growth are examined in Section III, and an analysis of regional inequality in income is presented in Section IV. Section IV also highlights the relationship between trend in regional inequality and spatial associations. Convergence of regional income and the spatial spillover process through simulation are examined in Section V. The last section presents a summary and conclusions.

The directorate of economics and statistics, government of Maharashtra, Mumbai has compiled district-wise ‘Net Domestic Product’ for the state from 1993-94 onwards. The latest year for which the data are available is 2002-03. This 10-year data (199394 to 2002-03) for the districts in the state have been used in the present study. There were 30 districts in the state in 199394, and since then five new districts have been created. In order to maintain comparability of the data of spatial units, the data for newly created districts have been clubbed with their parent districts. To analyse regional inequality and convergence, various statistical methods, besides “different ratios and proportions”, have been used. Some of these methods are briefly presented below:

Measures of Regional Inequality

To measure district level inequality in per capita income, the Gini coefficient, Theil’s inequality index (global and decomposed), and the coefficient of variation (CV) have been used.

The Gini coefficient is derived from the Lorenz curve. There are several ways to compute the Gini coefficient for a dataset.

The present study uses the following formula to calculate the Gini coefficient (G). n

G = Σi–1 (2i – n – 1)x' i/n2 μ …(1)

Where i is the individual’s rank order number, n is the number of total individuals, xi' is the individual’s value, and μis the population average. The Gini coefficient is a full-information measure, looking at all parts of the distribution. G ranges between zero and 1: a zero shows perfect equality among regions/individuals and 1 indicates that all development is concentrated to only one region/individual. It facilitates direct comparison between two populations regardless of their sizes.

Among regional inequality measures, another preferred method is Theil’s index of inequality (T) as it allows easy decomposition of total inequality between and within regions. T is computed as follows [Rey 2001]:

T = Σi=1 siln(nsi) …(2) Where n is the number of regions, yi is the variable in question in regions i, and n

si = yi/Σ…(3)

The decomposition property of T has been exploited to investigate the extent to which global inequality is attributable to inequality “between” or “within” a regional grouping. By partitioning the n spatial observations into ωmutually exclusive and exhaustive groups, T can be decomposed as follows:

T = Σg=1sg ln(n/ngsg) + Σg=1 Σi∈g Si,g ln (ngsi,g) …(4)

Where ng is the number of observations in group g (and Εgng = n),

sg = Σi=g yi,g/Σi=lyi is the share of total value of the variable y ngaccounted for by group g, and si,g = yi,g / Σi=l yi,g is region i’s share of group g’s value. The first term on the right hand side of the above equation is the “between-group” (TB) component of inequality, while the second term is the ”within-group” group (T) component of

T = TB + T…(5)

In spatial context, the within-group term measures intraregional inequality, while the between-group component captures inter-regional inequality. In other words, the inter-regional term measures the distance between the mean values of the aggregate groups, while the intra-regional term measures distance between the values of units belonging to the same region.

Spatial autocorrelation can be defined in terms of value similarity with locational similarity [Anselin and Bera 1998]. Positive spatial autocorrelation occurs when similar values for a variable are clustered together, and negative spatial autocorrelation appears when dissimilar values are clustered in space. Although various methods have been proposed to measure the spatial autocorrelation, the present study uses Moran’s I statistics, which is most widely used measure of spatial autocorrelation. Moran’s I is computed as follows:

i=1 ...(6)

Where n is the number of observations, wij is the element in spatial weight matrix w corresponding to the region (i,j), the observations xi and xj are in deviation from their mean values for region i and j, respectively, and s0 is the normalising factor equal to the sum of the elements of the weight matrix, i e, s0 = ΣiΣj wij [Anselin 1992].

