AGRICULTURAL DEVELOPMENT IN MAHARASHTRA - AN INTER DISTRICT ANALYSIS.

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1 Bulletin of the Marathwada Mathematical Society Vol. 9, No. 2, December 2008, Pages AGRICULTURAL DEVELOPMENT IN MAHARASHTRA - AN INTER DISTRICT ANALYSIS. S.W. Jahagirdar and Shubhangi Alexander Department of Statistics, Dr. Punjabrao Deshmukh Krishi Vidyapeeth, Akola, M.S., INDIA Abstract This paper analyzes the degree of development of different districts and composite index of development computed with the help of Principal Component Analysis method. Principal components are the linear combinations of random or statistical variables which have special properties in terms of variances. Out of 29 districts of Maharashtra, 10 districts were developed, 13 developing and 6 districts poorly developed. Most of the developed districts belong to Western Maharashtra while developing were from Vidarbha and Marathwada region. 1 INTRODUCTION The existence of an agricultural infrastructure produces agricultural goods and services and the existence of human related services of education and health, provide the trained man power and also protect its health. As development is a multidimensional process, its impact can not be captured fully by any single indicator. Moreover, a number of indicators when analyzed individually do not provide an integrated and easily comprehensible picture. Growth process in agricultural sector does not operate at an even pace over a time. The experience is that agricultural growth pattern exhibits notable variation between crops, districts and even from year to year. The variation in agricultural growth among districts develop rapidly as compared to those who do not possess these facilities. Agricultural production in the country has increased at a compound growth of about 2.5 percent per annum over the last three decades. Keeping in view the importance of agricultural development in the overall economic development of a region and the role of infrastructure in agriculture to quantify agricultural development in Maharashtra state with the objective of 1 To estimate the composite index of agricultural development for each district by using Principal Component Analysis method. 2 To study the contribution of variables towards development. 3 Classify districts on the basis of development index. 13

2 Agricultural Development in Maharashtra 14 The study is based on the secondary data collected from the various official publications of Government of Maharashtra. The data were colleted for the period from to i) Districtwise statistical abstract and socio-economic review for all the districts in Maharashtra from , and ii) Epitome of agriculture in Maharashtra , , and To measure the degree of development of different districts, the composite index of development was computed with the help of Principal Component Analysis method. The indices of level of development in districts of the State have been obtained by using data over three time stages. (i) (ii) (iii) In all 28 indicators of agricultural development were selected for the study. 2 PRINCIPAL COMPONENT ANALYSIS METHOD The component analysis, takes the correlation matrix into account and produces components which are uncorrelated with one another, to bypass the problem of multicollinearity. Secondly the component analysis produces components in descending order of their importance that is the first component explain the maximum amount of variation and the last component minimum. It is further found that first 7 or 8 variables account for a sizeable amount of variation of about 75 per cent. It is therefore, possible to represent all 28 variables in terms of seven or eight components. Principal components are the linear combinations of random or statistical variables which have special properties in terms of variances. Consider a random vector X of P components and covariance matrix Σ. As our interest is in variances and covariances, we assume that mean vector is 0. Normal distribution of X will give more meaning of principal components. The treatment will include the cases where Σ is positive semidefinite (i.e. singular) and where Σ has multiple roots. A p dimensional random vector U with the dispersion matrix Σ. Let λ 1 λ 2 λp be the eigen values and P i... P p be the corresponding eigen vectors of Σ then, Σ = λ 1, P 1 P 1 + λ 2, P 2 P λ p P p P p (2.1) I = P 1 P 1 + P 2 P P p P p P 1ΣP 1 = λ i, P iσp j = 0, i j (2.2) Consider the transformed random vectors Y i = P iu, i = 1,..., P. If Y denotes the vector of the new random vectors and P denotes the orthogonal matrix with P 1, P 2,..., P p as its columns, then Y is obtained from U by the orthogonal transformation Y = P.u. The random vector Y i is called the i th Principal component of U. From (2.2) above we get the following properties of Principal components :

