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Abstract:
This paper gives an outline of evolution of the concept and econometrics of production function, which was one of the central apparatus of neo-classical economics. It shows how the famous Cobb-Douglas production function was indeed invented by von Thunen and Wicksell, how the CES production function was formulated, how the elasticity of substitution was made a variable and finally how Sato's function incorporated biased technical changes. It covers almost all specifications proposed during 1950-1975, and further the LINEX production functions and incorporation of energy as an input. The paper is divided into (1) single product functions, (2) joint product functions, and (3) aggregate production functions. It also discusses the 'capital controversy' and its impacts.

Production function, Cobb-Douglas, CES, Transcendental, translog, Zellner-Revankar, VES, Bruno, Kadiyala, Diewert, Kummel, Mundlak, Engineering, Kmenta, McCarthy, Fare, Mitchell, Multi-output, joint product, Data Envelopment, Household, Humbug, Cambridge capital controversy

Abstract:
Econometricians generally take for granted that the error terms in the econometric models are generated by distributions having a finite variance. However, since the time of Pareto the existence of error distributions with infinite variance is known. Works of many econometricians, namely, Meyer & Glauber (1964), Fama (1965) and Mandlebroth (1967), on economic data series like prices in financial and commodity markets confirm that infinite variance distributions exist abundantly. The distribution of firms by size, behaviour of speculative prices and various other recent economic phenomena also display similar trends. Further, econometricians generally assume that the disturbance term, which is an influence of innumerably many factors not accounted for in the model, approaches normality according to the Central Limit Theorem. But Bartels (1977) is of the opinion that there are limit theorems, which are just likely to be relevant when considering the sum of number of components in a regression disturbance that leads to non-normal stable distribution characterized by infinite variance. Thus, the possibility of the error term following a non-normal distribution exists.

The Least Squares method of estimation of parameters of linear (regression) models performs well provided that the residuals (disturbances or errors) are well behaved (preferably normally or near-normally distributed and not infested with large size outliers) and follow Gauss-Markov assumptions. However, models with the disturbances that are prominently non-normally distributed and contain sizeable outliers fail estimation by the Least Squares method. An intensive research has established that in such cases estimation by the Least Absolute Deviation (LAD) method performs well.

This paper is an attempt to survey the literature on LAD estimation of single as well as multi-equation linear econometric models.

Lad estimator, Least absolute deviation estimation, econometric model, Review of literature

Abstract:
India's globalization is a conscious and deliberate effort to permit the factors of production, the produce and the socio-economic forces to permeate across the national boundaries and remove any obstacle to such permeance. In short, it has been a deliberate decision to open up a national economy to the forces of product, factor and money markets, followed by a sequence of requisite policies and actions, leading to structural reforms.

Unlike how the presently developed economies expanded and went global in their hoary past, the main reform initiatives in India (like in many other developing countries), were undertaken after a fiscal and foreign exchange crisis which brought it to the verge of default on the foreign loans. Thus, the Indian globalization is a result of the decadence within and the pressure from without.

The effects of globalization on the Indian economy in the post-globalization years are clearly visible in the foreign sector - foreign exchange reserves, international trade, inflow of foreign capital, etc. However, structural changes in the domestic economy are not significant. The source-wise structure of savings and capital formation has changed, but trends in the macro-economic indicators such as national income are more or less traditional. The relative contributions of agriculture and industry to national income have followed the historical trends. The contribution of area under cultivation to production also remains largely unchanged.

Although economic in the core, globalization has pervasive effects on the society. It has its impact on the social structure, values, social institutions and attitudes. India is a multilingual, multiethnic and multi-cultural society. Globalization has impacted noticeably on cultural identity and social harmony among various social groups. The Indian social structure is basically pluralistic, replete with a multitude of enclaves of several types and strata. There are enclaves making rural-urban, men-women, caste-dalits, organized-unorganized, formal-informal, and so on. Globalization has led to an increase in disparities among these enclaves.

Globalization, Globalisation, India, Impacts, social, socio-economic, national income, components of agricultural growth, savingd, capital formation, import, export, foreign reserves

Abstract:
In simulation we often have to generate correlated random variables by giving a reference intercorrelation matrix, R or Q. The matrix R is positive definite and a valid correlation matrix. The matrix Q may appear to be a correlation matrix but it may be invalid (negative definite). With R(m,m) it is easy to generate X(n,m), but Q(m,m) cannot give real X(n,m). So, Q has to be converted into the near-most R matrix by some procedure.

NJ Higham (2002) provides a method to generate R from Q that satisfies the minimum Frobenius norm condition for (Q-R). Ali Al-Subaihi (2004) gives another method, but his method does not produce an optimal R from Q.

In this paper we propose an algorithm to produce an optimal R from Q by minimizing the maximum norm of (Q-R). A Computer program (in FORTRAN) also has been provided.

Having obtained R from Q, the paper gives an algorithm to obtain X(n,m) from R(m,m). The proposed algorithm is based on factorization of R, yet it is different from the Kaiser Dichman (1962) procedure. A computer program also has been given.

Positive semidefinite, negative definite, maximum norm, frobenius norm, correlated random variables, intercorrelation matrix, correlation matrix, Monte Carlo experiment, multicollinearity, cointegration, computer program, multivariate analysis, simulation, generation of collinear sample data

Abstract:
The nearest correlation matrix problem is to find a valid (positive semidefinite) correlation matrix, R(m,m), that is nearest to a given invalid (negative semidefinite) or pseudo-correlation matrix, Q(m,m); m larger than 2. In the literature on this problem, 'nearest' is invariably defined in the sense of the least Frobenius norm. Research works of Rebonato and Jaeckel (1999), Higham (2002), Anjos et al. (2003), Grubisic and Pietersz (2004), Pietersz, and Groenen (2004), etc. use Frobenius norm explicitly or implicitly.