Different definitions of interaction between regions cause different spatial weight matrices. The study adopts the simplest but most powerful the binary contiguity matrix, where the element (i,j) of the spatial weight matrix, wij = 1 if region i and j share a border, and zero otherwise [Anselin 1992; Hanning 1990; Upton and Fingleton 1985]. When the spatial weight matrix is row standardised such that sum of each row equals 1, the expression [Lim 2003] given above simplifies to:

nn ΣΣ wij xi xji=1 j=1 I = n Σxi 2 …(7) i=1 or, in matrix notation:

I = ——— ...(8)

Where w is a spatial weight matrix and x is vector of observed value in deviation from the mean. The value of Moran’s I ranges between -1 and +1. Negative value of Moran’s I shows negative spatial autocorrelation and vice versa. When the spatial weight matrix is row standardardised, the spatial lag value of the region is equal to the mean value of the neighbouring regions.

If regions with similar values/per capita income are clustered together, the positive spatial autocorrelation is observed, and if the arrangement of spatial units in geographic space is such that they form a check-board pattern, a negative spatial autocorrelation is the outcome. Comparing the spatial autocorrelation in per capita income for each year, the study traces the trajectory of regional dynamics and distribution patterns of income over time.

In order to have a more disaggregated view of spatial autocorrelation/association, the Moran Scatter Plot suggested by Anselin (1996), has been used to capture the local structure of spatial associations. Since the elements in the vector x in the above equation are deviations from the mean, the Morna’s I statistic is formally equivalent to the slope coefficient in the linear regression of spatial lag wx on x. With the help of the Moran scatter plot, one can decompose the global spatial association into four different quadrants, which correspond to four different kinds of local spatial associations between a region and its neighbour. These four quadrants and association types are:

Regression Analysis

A conventional “ordinary least square” (OLS) regression equation can be stated as,

y = α + βX + ε ...(9)

where y shows a vector of dependent variable, and X presents independent variables. The above equation assumes that random error terms, ε, is normally distributed with zero mean and homoscedastic variance σ2.

However, in the above equation, there are no parameters that take care of spatial effects or spatial autocorrelation in the data. The equation treats regions as “isolated islands” [Quah 1996]. It does not capture the fact that one region’s economic destiny is dependent upon those of other regions. Indeed, the evolution of each region is closely related to the evolution of, at least, neighbouring regions. We, therefore, assume that regional distribution of income is unlikely to be spatially independent and random. When models are estimated for cross-sectional data on spatial units, the lack of independence across these units can cause a serious problem of model misspecification when ignored [Anselin 1988; Lim 2003]. Three kinds of models/specifications can be used to deal with spatial dependence of observations: The spatial lag model, the spatial error model, and spatial cross-regressive1 model [Rey and Montouri 1999; Anselin 1988; Anselin and Bera 1998].

In spatial lag model, substantive spatial dependence (through spatial externalities and spillover effects) is incorporated through a spatially lagged dependent variable:

y = α + βln X + ρwy + ε ...(10)

where ρ is a scalar spatial autoregressive coefficient, wy is spatial lagged dependent variable for a spatial weight matrix w. Thus, in this model the resulting per capita income in a region is also considered to be dependent on per capita income in its neighbouring region. The ordinary least square (OLS) estimator of this model yields biased and inconsistent estimates for the coefficients due to the simultaneity between the error term and the spatially lagged variable. Therefore, alternative estimators based on maximum likelihood (ML) and instrumental variables have been suggested for the estimation to get consistent results [Anselin 1988; Anselin and Bera 1998]. The paper uses the ML estimate of this model.

The spatial error model is applied when spatial dependence is expected while working through the error process, which can result from a measurement problem [Rey and Montouri 1999]. Spatial error dependence may be interpreted as a “nuisance” in that it reflects spatial autocorrelation in measurement errors in variables that are otherwise not crucial for the model. The spatial process pertaining to the error term can be expressed as [Lim 2003; Rey and Montouri 1999]:

ε = λwε + ξ

...(11)ε = (I–λw)–1ξ

where ε is a vector error terms, λ is a spatial error coefficient. ξ is a vector of error terms, which is normally distributed with zero mean and homoscedastic variance σ2 ξ. Including the spatial autocorrelation of the error terms, the above given regression model becomes:

y = α + βX + (I -λw)–1ξ ...(12)

The OLS estimator will again give biased estimates of the parameters’ variance. Therefore, the spatial error model is estimated with ML method [Anselin 1988; Anselin and Bera 1998]. From the equation (12) it is evident that a random shock introduced into a specific district will not only affect the growth rate in that district, but through spatial transformation (I -ξW)–1, will impact the growth rate of other districts as well. The inverse operator in the transformation defines an error covariance structure that diffuses district specific shocks not only to the district’s neighbours but throughout the system [Rey and Montouri 1999].