3 Agricultural Development in Maharashtra 15 (i) The Principal components are all uncorrelated. component is λ i The variance of the i th Principal V (P iu) = P i ΣP i = λ i, CoV (P iu, P ju) = P iσp i = 0, i j. Thus the linear transformation Y = P U reduces correlated set of variables into an uncorrelated set by an orthogonal transformation. (ii) Let Gi = λ 1/2 i P iu for λ i 0 and further let r be the rank of Σ so that only the first r eigen values of Σ are non zero. (iii) Let B be any vector such that B = 1. Then V (B U) is maximum when B = P 1 and the maximum variance is λ i. Since V (B U) = B ΣB, we need the space Max B ΣB subject to the condition B = 1. But the maximum is attained when B = P 1. The following are consequences of the results. (iv) (a) min V (B U) = λp = V (P p.u). B = 1.V (B U) = λ i = V (P iu). (b) max B = 1, B P i Pi 1, V (B U) = λ i = V (P iu) (c) min max δ i 1 B =1,B S i 1 where S i 1 is a space of (i 1) dimension in Ep. (d) Let B 1, B 2 B k be a set of orthogonal vectors in Ep. Then λ 1 + λ λ k = max [V (B iu) + + V (B ku)]b i B k = V (P iu) + + V (P ku) (v) Let B iu i... B ku k be k linear functions of U and σi 2 be the residual variance in predicting U i by the best linear predictor based on B iu... B ku Then min p σ 2, i=1 B B k is attained when the set B iu... B ku is equivalent to P iu... P ku, that is each B iu is a linear combination of the first k principal components. Without loss of generality we can replace B iu B ku by an equivalent set of uncorrelated functions and each with variance unity. It is also clear that the functions B iu B ku should be linearly independent for the optimum solution.

4 Agricultural Development in Maharashtra 16 The residual variance in predicting U i on the basis of B iu B ku is σ 2 = σ ii [CoV (U i, B iu)] 2 [Cov(U i B ku)] = σ ii (B iσ i ) 2 B kσ i Σ ib k where Σ i, is the i th column of Σ and σ ii is the variance of U i. Now p σi 2 = i=1 p p p σ ii B i( Σ i Σ i)b i B i( Σ 1 Σ i)b i i=1 i=1 i=1 = traceσ B iσσb i B kσσb k. To minimize Σσi 2 we need maximize B iσσb i + + B i ΣΣB k subject to the conditions B i ΣB i = 1, B iσb i = 0 i j (i.e. B iu B ku are un correlated and each has variance unity.) The optimum choice of B i in such a case is, M(B 1, B 2 B k ) = M(P 1 P 2 P k ) Where P 1 P 2 P k are the first k eigen vectors of Σ λ i = 0 The result in (v) provides an interesting interpretation of the principal components to replace the p- dimensional random vector U by k < p linear functions without much loss of information. How are the best k linear functions to be chosen? The efficiency of any choice of k linear functions depends on the extent to which the k linear functions enable us to reconstruct the p original variables. One method of reconstructing the variable U i is by determining its best linear predictor on the basis of the k linear functions, in which case the efficiency of prediction may be measured by the residual variance σi 2. An overall measure of the predictive efficiency is Σσ2 i. The best choice of the linear functions, for which Σσi 2 is minimum, is the first k principal components of U. 3 RESULTS AND DISCUSSION Principal component technique was used to determine the composite index of development. The composite indices were constructed by combining various indicators of development. The values of composite indices varying up to 60 per cent, 61 to 70 per cent and above 70 per cent were grouped into poorly developed, developing and developed districts respectively. The results obtained are presented in Table 1 and 2