However, it is not necessary to define 'nearest' in this conventional sense. The thrust of this paper is to define 'nearest' in the sense of the least maximum norm (LMN) of the deviation matrix (R-Q), and to obtain R nearest to Q. The LMN provides the overall minimum range of deviation of the elements of R from those of Q.

We also append a computer program (source codes in FORTRAN) to find the LMN R from a given Q. Presently we use the random walk search method for optimization. However, we suggest that more efficient methods based on the Genetic algorithms may replace the random walk algorithm of optimization.

Nearest correlation matrix problem, Frobenius norm, maximum norm, LMN correlation matrix, positive semidefinite, negative semidefinite, positive definite, random walk algorithm, Genetic algorithm, computer program, source codes, FORTRAN, simulation

Abstract:
The paper discusses how and why the theories of neo-classical economics are inadequate to provide a framework to human resource management and therefore must give way to dynamic gradual optimization procedure based on the principles of bounded rationality and satisficing behaviour in dealing with the problems of an adaptive complex system of business organization. It also widens the scope of human resource management to include crowd-sourcing.

Human resource management, bounded rationality, adaptive complex system, satisficing behaviour, dynamic gradual optimization, Crowd-sourcing

Abstract:
Programs that work very well in optimizing convex functions very often perform poorly when the problem has multiple local minima or maxima. They are often caught or trapped in the local minima/maxima. Several methods have been developed to escape from being caught in such local optima. The Particle Swarm Method of global optimization is one of such methods.

A swarm of birds or insects or a school of fish searches for food, protection, etc. in a very typical manner. If one of the members of the swarm sees a desirable path to go, the rest of the swarm will follow quickly. Every member of the swarm searches for the best in its locality - learns from its own experience. Additionally, each member learns from the others, typically from the best performer among them. Even human beings show a tendency to learn from their own experience, their immediate neighbours and the ideal performers. The Particle Swarm method of optimization mimics this behaviour. Every individual of the swarm is considered as a particle in a multidimensional space that has a position and a velocity. These particles fly through hyperspace and remember the best position that they have seen. Members of a swarm communicate good positions to each other and adjust their own position and velocity based on these good positions.

The Particle Swarm method of optimization testifies the success of bounded rationality and decentralized decisionmaking in reaching at the global optima. It has been used successfully to optimize extremely difficult multimodal functions. Here we give a FORTRAN program to find the global optimum by the Repulsive Particle Swarm method.

Bounded rationality, Decentralized decision making Jacobian Elliptic functions, Gielis super-formula, supershapes, Repulsive Particle Swarm method of Global optimization, nonlinear programming, multiple sub-optimum, global, local optima, fit, data, empirical, estimation, parameters, curve fitting

Abstract:
In this paper we compare the performance of the Differential Evolution (DE) and the Repulsive Particle Swarm (RPS) methods of global optimization. To this end, seventy test functions have been chosen. Among these test functions, some are new while others are well known in the literature; some are unimodal, the others multi-modal; some are small in dimension (no. of variables, x in f(x)), while the others are large in dimension; some are algebraic polynomial equations, while the other are transcendental, etc. FORTRAN programs of DE and RPS have been appended.

Among 70 functions, a few have been run for small as well as large dimensions. In total, 73 optimization exercises have been done. DE has succeeded in 65 cases while RPS has succeeded in 55 cases. In almost all cases, DE has converged faster and given much more accurate results. The convergence of RPS is much slower even for lesser stringency on accuracy. Some test functions have been hard for both the methods. These are: Zero-Sum (30D), Perm#1, Perm#2, Power-sum, and Bukin-6 functions.

From what we find, one cannot reach at the definite conclusion that the DE performs better or worse than the RPS. None could assure a supremacy over the other. Each one faltered in some cases; each one succeeded in some others. However, DES is unquestionably faster, more accurate and more frequently successful than the RPS. It may be argued, nevertheless, that alternative choice of adjustable parameters could have yielded better results in either method's case. The protagonists of either method could suggest that. Our purpose is not to join with the one or the other. We simply want to highlight that in certain cases they both succeed, in certain other case they both fail and each one has some selective preference over some particular type of surfaces. What is needed is to identify such structures and surfaces that suit a particular method most. It is needed that we find out some criteria to classify the problems that suit (or does not suit) a particular method. This classification will highlight the comparative advantages of using a particular method for dealing with a particular class of problems.

Global optimization, Stochastic search, Repulsive particle swarm, Differential Evolution, Clustering algorithm, Simulated annealing, Genetic algorithm, Tabu search, Ant Colony algorithm, Monte Carlo method, Box algorithm, Nelder-Mead, Nonlinear programming, FORTRAN computer program, local optima

Abstract:
The objective of this paper is to discuss various methods that are applied to find a pecuniary measure of the worth of environmental goods and services and evaluate them on the principles of institutional economics. Approaches to pecuniary valuation based on revealed, imputed and expressed willingness to pay that encompass (i) the market price method, (ii) the productivity method, (iii) the hedonic pricing Method, (iv) the travel cost method, (v) the damage cost avoided method, (vi) the replacement cost method, (vii) the substitute cost method, (viii) the contingent valuation method (ix) the contingent choice method, etc. have been discussed.