Geographically Weighted Regression:Spatially Drifting β-coefficients

When the usual regression methods are applied to spatial data, it is assumed that there exists a stationary spatial process. However, spatial data are seldom stationary. When spatial non-stationarity exists, the same stimulus or shock produces a different response in different parts of the study region. The non-stationarity may emerge due to: (i) sampling variation – called nuisance variation or not real spatial non-stationarity, (ii) relationship intrinsically different across space – real spatial non-stationarity, and (iii) model misspecification. If non-stationary data is modelled with a stationary model, the consequence may be (i) wrong conclusions are drawn, and (ii) the residuals of the model might be highly autocorrelated.

In global models, spatial processes are assumed to be stationary and as such are location independent. The local models like spatial expansion method [Casetti 1972, 1997; Jones and Casetti 1992], and geographically weighted regression (GWR) model decompose the global model and produce results that are location dependent. These models are based on the first law of geography: “everything is related to everything else, but closer things are more related”. These models address the spatial/geographical non-stationarity directly as they allow the relationship to vary over space, i e, regression coefficients need not be the same everywhere over the space. The expansion model suggested by Casetti (1972, 1997) suffers from some limitations like: (i) the technique has been restricted to displaying trends in relationships over space with the complexity of measured trends being dependent upon the complexity of expansion equations, and, therefore, the spatially varying parameters obtained through the expansion method might obscure important local variations to the broad trends represented by the expansion equations; (ii) the form of expansion equations needs to be assumed a priori; (iii) the expansion equations must be deterministic to remove problems of estimation in the terminal model [Fotheringham, Brusdon and Charlton 2002]. All these problems are overcome by GWR. We, therefore, have used GWR in our analysis for detecting spatial heterogeneity and patterns in regression parameters.

In the regular OLS model, regression parameters at ith location

where X and Y are independent and dependent variables respectively, and Wi is an n-by-n local weight matrix, whose offdiagonal elements are zero and diagonal elements denote the

geographical weighting of observed data for point/region i. urbanised districts – Mumbai, Thane, Pune and Nagpur account

...(15)0 0 ...

win Where win denotes the weight of the data at point n on the calibration of the model around point i. These weights will vary over space with i, which distinguishes GWR from the traditional weighted least square, where the weighting matrix is constant. The study uses the Gaussian weighting method.

III Regional and Sectoral Distribution of Income and Its Growth

The regional shares of aggregate and sectoral income in Maharashtra, presented in Table 1 for the year 1993-94 and 200203 show the following: (1) Economic development in the state is highly polarised and metropolitised, as about two-fifths of the Net State Income comes from the Konkan region; also four highly for about one-half of the NSDP. (2) Not only the four major urbanised districts just mentioned also account for more than 55 per cent of the tertiary sector income, but the Konkan region alone accounts for about 46 per cent of this sector. (3) There has been a significant dispersal of industrial activities from the Konkan to other regions in the state. (4) Whereas shares of other regions in primary sector income have stagnated or declined, there has been a significant increase of the share of western Maharashtra in this sector. (5) Although there has been a marginal increase in the shares of the four highly urbanised districts in NSDP over the years, inter-district inequalities in sectoral as well as aggregate income have declined in 2002-03 in comparison to 1993-94.