5 Agricultural Development in Maharashtra 17 Table 1 Development Indices alongwith Ranks Obtained by Principal Component Analysis Method Score Dist. Rank Score Dist. Rank Score Dist. Rank Kolhapur Pune Satara Osbad Kolhapur Sangli Solapur Ratnagiri Solapur Jalgaon Sangli Nasik A nagar Solapur Kolhapur Sangli Satara Pune Nanded Nasik A nagar Yavatmal Raigad Jalgaon Beed S.Durga Bhandara Parbhani Jalgaon A bad A bad A nagar Nagpur Akola Bhandara Buldana Satara Akola Latur Buldana A bad Os bad Wardha Nagpur Dhule Dhule Thane Beed Amravati Yavatmal Thane Nasik Dhule Amravati Ratnagiri Nanded Parbhani Pune Buldana Nanded Chandrapur Wardha Akola Kulaba C pur Jalna Bhandara Beed Wardha Nagpur Os bad Ch pur Thane Jalna Raigad Latur Ratnagiri Parbhani S.Durg Amravati Yavatmal G.Chiroli G.Chiroli 29

6 Agricultural Development in Maharashtra 18 Table 2 Development Indices in percent alongwith Ranks Obtained by Principal Component Analysis Method Score Dist. Rank Score Dist. Rank Score Dist. Rank 1 Kolhapur 1 1 Pune 1 1 Satara Os bad Kolhapur Sangli Solapur Ratnagiri Solapur Jalgaon Sangli Nasik A.Nagar Solapur Kolhapur Sangli Satara Pune Nanded Nasik A.Nagar Yavatmal Raigad Jalgaon Beed S.Durg Bhandara Parbhani Jalgaon A bad A bad A.Nagar Nagpur Akola Bhandara Buldana Satara Akola Latur Buldana A bad Os bad Wardha Nagpur Dhule Dhule Thane Beed Amravati Yavatmal Thane Nasik Dhule Amravati Ratnagiri Nanded Parbhani Pune Buldana Nanded Ch pur Wardha Akola Kulaba Ch pur Jalna Bhandara Beed Wardha Nagpur Os bad Ch pur Thane Jalna Raigad Latur Ratnagiri Parbhani S.Durg Amravati Yavatmal G.Chiroli G.Chiroli 29

7 Agricultural Development in Maharashtra 19 Economic planning was started in the State as an instrument for bringing out uniform development in districts overtime. In this, context it would be of interest to examine the extent of variability in developmental indices over different points of time. The development indices for different districts were worked out at three points of time. In the first period the values of composite indices varied from 0.49 to The districts whose index of development was below 60 per cent i.e. Kulaba, Bhandara, Nagpur and Thane were grouped into poorly developed districts. This shows that various developmental programmes did not result in an improvement in agriculture in these districts. The districts like Satara, Buldana, Wardha, Dhule, Amravati, Nasik, Ratnagiri, Pune and Chandrapur were found to be developing districts as compared to other districts of the State. The situation regarding agricultural development is slightly different in districts of Kolhapur, Osmanabad, Solapur, Jalgaon, Ahamadnagar, Sangali, Nanded, Yavatmal, Beed, Parbhani, Aurangabad and Akola. These districts were observed to be better developed in comparison to the other districts of the State. The values of development indices for these districts ranged between 0.80 to In the second period the values of indices varied from 0.45 to The district Pune which was categorized as developing district in I st period, shifted to developed district. Most of the developed districts belonged to the Western Maharashtra while the under developed districts were from Vidarbha and Marathwada region. In the third period agricultural sector played an important role in the State economy. The development of different districts of Maharashtra State was studied by the composite index of development and it was observed that the districts of Konkan, Marathwada and Vidarbha were observed to be poorly developed, the development indices of these districts varied from 0.28 to While Pune, Ahmadnagar, Jalgaon, Bhandara, Aurangabad, Nagpur and Buldana were observed to be developing districts. The position of Satara, Sangli, Solapur, Nasik and Kolhapur is far better than other districts of the State and were grouped into developed districts. The overall development of the different districts was greatly influenced by agricultural development. The Infrastructural facilities also influenced the development in the positive direction in almost all the districts of the State. The results of the study indicated disparities in the development of the different districts of the State. 4 FACTORS CAUSING DISPARITIES IN INTER DISTRICT DEVELOP- MENT AND THEIR CONTRIBUTION Principal component analysis technique was used to condense the inter-district disparities observed due to different variables. This method utilized the correlation matrix based on the set of observations and condensed into smaller number of orthogonal factors. This is of special interest as each successive generated factor extracts the maximum amount of variance and ensured the smallest residual. The results obtained are presented in Table 3.