Valuation, environmental goods and services, pecuniary, non-pecuniary, revealed, imputed, expressed willingness to pay, market price, productivity, hedonic pricing, travel cost, damage cost, replacement cost, substitute cost, contingent valuation, contingent choice, institutional economics

Abstract:
Correlation matrices have many applications, particularly in marketing and financial economics - such as in risk management, option pricing and to forecast demand for a group of products in order to realize savings by properly managing inventories, etc.

Various methods have been proposed by different authors to solve the nearest correlation matrix problem by majorization, hypersphere decomposition, semi-definite programming, or geometric programming, etc. In this paper we propose to obtain the nearest valid correlation matrix by the differential evaluation method of global optimization.

We may draw some conclusions from the exercise in this paper. First, the "nearest correlation matrix problem" may be solved satisfactorily by the evolutionary algorithm like the differential evolution method. Other methods such as the Particle Swarm method also may be used. Secondly, these methods are easily amenable to choice of the norm to minimize. Absolute, Frobenius or Chebyshev norm may easily be used. Thirdly, the "complete the correlation matrix problem" can be solved (in a limited sense) by these methods. Fourthly, one may easily opt for weighted norm or un-weighted norm minimization. Fifthly, minimization of absolute norm to obtain nearest correlation matrices appears to give better results.

In solving the nearest correlation matrix problem the resulting valid correlation matrices are often near-singular and thus they are on the borderline of semi-negativity. One finds difficulty in rounding off their elements even at 6th or 7th places after decimal, without running the risk of making the rounded off matrix negative definite. Such matrices are, therefore, difficult to handle. It is possible to obtain more robust positive definite valid correlation matrices by constraining the determinant (the product of eigenvalues) of the resulting correlation matrix to take on a value significantly larger than zero. But this can be done only at the cost of a compromise on the criterion of "nearness." The method proposed by us does it very well.

Correlation matrix, product moment, nearest, complete, positive semi-definite, majorization, hypersphere decomposition, semi-definite programming, geometric programming, Particle Swarm, Differential Evolution, Global Optimization, risk management, option pricing, financial economics, marketing

Abstract:
The mammoth system of higher education in India, which is almost wholly government supported, is in deep financial strain, with increasing needs, escalating costs and shrinking budgetary resources. Of late, it is thought necessary to devise means to self-finance these institutions of higher learning. However, the mal-adjustment of higher education with the development of the economy lies in the root of the crisis. In 1998 there were 7.2 thousand colleges imparting graduate and post-graduate education in humanities, social sciences and "academic" natural sciences to 5.7 million students. On the other hand, 600 engineering/technology colleges, nearly 100 agriculture and forestry colleges and about 450 medical colleges, totaling 1150 in number, imparted degree level professional or technical education to about 0.21 million students. The distribution of students in 'general' vs. 'professional' education is 96:4. The revealed preference of students for general education is so much that we find that only 1.86 lakh students have gone in for diploma in engineering and only 26 thousand students have opted for paramedical education. Students passing out from secondary schools seldom think of joining institutions of technical training.

The ailment of the higher education system in India is not a matter of financial constraint and therefore, its remedy is not a program for self-financing. It is erroneous to think that as long as the institutions of higher learning are financed by the government, they educate students at the lower private cost - that no sooner will the government stop financing them than they will tap their fuel from the market - that the demand for higher education is potent and large, and so on. On the contrary, the demand for higher education is large as long as its price is abysmally low. Higher education - what it means today - is unproductive, nothing other than a conspicuous consumption. The ailment of higher education lies in its being misdirected, ill structured, wrongly prioritized and pitiably obese and corpulent. Establishment of colleges and universities for appeasement of the populist sentiments must give way to productivity-based education. Myrdal predicted the imminent crisis long back. There is need to restructure higher education in India - making it much less 'academic' and much more professional/technical.

self-financing higher education in India, Myrdal's observations on education in India

Abstract:
Deleterious effects of a high degree of multicollinearity on estimation of regression coefficients (beta) of a linear model are well known. As a remedial measure, Hoerl & Kennard (1970) introduced Ridge Regression, but as Theobald (1974) pointed out, its optimality depends on unknown parameters and replacing the unknown population parameters by their sample estimates does not ensure its advantage over the OLS. Golan et al. (1996) introduced the Generalized Maximum Entropy (GME) estimator to resolve the multicollinearity problem. The GME requires a number of support values supplied subjectively by the researcher, which in a real life situation are hard to obtain. Consequently, GME estimator loses its practical significance.

Paris (2001) introduced the Maximum Entropy Leuven (MEL) estimator. It exploits the information available in the sample data more efficiently than the OLS does, and unlike GME estimator, it does not require any additional information to be supplied by the researcher. Paris concluded: under any level of multicollinearity, MEL estimator uniformly dominates the OLS estimator according to the mean squared error criterion. It rivals also the GME estimator without requiring any subjective additional information.

In this paper we look into the problem of multicollinerarity more closely and shed more light on the MEL estimator through discussion and simulation based on Monte Carlo experiments. We also propose a Modular MEL (call it MMEL) estimator.

In measuring the entropy, the MEL estimator obtains prob(beta) through normalizing the square of beta by the Euclidean norm of beta vector. Instead, the MMEL estimator obtains prob(beta) through normalizing the absolute value of beta by the absolute norm of beta vector. We observe that overall, the performance of the MMEL estimator (in terms of mean estimated coefficients as well as the RMS values in 50 trials) is much superior to that of the MEL estimator.