The Konkan region has had a significantly high share of the state income over the years. The region accounts for about 25 per cent of the state population, but its share in state’s income has been more than 40 per cent. Table 2 shows that as against per capita state income of Rs 12,326 and Rs 15,484 in 199394 and 2002-03, the region had per capita income of Rs 20,424 and Rs 23,938, respectively, in the same years. Although, Konkan is a highly developed region of the state, spatially polarised

IV Spatial Association and Inequality

Moran scatter plots for the total as well as the sectoral per capita incomes of the districts in the state are given in Figures 1A through 1H. The figures show a strong positive spatial association in economic development in the state. In fact, global Moran’s I for all the sectors establishes this fact (Table 4). The strong spatial association shows that the relatively highly developed districts are lying in a geographically contiguous area or beside one another. This indicates strong regional inequality in economic development in the state. Table 5 presents the frequency distribution of locations of districts in different quadrants of the Moran scatter plots of all the districts for all the three sectors as well as total per capita income together. The high frequency of location of the districts of Marathwada and Vidarbha in quadrant III indicates a contiguous geographical area of underdevelopment and deprivation. And, high frequency of location of districts of Konkan and western Maharashtra in quadrant I shows relatively high development in the regions. The location of Greater Mumbai, Thane, and Raigad in quadrant III is because of low development of the primary sector and due to that they have a frequency of 10 each, equal to the number years of data used in the analysis.

Along with Global Moran’s I, Table 4 also provides the Gini coefficient, CV and Theil’s global as well as decomposed inequality indices. All the inequality indices show that there has been only a very marginal decline in district level inequality in total as well as tertiary sector per capita income in the state. However, the decline of inequality in the primary and secondary sector per capita income has been more significant. What is obvious from the indices given in Table 4 is that there has not been a smooth decline in the inequality in per capita income but it has fluctuated over the years in case of the aggregate as well as the sectoral incomes.

Decomposed Theil’s inequality index shows that till 1998-99, interregional inequality (read as inter-divisional inequality, as division-wise data is used for this) accounted for the major proportion of the “global” inequality. However, after that the contributions of inter-regional and intra-regional inequality in the “global” inequality have become almost equal. Intra-regional inequalities are the main cause of inequality in primary sector income. While in the secondary sector, intra-regional and interregional inequalities contribute almost equally to global inequality. Global inequality in tertiary sector income has been high due to intra-regional inequality, but over the years the gap between both the inequalities has narrowed down due to a decline in intraregional inequality and increase in inter-regional inequality. However, intra-regional inequality still remains high. It is

Table 5:Location of Districts in Different Quadrants Based

Three Sectors and Total Per Capita Income Together

Districts Quadrant I Quadrant II Quadrant III Quadrant IV

Greater Mumbai 30 0 10 0 Thane 30 010 0 Raigad 29 1 10 0 Ratnagiri 13 27 0 0 Sindhudurg 23 15 1 1 Nashik 17 10 0 13 Dhule 032 8 0 Jalgaon 0 0 24 16 Ahmadnagar 7 24 6 3 Pune 30082 Satara 19 18 0 3 Sangli 35 1 1 3 Kolhapur 29 0 0 11 Solapur 14 15 5 6 Aurangabad 0 9 12 19 Jalna 6 034 0 Parbhani 5 0 31 4 Beed 6031 3 Nanded 0 931 0 Osmanabad 6 0 31 3 Latur 4 531 0 Buldhana 0 9 31 0 Akola 3 625 6 Amravati 16 0 19 5 Yavatmal 6 4 30 0 Wardha 19 11 9 1 Nagpur 4 7 029 Bhandara 8 13 15 4 Chandrapur 11 0 10 19 Gadchiroli 7 13 16 4

Note and Source:As in Table 1.

Table 6:

σσσσσ

-Convergence of Sectoral and Total Per CapitaIncome in Districts of Maharashtra, 1992-93 - 2002-03

Parametres Primary Sector Secondary Sector Tertiary Sector Total

α 7.316(0.000) 10.237(0.000)	4.586(0.000) 3.758(0.000)
β -0.158(0.001) -0.269(0.000) R 2 0.740 0.899	-0.057(0.000) -0.041(0.098) 0.871 0.217
Notes: p-values are in parentheses.
Source: The same as in Table 1.