8 Agricultural Development in Maharashtra 20 Table 3 Eigen value and Percentage of total variance explained by each Factor. Sr. Period Period Period N0. Eigen Percent Cumu- Eigen Percent. Cumu- Eigen Percent. Cumuvalue lative value lative value lative percent percent percent It could be seen from Table 3 that among 28 variables selected for examining the disparities in development of districts, only seven variables were found to be significantly affecting the development process during first and second period i.e and and eight variables in third period ( ). Their overall contribution towards development of a district worked out to be 75 per cent. 5 INTER-DISTRICT IMBALANCE IN DEVELOPMENT One of the objectives of present study was to classify districts on the basis of index of development into developed, developing and poorly developed districts. Using random variable Z with Beta distribution in the interval (0, 1), the linear intervals (0, Z 1 ), (Z 1, Z 2 ), (Z 2, Z 3 ) such that, each interval had a same probability weight of 33 per cent. These fractile groups were used to characterize the various stages of development. The cutoff points Z1, Z2, Z3 were obtained from the table of incomplete Beta function. On the basis of cutoff points three intervals were used as (0, Z 1 ), (Z 1, Z 2 ), and (Z 2, Z 3 ). There after the districts in the group of (0, Z 1 ), (Z 1, Z 2 ), and (Z 2, Z 3 ) were called as developed districts, developing districts and poorly developed districts respectively. The results obtained are presented in Table 4

9 Agricultural Development in Maharashtra 21 Table 4 Classification of Districts on the basis of index of Development at a point of Sr. No. Developed Districts Developing Districts Poorly Developed Districts 1. Satara Nagpur Chandrapur Sangli Buldana Raigad Solapur Latur Sindhudurg Nasik Osmanabad Yavatmal Kolhapur Dhule Gadchiroli Pune Beed Ratnagiri Ahmednagar Thane Jalgaon Amravati Bhandara Parbhani Aurangabad Nanded Akola Jalna Wardha It could be seen from Table 4 that out of 29 districts of Maharashtra State, 10 districts, 13 districts and 6 districts were identified as developed, developing and poorly developed districts respectively. Most of the developed districts belonged to Western Maharashtra region, while the developing districts were fromvidarbha and Marathwada region. The results obtained in the present study are in agreement with the study of Seeta Prabhu and Sarkar [2]. The districts like Chandrapur, Gadchiroli and Yavatmal from Vidarbha and Raigad, Ratnagiri and Sindhudurg from Konkan were found to be poorly developed districts. The results of the study indicated the regional imbalance in development of districts. This would help the planners in preparing the plan especially for the development of Tribal Districts of Vidarbha and Konkan region. 6 CONCLUSION 1 Over a period time, the ranking and rate of development of the district changed. 2 Out of 29 districts of Maharashtra 10 districts were developed, 13 developing and 6 districts poorly developed. 3 Most of the developed districts belonged to Western Maharashtra while developing were from Vidarbha and Marathwada region. 4 Infrastructure is closely associated with development. Developed districts have better performance in agricultural production.

10 Agricultural Development in Maharashtra 22 References [1] Anderson, T.W., An Introduction to Multi Variate Statistical Analysis, (1972). [2] K. Seeta Prabhu and P.C.Sarkar, Identification of Levels of Development Case of Maharashtra, Economic and Political weekly September. [3] Wharton C.R. (Jr.), The Infrastructure for Agriculture Growth in Herman M. South Worth and Brsuce F. Jonston (Ed), Agricultural Development.