Multicollinearity, maximum entropy, MEL estimator, Leuven estimator, condition number

Abstract:
We investigate into the simulated (Monte Carlo) performance of some LAD-based estimators vis-a-vis that of the LS-based estimators for multi-equation linear econometric models of various error specifications - such as Normal, Cauchy, Gamma, Beta1 and Beta2 - in presence of outliers different in number and size. It is found that in case of models with non-normal disturbances or outlier-infested disturbances, LAD-based estimators outperform the LS-based estimators. In particular, findings on relative performance of Khazzoom (Generalized Indirect Least Squares - GILS) estimator and its LAD variant, Amemiya estimator and LAD-LAD estimator are illuminating.

Multi-equation linear econometric models, Monte Carlo simulation, LAD estimator, Least absolute deviation estimation, Khazzoom estimator, Amemiya estimator, Outliers, Cauchy distribution

Abstract:
In this paper we introduce some new test functions to assess the performance of global optimization methods. These functions have been selected partly because several of them are aesthetically appealing and partly because a few of them are really difficult to optimize, while all the functions are multi-modal. Each function has been graphically presented to appreciate its geometrical appearance. To optimize these functions we have used the Repulsive Particle Swarm (RPS) method. We have also appended a computer program of the RPS method. Except two functions, namely the 'crowned cross' and the 'cross-legged table' functions all other new test functions are optimized by the RPS program.The program has also been tested with success on a number of well-established benchmark functions. However, the program fails miserably in optimizing the Bukin and a couple of other functions.

Repulsive particle swarm method, Global optimization, New test functions, Bird function, Pen-holder function, Crowned cross function, Cross-legged table function, Cross function, Cross in tray function, Carrom table function, Holder table function, Test-tube holder function

Abstract:
Quality of higher education is a multi-dimensional concept. It lies in effectiveness of transmitting knowledge and skill; the authenticity, content, coverage and depth of information; availability of reading/teaching materials; help in removing obstacles to learning; applicability of knowledge in solving the real life problems; fruitfulness of knowledge in personal and social domains; convergence of content and variety of knowledge over space (countries and regions) and different sections of the people; cost-effectiveness and administrative efficiency. Information technology has progressed very fast in the last three decades; it has produced equipments at affordable cost and it has now made their wider application feasible. This technology has made search, gathering, dissemination, storing, retrieval, transmission and reception of knowledge easier, cheaper and faster. Side by side, a vast virtual library vying with the library in prints has emerged and continues growing rapidly. One may hold that the e-libraries are the libraries of tomorrow when the libraries in prints will be the antiques or the archival objects of the past. This paper discusses in details how information technology can be applied to enhance the quality of higher education at affordable cost. It also discusses the major obstacles to optimal utilization of information technology and measures to remove them.

Information Technology, Higher Education, Quality, e-library, e-journals, e-books, World-Wide Web

Abstract:
Development of village, micro and small enterprises in India has a special significance with regard to bridging up the disparities between urban and rural sectors of the economy on the one hand and the more industrialized and the less industrialized states on the other. It would also channelize to the mainstream the forces of development in the rural and remote areas presently strewn with the immense possibilities of manufacturing and service activities. Mahatma Gandhi had envisioned this long back, but Indian planners exhibited their preference to development of large-scale industries first. However, after having taken a step further to globalization and liberalization, India has recognized the relevance of small enterprises. Enactment of the Micro, Small and Medium Enterprises Development Act, 2006 is an instance of the action taken in the wake of this recognition.

The North Eastern Region (NER) of India comprises eight states: Arunachal Pradesh, Assam, Manipur, Meghalaya, Mizoram, Nagaland, Sikkim and Tripura, all well known for their handicrafts. The Schedule Tribes form the majority of population there. Most of these states are hilly and have remained agriculturally as well as industrially backward. Promotion of small enterprises is most suitable for their timely development.

In this paper we present a statistically detailed profile of small enterprises in the NER. We explore the possibilities of development of the small enterprises sector and discuss the constraints on the same.

Micro and small enterprises, small-scale industries, North Eastern Region, India, MSME, MSE, rural, village, Arunachal Pradesh, Assam, Manipur, Meghalaya, Mizoram, Nagaland, Tripura, Sikkim, development, prospects, constraints

Abstract:
The Repulsive Particle Swarm (RPS) method of global optimization is perhaps the simplest to understand and implement. Due to its simplicity, it can be easily modified to suit the purpose and therefore, it has better prospects as well. The method has been frequently used in the field of artificial intelligence. It is well founded on philosophical and methodological grounds (bounded rationality and efficacy of decentralized decision-making to reach the global best) also.

The method of RPS has been programmed (in FORTRAN) and run to optimize 32 test functions (such as Ackley, Beale, Booth, Dixon & Price, Easom, Griewank, Himmelblau, Hump, Levy, Michalewics, Rastrigin, Rosenbrock, Schwefel, Shubert, Trid, etc). The program has successfully optimized these functions. The paper also provides graphical presentations of most of these functions and the FORTRAN codes of RPS method.

Global optimization, multi-modal, Repulsive Particle swarm, Ackley, Beale, Booth, Dixon & Price, Easom, Griewank, Himmelblau, Hump, Levy, Matyas, Michalewics, Rastrigin, Rosenbrock, Schwefel, Shubert, Trid, Weierstrass, Shekel, Branin, Zakharov, test functions, Fortran, computer program, non-convex

Abstract:
This paper presents a Fortran 77 computer program of nonlinear least squares and a help on how to use the program. The codes are given. It is very easy to use. The user has to specify the function to be fitted to data and name the data file. It has been tested on the NIST, USA data. It has been successful to fit functions to the data posed as challenge problems by the CPC-X Software. The link to download the program in directly useable form (txt format) has also been given.