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 -2.0 0.0 2.0 1.0 3

Figure 1: Moran Scatter Plots of Total and Sectoral Per Capita Income of Districts in Maharashtra

A Per Capita Total Income, 1993-94 B Per Capita Total Income, 2002-03

Spatial Lag of Standardised log

Spatial Lag of StandardisedSpatial Lag of StandardisedSpatial Lag of Standardised

Per Capita Income

log Per Capita Income log Per Capita Income log Per Capita Income

-1.0-0.50.00.51.01.52.02.5-2.0-1.00.01.02.03.0

Spatial Lag of Standardised

Spatial Lag of StandardisedSpatial Lag of StandardisedSpatial Lag of Standardised

Log Per Capita Income

log Per Capita Income log Per Capita Income log Per Capita Income

-1.0 -0.5 0.0 0.5 1.0 1.5 -4.0 -2.0 0.0 2.0 4.0

Standardised log Per Capita Income Standardised log Per Capita Income C Primary Sector Per Capita Income, 1993-94 D Primary Sector Per Capita Income, 2002-03

-1.5 -1.0 -0.5 0.0 0.5 1.0 -4.0 -2.0 0.0 2.0 4.0

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 -4.0 -2.0 0.0 2.0

Standardised log Per Capita Income Standardised log Per Capita Income E Secondary Sector Per Capita Income, 1993-94 F Secondary Sector Per Capital Income, 2002-03

-1.0-0.50.00.51.01.52.02.5-2.0-1.00.01.02.03.0

.0

Standardised log Per Capita Income

Standardised log Per Capita Income

H Tertiary Sector Per Capita Income, 2002-03

G Tertiary Sector Per Capita Income, 1993-94

-1.0 -0.5 0.0 0.5 1.0 1.5 -2.0 0.0 2.0 4.0

-1.0 -0.5 0.0 0.5 1.0 1.5 -4.0 -2.0 0.0 2.0 4.0

Standardised log Per Capita Income

Standardised log Per Capita Income

Note and Source:As in Table 1.

interesting to note that inter-regional inequality in the primary and tertiary sector has risen over the years, while its counterpart, intra-regional inequality has declined. This indicates that greater divisional homogeneity in development of these two sectors is emerging in the state. Increase in Global Moran’s I points out increased spatial association in tertiary sector and secondary sector income. However, at the aggregate level, spatial association has steadily weakened since 1997-98, indicating weakening of the nearest-neighbour bond in similarity of development in recent years.

Regression of cross-sectional regional inequality in per capita income (coefficient of variation of log of per capita income in our case) on time is called σ-convergence analysis. If the estimated regression coefficient is negative, the regions are said to be converging and viceversa. The σ-convergence results presented in Table 6 show that at sectoral level, the convergence coefficientsthough not very high, are statistically significant at 1 per cent level of significance. However, the convergence coefficient for total/aggregate per capita income is significant only at about 10 per cent level. The speed of convergence of districts is highest in case of the secondary sector, followed by the primary and tertiary sectors.

With the help of the OLS method and other spatial econometric methods, an attempt has been made to measure β-convergence of sectoral and aggregate per capita income of the districts in the state. After statistical check and evaluation, the best results are reported in Table 7. Robust LM-lag test suggests that the OLS model for aggregate per capita income suffers from spatial lag autocorrelation. Therefore, inclusion of spatial lag value in the model has been done to overcome this problem. The Akaike information criterion and R2 also indicate that the spatial lag model is the relatively best model for aggregate per capita income data. The rate of β-convergence of districts income has been statistically significant indicating that homogeneity in economic development in the district is emerging. The implied annual rate of β-convergence of aggregate income is 2.6 per cent. This means that, on an average, it will take about 27 years to close one-half of the gaps between any district’s initial level of per capita income and common long-term per capita income of all the districts.