Nonlinear least squares, Differential Evolution, Global optimization, Fortran, program

Abstract:
This paper generalizes the method of Indirect Least Squares (ILS) and shows that such a generalization, call it the Generalized Indirect Least Squares (GILS), yields Two-Stage Least Squares (2-SLS) under the zero restriction on some structural coefficients characterizing over-identification.

Indirect Least Squares, ILS, Generalized, GILS, Two-Stage Least Squares, Identification

Abstract:
This essay portrays the major currents in recent economic thinking against the orthodoxy and dogmatism of neoclassical economics. It places behavioral economics, experimental economics, evolutionary economics, ecological economics, new institutional economics, agent-based computational economics and post-autistic economics vis-a-vis the classical and the neoclassical economics. It concludes that we may expect a synthesis of all these strands of economic thinking in the near future that will replace neoclassical economics from the citadel of mainstream. Teaching of these strands of new economics has already begun in many universities, although in an un-integrated manner. However, until the neoclassical microeconomics and macroeconomics are replaced by their alternatives and necessary as well as convincing tools of economic analysis are developed, neoclassicism would not give way to modern economics.

Behavioral, experimental, evolutionary, ecological, new institutional, agent-based computational, post-autistic, classical, neoclassical, economics, bounded rationality, heterodox, individualism, pluralism

Abstract:
Nagaland (India) presently has 36 colleges. Of them, 28 are private and 8 are government colleges. Private colleges enroll 14000 students and thus serve over 80 percent of the customers of college-level higher education. The market share of private colleges is increasing over time, while the market share of govt. colleges is decreasing. Production function of private college industry indicates that it is a labour-intensive industry with a good substitutability of labour to capital. These colleges make a monopolistic competition market, bordering on oligopoly. Four bands of prices (fees) are observed. The mark-up of prices (fees) over average cost varies between 187 to 5 percent. Colleges enjoying cost and location advantages mark up fees much higher, but there is no significant relationship between academic performance and pricing of services.

: Nagaland, India, Private colleges, monopolistic competition, oligopoly, Higher education industry, academic performance, moral hazards, production function, Price bands, labour-intensive, location, cost advantage.

Abstract:
This paper aims at comparing the performance of the Differential Evolution (DE) and the Repulsive Particle Swarm (RPS) methods of global optimization. To this end, some relatively difficult test functions have been chosen. Among these test functions, some are new while others are well known in the literature.

We use DE method with the exponential crossover scheme as well as with no crossover (only probabilistic replacement). Our findings suggest that DE (with the exponential crossover scheme) mostly fails to find the optimum in case of the functions under study. Of course, it succeeds in case of some functions (Perm #2, Zero-sum) for very small dimension, but begins to falter as soon as the dimension is increased. In case of DCS function, it works well up to dimension=5. When we use no crossover (only probabilistic replacement) we obtain better results in case of several of the functions under study. In case of Perm #1, Perm #2, Zero-sum, Kowalik, Hougen and Power-sum functions, a remarkable advantage is there.

Whether crossover or no crossover, DE falters when the optimand function has some element of randomness. This is indicated by the functions: Yao-Liu #7, Fletcher-Powell, and "New function #2". DE has no problems in optimizing the "New function #1". But the "New function #2" proves to be a hard nut. However, RPS performs much better for such stochastic functions. When the Fletcher-Powell function is optimized with non-stochastic vector, DE works fine. But as soon as is stochastic, it becomes unstable. Thus, it may be observed that an introduction of stochasticity into the decision variables (or simply added to the function as in Yao-Liu #7) interferes with the fundamentals of DE, which works through attainment of better and better (in the sense of Pareto improvement) population at each successive iteration.

The paper concludes: (1) for different types of problems, different schemes of crossover (including none) may be suitable or unsuitable, (2) Stochasticity entering into the optimand function may make DE unstable, but RPS may function well.

Differential Evolution, Repulsive Particle Swarm, Global optimization, non-convex functions, Fortran, computer program, benchmark, test, Stochastic functions, Fletcher-Powell, Kowalik, Hougen, Power-sum, Perm, Zero-sum, New functions, Bukin function

Abstract:
This study is an attempt to identify the determinant factors of quality of life in Dimapur and its periphery. Dimapur town is the most important and cosmopolitan commercial centre of Nagaland, India. We delineate the township into five concentric rings around the CBD and every ring into several sectors. Then twenty one sites have been chosen randomly from these sectors; four each from the first and the second sectors, five each from the third and the fourth sectors, and three from the fifth sector (control). From each site, we have selected eleven households randomly to collect information on the scheduled variables - 113 in number - reflecting various aspects of quality of life (e.g. education, housing, utilities and amenities, accessibility, waste disposal and environment, income & expenditure, entertainment, health condition, etc.). In total, we have surveyed two hundred thirty one (231) households.

Factor analysis is used for resolving the multivariate complex of data into a handful of composite variables identified as: (1) High-End Consumption, (2) Low-End Consumption; (3) Consumption of Public Goods, Commons and Negative Spillovers, (4) Supplementary Consumption, and (5) Health-related Attributes.

A regression analysis of spatial distribution of mean factor scores over the sectors of the township reveals that mean scores of factors #1, #2, and #4 (that are closely related with standard of living) are lower in the CBD and rise as we move away to sectors #2 and #3. They attain their peak in sector #3 and after that the experience a decline as we move away further to sectors #4 and #5.

On the other hand, factor #3, monotonically decreases as we move away from the central business district (CBD) to the periphery. The CBD is more crowded and polluted. It caters to the largest floating population who over-use the public facilities there. Factor #5 (related with poor health conditions) scores higher in the CBD and as we move away to sectors # 3 and #4, a decline is observed. Health conditions are poorer in the CBD and better in sectors #3 and #4. But due to poor conditions of living, health in the rural areas scores poorer.

We conclude that standard of living and consumption of public goods/services including negative spillover determine quality of life. The QOL in the medial sector between the CBD and the periphery is better than that in other sectors mainly due to higher standard of living but QOL due to consumption of public goods/externalities monotonically improves as we move away from the CBD. The overall index of quality of life has a weak relationship with the nature of employment of the respondents. The advance Nagas (Semas, Angamis, Aos and Lothas) score favourably on the Factors of QOL relating to the standard of living, but they also share the negative spillovers of urban living more in proportion. Zeliangs and Kukis score unfavourably on the standard of living but they share the urban externalities and negative spillover of urban living lesser in proportion.

Quality of life, factor analysis, Dimapur, Nagaland, Institutional economics, quantitative measure of quality of life

Abstract:
In 1991 India chose to open her economy and formulated the New Economic Policy (NEP). Under the structural adjustment and reform programmes, the NEP aimed at promoting growth by eliminating supply bottlenecks that hinder competitiveness, efficiency and dynamism in the economic system

This study investigates into the structural changes in the manufacturing sector of India brought about by liberalization and globalization of the economy. Structural changes in terms of employment of labour and capital, indicated by replacement of the former by the latter, and changes in returns-to-scale have been examined by estimating CES, Zellner-Revankar, Transcendental, Diewert and Bruno's CMS production functions. State-wise data for 1990-91 and 2003-04 have been analyzed.

The findings have indicated that the rise in industrial output during the reference period is accountable to substitution of capital for labour in almost all states. Elasticity of substitution has declined for most of the industrialized states. In the pre-globalization period the industries experienced increasing returns to scale. Globalization has possibly given way to diminishing returns to scale. Along with a rise in industrial output, globalization has led to a decline in regional disparities in terms of population-deflated indices of employment of manpower and capital, and the resultant output.

India, Manufacturing sector, industry, globalization, liberalization, production function, returns to scale, substitution, labour, capital, Zellner-Revankar, CES, Transcendental, Diewert, Bruno, Variable elasticitiy of substitution, nonlinear, optimization, Differential evolution

Abstract:
A high degree of multicollinearity among the explanatory variables severely impairs estimation of regression coefficients by the Ordinary Least Squares. Several methods have been suggested to ameliorate the deleterious effects of multicollinearity.

In this paper we aim at comparing the Restricted Liu estimates of regression coefficients with those obtained by applying the Maximum Entropy Leuven (MEL) family of estimators on the widely analyzed dataset on Portland cement. This dataset has been obtained from an experimental investigation of the heat evolved during the setting and hardening of Portland cements of varied composition and the dependence of this heat on the percentage of four compounds in the clinkers from which the cement was produced. The relevance of the relationship between the heat evolved and the chemical processes undergone while setting takes place is best stated in the words of Woods et al.: "This property is of interest in the construction of massive works as dams, in which the great thickness severely hinder the outflow of the heat. The consequent rise in temperature while the cement is hardening may result in contractions and cracking when the eventual cooling to the surrounding temperature takes place."

Two alternative models have been formulated, the one with an intercept term (non-homogenous) that exhibits a very high degree of multicollinearity and the other with no intercept term (extended homogenous) that characterizes perfect multicollinearity.

Our findings suggest that several members of the MEL family of estimators outperform the OLS and the Restricted Liu estimators. The MEL estimators perform well even when perfect multicollinearity is there. A few of them may outperform the Minimum Norm LS (OLS+) estimator. Since the MEL estimators do not seek extra information from the analyst, they are easy to apply. Therefore, one may rely on the MEL estimators for obtaining the coefficients of a linear regression model under the conditions of severe (including perfect) multicollinearity among the explanatory variables.

Multicollinearity, Estimator, Restricted Liu, Maximum Entropy Leuven, MEL family, Modular Maximum Entropy Leuven, Least Absolute Deviation, Minimum Norm Least Squares, Moore-Penrose inverse, Portland cement dataset

Abstract:
The classical canonical correlation analysis is extremely greedy to maximize the squared correlation between two sets of variables. As a result, if one of the variables in the dataset-1 is very highly correlated with another variable in the dataset-2, the canonical correlation will be very high irrespective of the correlation among the rest of the variables in the two datasets. We intend here to propose an alternative measure of association between two sets of variables that will not permit the greed of a select few variables in the datasets to prevail upon the fellow variables so much as to deprive the latter of contributing to their representative variables or canonical variates.

Our proposed Representation-Constrained Canonical correlation (RCCCA) Analysis has the Classical Canonical Correlation Analysis (CCCA) at its one end (lambda=0) and the Classical Principal Component Analysis (CPCA) at the other (as lambda tends to be very large). In between it gives us a compromise solution. By a proper choice of lambda, one can avoid hijacking of the representation issue of two datasets by a lone couple of highly correlated variables across those datasets. This advantage of the RCCCA over the CCCA deserves a serious attention by the researchers using statistical tools for data analysis.

Representation, constrained, canonical, correlation, principal components, variates, global optimization, particle swarm, ordinal variables, computer program, FORTRAN

Abstract:
On many occasions we need to construct an index that represents a number of variables. Cost of living index, general price index, human development index, index of level of development, etc are some of the indices that are constructed by a weighted (linear) aggregation of a host of variables. The criterion on which importance of a variable (vis-à-vis other variables) is determined may be varied. In constructing a cost of living index, for instance, importance of a commodity is determined by the proportion of consumption expenditure allocated to it, and in constructing the human development index the variables such as literacy, life expectancy or income are weighted according to the importance assigned to them in accordance with their perceived roles in determining human development status.