The β-convergence for all the sectoral incomes is also statistically significant. While the best regression models for primary and secondary sector incomes is OLS, it is the spatial error model, which gives the best result for tertiary sector income. The highest implied annual rate of β-convergence is found for the primary sector income (convergence rate 4.6 per cent), followed by the secondary (2.8 per cent) and tertiary sector (1.7 per cent) incomes. This means that these sectors would take about 15 years, 25 years and 41 years, respectively for half of the distance between the initial level of income and the sector specific steady-state levels to vanish [Fischer and Stirbock 2004].

This finding of the convergence (σ and β) of district income in Maharashtra is noteworthy in the context that state level per capita income in India shows divergence rather than convergence. The estimated coefficients for σ-convergence and β-convergenc2 for the period 1993-2003, for 29 states (except Mizoram) including Chandigarh union territory, are found to be 0.0662 (p-value= 0.000; R2 =0.877), and 0.127 (p-value= 0.050; R2 =0.126), respectively. The other studies, which have taken even longer periods into account also show the similar results [Dasgupta et al 2000; Ghosh et al 1998; Marjit and Mitra 1996; Raman 1996; Shaban 2002]. This shows that regional economies evolve in multiple ways. They can converge and diverge simultaneously at different regional scales. Due to this reason, the regional scale at which a study is undertaken becomes extremely important as it influences the results and conclusions.

It is possible that within Maharashtra some geographically contiguous group of districts may converge at a higher rate than the other groups, or there may be group of districts that may be diverging instead of converging, thus forming convergence/ divergence clubs. The global regression coefficients reported in Table 7 are not able to capture this. Therefore, a geographically weighted regression method, which provides convergence coefficient for all the districts, is used for this purpose.

Figures 2A through 2D show choropleth maps of local regression/convergence coefficient of districts of total as well as sectoral per capita income. The regression coefficients have been classified using Jenk’s method of classification/clustering. This method identifies breakpoints between classes using a statistical formula (Jenk’s optimisation). It minimises the sum of the variance within each of the classes and finds groupings and patterns inherent in data. This method of classification is highly efficient and reveals regional structures. The maps show that though all the districts in the state have experienced convergence (as they have negative regression coefficients), there are marked “convergence clubs” of districts in the aggregate as well as in sectoral per capita income. In total per capita income, districts of eastern and central Vidarbha show a high β-convergence rate, while districts of western Vidarbha, northern Konkan, along with Pune, Osmanabad and Solapur have a relatively low level of convergence. A geographically contiguous area comprising of north-western Maharashtra (Nashik division) and Akola and Beed districts shows a very low level of convergence.

In the primary sector, the per capita income for eastern and central Vidarbha again show a relatively higher rate of convergence. Southern Maharashtra (south-western Maharashtra and south Marathwada) shows moderate level of convergence, while the least level of convergence is found for the districts of Nashik division. β-convergence in secondary sector per capita income is higher in the districts of Konkan and south-western Maharashtra. Central Maharashtra has a moderately high rate of convergence, while the least rate of convergence is found in eastern Vidarbha, and southern Marathwada.

In case of the tertiary sector, the per capita incomes in the districts of Vidarbha, particularly northern Vidarbha is converging at a higher rate than the rest of the districts in the state. Konkan

Table 7: Estimates of

βββββ

Parametres Primary Secondary Tertiary Total Per Capita Sector Sector Sector Income OLS OLS Spatial OLS Spatial Error(ML) Lag(ML)

α 2.635 1.853 1.614 2.197 2.363

(0.011) ρ – – – – -0.198

(0.455) τ ––––– R2 0.308 0.562 0.253 0.125 0.148 AIC 14.454 -27.567 -46.851 -11.998 -10.541 Moran’s I 0.091 0.063 – -0.025 –

(0.227) (0.299) (0.812) LM-Lag Test 0.232 0.293 – 0.484 –

(0.629) (0.588) (0.486) Robust LM-Lag Test 0327 2.389 – 4.493 –

(0.566) (0.122) (0.034) LM-Error Test 0.514 2.347 – 0.039 –

(0.435) (0.267) (0.054) Implied convergence rate (θ) 0.046 0.028 0.017 0.025 0.026

Time taken (in years) to complete ½ distance to the steady-state 15.07 24.76 40.77 27.73 26.66

Notes: p-values are in parentheses. The implied convergence rate θ is calculated as θ = ln(β+1)/-t, where t is the length of time. AIC = Akaike Information Criterion; LM = Lagrange Multiplier Test; the ½ distance to the steady state is computed using formula ln(2)/θ.