In absence of any preferred means or logic to determine the relative importance of different variables, weights are assigned mathematically. One of the methods to determine such mathematical weights is the Principal Components (PC) analysis where weights are determined such that the sum of the squared correlation coefficients of the index with the constituent variables (used to construct the index) is maximized.

Although the PC analysis has excellent mathematical properties, one may face some difficulties in using it to construct a single index of poorly correlated variables. The method has a tendency to pick up the subset of highly correlated variables to make the first component, assign marginal weights to relatively poorly correlated subset of variables and/or relegate the latter subset to construction of the subsequent principal components. Consequently, the index obtained by PC analysis is elitist in nature that has a preference to the highly correlated subset over the poorly correlated subset of variables. Further, since there is no dependable method available to obtain a composite index by merging two or more principal components, the deferred set of variables may never find its representation in the index.

In this paper we propose to construct indices either (i) by maximization of the minimal correlation (I-M) or (ii) by maximization of the sum of absolute correlation (I-1) between the index and its constituent variables. Maximization has been done by the Differential Evolution method of global optimization. We find that I-1 is more inclusive, and has a tendency to represent even the poorly correlated variables. The I-M indices are egalitarian in nature. It would depend on the analyst whether he is interested in egalitarian, inclusive or elitist method of constructing indices when the constituent variables are not very highly correlated among themselves. This paper has opened up the option to choose the method of constructing a desired type of index.

Index, construction, weighted linear aggregation, principal components, elitist, egalitarian, inclusive, maximin correlation index, sum of absolute correlation coefficients, Differential evolution

Abstract:
The objective of this short paper is to provide an algorithm that generates X(n,m) with a desired intercorrelation matrix, R(m,m). In computer-based simulations (such as Monte Carlo experiments) that evaluate performance of competing estimators of regression coefficients (or evaluate the efficacy of a method of estimation of parameters) under severe multicollinearity conditions, one requires to generate X(n,m) that are highly multicollinear across the variables. Sometimes two variables Y and Z are each cointegrated with another variable X, but Y and Z do not appear to be cointegrated with each other, though, intuitively, one would expect that they should be cointegrated with each other and the transitivity property would be exhibited. By using the algorithm presented here, several examples of X(n,m) may be generated for experiments and further investigation in this line. Experiments that directly or indirectly use multivariate analysis methods (such as Principal components analysis, Factor analysis or Cluster analysis) as a procedure may require X(n,m) with a desired R matrix. In such experiments our algorithm may be useful.

We also provide here the source codes of the computer program (in FORTRAN) that implements the algorithm given in the paper. These source codes may easily be translated into any other computer language such as Pascal, BASIC etc, if needed. Some languages may not have a provision to perform double precision arithmetic. In that case, single precision arithmetic may be used. The results would be sufficiently accurate for the desired purpose. In its present FORTRAN codes, the program may be compiled by any suitable FORTRAN compiler.

Intercorrelation matrix, correlation matrix, Monte Carlo experiment, multicollinearity, cointegration, Computer program, multivariate analysis, Simulation, generation of collinear sample data

Abstract:
In this paper we test a particular variant of the (Repulsive) Particle Swarm method on some rather difficult global optimization problems. A number of these problems are collected from the extant literature and a few of them are newly introduced. First, we introduce the Particle Swarm method of global optimization and its variant called the 'Repulsive Particle Swarm' (RPS) method. Then we endow the particles with some stronger local search abilities - much like tunneling - so that each particle can make a search in its neighbourhood to optimize itself. Next, we introduce the test problems, the existing as well as the new ones. We also give plots of some of these functions to help appreciation of the optimization problem. Finally, we present the results of the RPS optimization exercise and compare the results with those obtained by using the Genetic algorithm (GA)and/or Simulated annealing (SA) method. We append the (Fortran) computer program that we have developed and used in this exercise.

Our findings indicate that neither the RPS nor the GA/SA method can assuredly find the optimum of an arbitrary function. In case of the Needle-eye and the Corana functions both methods perform equally well while in case of Bukin's 6th function both yield the values of decision variables far away from the right ones. In case of zero-sum function, GA performs better than the RPS. In case of the Perm #2 function, both of the methods fail when the dimension grows larger. In several cases, GA falters or fails while RPS succeeds. In case of N#1 through N#5 and the ANNs XOR functions the RPS performs better than the Genetic algorithm.

It is needed that we find out some criteria to classify the problems that suit (or does not suit) a particular method. This classification will highlight the comparative advantages of using a particular method for dealing with a particular class of problems.

Repulsive Particle Swarm, Global optimization, non-convex functions, Bounded rationality, local optima, Bukin, Corana, Rcos, Freudenstein Roth, Goldenstein Price, ANNs XOR, Perm, Power sum, Zero sum, Needle-eye, Genetic algorithms, variants, Fortran, computer program, benchmark, test

Abstract:
A high degree of multicollinearity often has a detrimental effects on the estimation of a linear econometric (regression) model due to an intricate internecine sharing among the estimated regression coefficients (beta).

Paris (2001) introduced the Maximum Entropy Leuven (MEL) estimator. It exploits the information available in the sample data more efficiently than the OLS does, and unlike GME estimator, it does not require any additional information to be supplied by the researcher. Paris concludes: "under any level of multicollinearity, MEL estimator uniformly dominates the OLS estimator according to the mean squared error criterion. It rivals also the GME estimator without requiring any subjective additional information."