Figure 2: Spatial Differences in Beta Convergence of Total and Sectoral Per Capita Income in Maharashtra, 1993-94 to 2002-03

A Total Income B Primary Sector

0 70 140 280 kilometres

Note:The classification of beta-coefficients (regression coefficients) for all the above figures is based on Jenk’s method.

along with Kolhapur seems to be evolving together at a moderate β-convergence rate, while the least rate of convergence is in Marathwada. The GWR results show that there is no spatial stability in regression coefficients but marked presence of heterogeneity in convergence, which was well masked by global β-convergence coefficients.

The presence of significant spatial error dependence in tertiary sector per capita income implies that the random shocks to a specific district would be propagated throughout the state. This is illustrated in Figures 3A through 3D, where we introduce shocks (equal to two times the standard error of the estimated spatial error specification) to the error terms for the four districts, viz, Greater Mumbai, Pune, Nagpur and Parbhani, and substituted the maximum likelihood estimates of the spatial error model coefficient into equation (12) to estimate the degree of spillover.

The selection of Greater Mumbai, Pune and Nagpur for the simulation is based on their regional demographic and economic prominence, while Parbhani was selected due to its interior location amidst underdeveloped districts. As expected, the shocks equal to two times of the standard error have highest impact on the districts they are applied to. Due to the shocks, the growth rates of tertiary sector per capita income over the period 199394 – 2002-03 in Greater Mumbai, Pune, Thane and Parbhani become about 15 per cent, 11 per cent, 12 per cent and 9 per cent higher than the estimates without the shocks to these districts.

There are clear spatial patterns of propagation of these shocks to other districts. The immediate neighbours of the districts, which are given shocks, experience a higher change in the growth rate, while the magnitude of shock/spillover dampens as distance from the focus increases. The simulation shows that shock (investment) in the district of Parbhani would be more beneficial for balanced regional development, as spillover due to the shock to the districts are propagated mostly to the underdeveloped districts.

The present paper analyses the growth and distribution of sectoral and aggregate incomes in the 10-year period 1993-94 to 2002-03 in various regions of Maharashtra. It is found that notwithstanding its overall high economic development, Maharashtra suffers from acute regional inequality. About a half of the total income in the state is accounted for only by the Konkan region, comprising the districts of Greater Mumbai, Thane, Raigad, Sindhudurg, and Ratnagiri. After the Konkan, western Maharashtra is the next highest developed region and is followed by Vidarbha and Marathwada. Four highly urbanised districts of Greater Mumbai, Thane, Pune and Nagpur also account for about onehalf of the total state income, and about 60 per cent of tertiary

Annual Growth Rate (per cent) 0 150 300 kilometres Annual Growth Rate (per cent) Annual Growth Rate (per cent) Annual Growth Rate (per cent) 0 155 310 kilometres C Shock to Nagpur D Shock to Prabhani 0 150 300 kilometres 1.31642 – 15.49111 0.25877 – 1.31641 0.09311 – 0.25876 0.02266 – 0.09310 0.00000 – 0.02265 1.47949 – 10.80311 0.38376 – 1.47948 0.11745 – 0.38375 0.05542 – 0.11744 0.00000 – 0.05541 1.79655 – 8.64743 0.38065 – 1.79654 0.13067 – 0.38064 0.04588 – 0.13066 0.00000 – 0.04587 0 155 310 kilometres 1.59842 – 11.54744 0.63163 – 1.59841 0.30673 – 0.63162 0.06076 – 0.30672 0.00000 – 0.06075 Note:The same as in the Figure 2.

Figure 3: Changes in Annual Growth Rate of Tertiary Sector Per Capita Income Due to Shock to Some Districts in Maharashtra,1993-94 to 2002-03

(Per cent)

sector income. This shows that the state economy has become highly metropolitised.

The composition of the state income has changed much more in favour of the tertiary sector, which presently accounts for about 60 per cent of the NSDP, while the primary sector has got further marginalised, accounting for less than 13 per cent of the total income in the state in recent years. Significantly, about twothirds of the state’s population directly depends upon the primary sector for its livelihood. Therefore, the marginalisation of the primary sector is the marginalisation of two-thirds of the population of the state. Not only the share of the primary sector has gone down in different regions over the years but in absolute terms as well it has declined. Stagnation in forestry, mining and fishing has mainly led to the decline in primary sector per capita income. It was expected that the development of agriculture would compensate the losses (depletion of forest, mineral and fishing resources), however, it has not been so except in the western Maharashtra. One major spatial transformation that the state economy has experienced is in the secondary sector: the industries, which were concentrated in the Mumbai-Thane belt, have moved to other regions of the state (as well as out of the state).

There has been marked stability in the ranking of regions in economic development over the years in almost all the sectors. The Konkan region has been the highest developed region, followed by the western Maharashtra, Vidarbha and Marathwada.

The growth of regional economies in the state is mainly led by the tertiary sector. The share of the secondary sector is stagnating, while that of the primary sector has been declining. In comparison to 1993-94, the inequality in per capita district income (aggregate as well as sectoral) has declined in 2002-03. However, inequality in the secondary sector per capita income is higher than other sectors and the aggregate income, albeit the inequality in this sector has declined higher than the other sectors.

Conventional econometric (regression) methods have often been used to find outβ-convergence of regional incomes. However,the conventional econometric methods used for spatial data often yield imprecise or wrong results as spatial data are seldom stationary. To overcome this problem, the present study has used spatial econometric techniques to estimate coefficients for ßconvergence wherever needed.

District-wise sectoral and total per capita incomes in the state show σ and β-convergence. The local regression coefficients show marked presence of “convergence clubs”. The convergence is relatively higher in districts of Vidarbha in the primary, tertiary and aggregate per capita income, while in case of the secondary sector income, it is higher in the Konkan and western Maharashtra regions. District level sectoral as well as aggregate per capita income data show marked spatial association and so the spatial spillover and contagion effects. However, this contagion effect is higher in central Maharashtra than others, meaning thereby that shocks given in some regions are able to significantly affect larger number of districts. Shock to Parbhani due to its central location significantly affects larger number of districts than the shocks to other districts. This differential spatial spillover process of the same level of shocks at various locations in the state has implications for planning and development. The findings show that giving a boost to economies of interior and backward districts like Parbhani, instead of Greater Mumbai, Pune or Nagpur, would be more beneficial for balanced regional development of the state, as beneficial effects generated due to the shocks are propagated mainly to backward districts. The study shows that it is likely that most of the benefits due to investment and development in Greater Mumbai and Pune would remain concentrated in the Konkan and western Maharashtra region, already relatively highly developed regions in the state.

The convergence (σ and β) of regional economies within Maharashtra is also noteworthy in the context that state economies in India show divergence of per capita income rather than convergence. This shows that regional economies evolve in multiple ways. At one regional scale, they may be converging (or maintaining the same level of inequality), but at other regional scales, they may diverge. Due to this reason, the regional scale at which a study is undertaken becomes extremely important.

m

Email: shaban@tiss.edu

[The author is thankful to R N Sharma and an anonymous reviewer for helpful comments on the paper.]

1 In the spatial cross-regressive model, the spatial effect is dealt with the

introduction of a spatial lag of the explanatory variables, wX [Rey and

Montouri 1999], and, thus, the regression model becomes:

This specification implies that per capita income in a region is affected

not only by the independent variables, but also the spatial lag of the

independent variables. As the spatially lagged explanatory variable is

exogenous, the estimation of the spatial cross-regressive model can be

based on OLS [Rey and Montouri 1999]. 2 OLS estimator is used as no spatial dependence/association in the state

level per capita income is found.

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