Paris used the Euclidean norm to obtain prob(beta). In this paper we obtain prob(beta) using the absolute norm of beta and investigate into its effects on the performance of the Maximum Entropy estimator. We obtain a new estimator of regression coefficients by solving the reformulated problem.

This new estimator is not fully a la Paris (2001) and hence we name it as the Modular Maximum Entropy Leuven (MMEL) estimator. Monte Carlo study has been conducted to compare the performance of the MEL estimator (Paris) and the new MMEL estimator. We observe that overall, the performance of MMEL (in terms of mean estimated coefficients as well as the RMS values) is much superior to that of the MEL estimator.

It is pertinent to note that obtaining prob(beta) is the most crucial task before the scientist if he chooses to use the maximum entropy estimator (MEL, MMEL or any variant thereof). After all, the mathematics of probability suggests us that given a sample description space S, probability is a function which assigns a non-negative real number to every event A, denoted by P(A) and it is called the probability of the event A. The probability function is defined on a Borel field of events conformal to the axioms of positiveness, certainty and union. Under these axioms, there could be several different rules of assignment, ranging from subjective judgement backed up by a rational belief (JM Keynes) to counting the number of success in the repeated trials. In our study MEL does this assignment in the one way and the MMEL does that in the other way. There could be many more (possibly better) rules of assignment of probability. Thus, the subjective (or exogenous) element that was explicit in Golan et al. reappears in the MEL family of estimators, although in another garb.

multicollinearity, maximum entropy, MEL estimator, Condition number, regression analysis

Abstract:
This paper proposes an algorithm to fit an Archimedean spiral in the sample data obtained empirically. A Monte Carlo experiment has been carried out to assess the efficacy of the proposed algorithm. A computer program has also been appended.

Archimedean spiral, Logarithmic spiral, curve fitting, algorithm, Monte Carlo experiments, Computer program

Abstract:
No fool-proof method exists to fit nonlinear curves to data or estimate the parameters of an intrinsically nonlinear function. Some methods succeed at solving a set of problems but fail at the others. The Differential Evolution (DE) method of global optimization is an upcoming method that has shown its power to solve difficult nonlinear optimization problems. In this study we use the DE to solve some nonlinear least squares problems given by the National Institute of Standards and Technology (NIST), US Department of Commerce, USA and some other challenge problems posed by the CPC-X Software (the makers of the AUTO2FIT software). The DE solves the test problems given by the NIST and most of the challenge problems posed by the CPC-X, doing marginally better than the AUTO2FIT software in a few cases. Further, the DE does not require the search domains of parameters to be specified too narrowly (as in case of other methods of nonlinear least squares).

Nonlinear least squares, curve fitting, differential evolution, global optimization, AUTO2FIT, CPC-X Software, NIST, National Institute of Standards and Technology, test problems

Abstract:
Construction of (composite) indices by the PCA is very common, but this method has a preference for highly correlated variables to the poorly correlated variables in the data set. However, poor correlation does not entail the marginal importance, since correlation coefficients among the variables depend, apart from their linearity, also on their scatter, presence or absence of outliers, level of evolution of a system and intra-systemic integration among the different constituents of the system. Under-evolved systems often throw up the data with poorly correlated variables. If an index gives only marginal representation to the poorly correlated variables, it is elitist. The PCA index is often elitist, particularly for an under-evolved system.

In this paper we consider three alternative indices that determine weights given to different constituent variables on the principles different from the PCA. Two of the proposed indices, the one that maximizes the sum of absolute correlation coefficient of the index with the constituent variables and the other that maximizes the entropy-like function of the correlation coefficients between the index and the constituent variables are found to be very close to each other. These indices alleviate the representation of poorly correlated variables for some small reduction in the overall explanatory power (vis-à-vis the PCA index). These indices are inclusive in nature, caring for the representation of the poorly correlated variables. They strike a balance between individual representation and overall representation (explanatory power) and may perform better. The third index obtained by maximization of the minimal correlation between the index and the constituent variables cares most for the least correlated variable and in so doing becomes egalitarian in nature.

Principal components analysis, weighted linear combination, aggregation, composite index, egalitarian, inclusive, elitist, representation, under-developed systems

Abstract:
Median, a well known measure of central tendency, of a sample data x =(x1, x2, ... ,xn) is obtained through the traditional method as (xn-m + xm+1)/2, where m= int(n/2) and values of x are arranged in ascending (descending) order. Since, for odd n, n-m=m+1, the formula uses only one value from the sample data. For even n, only two middlemost values are used. This property of the formula invites the popular criticism of median being not based on all sample observations.

It is possible to use an alternative formula to compute median as a weighted arithmetic mean of all sample observations, where weights are non-trivial and iteratively obtained. This alternative formula yields median identical to that obtained by the conventional formula if n is odd. If n is even, the results differ, though both of them yield the same minimum absolute norm. This is due to indeterminacy of median for even n in which every z between xn-m and xm+1 minimizes the absolute norm.

The paper further makes a comparative study of other desirable properties of the conventional and the alternative methods by Monte Carlo experiments.

Median, alternative method, weighted arithmetic mean, Monte Carlo experiments, Efficiency, consistency

Abstract:
Correlation matrices have many applications, particularly in marketing and financial economics. The need to forecast demand for a group of products in order to realize savings by properly managing inventories requires the use of correlation matrices.

In many cases, due to paucity of data/information or dynamic nature of the problem at hand, it is not possible to obtain a complete correlation matrix. Some elements of the matrix are unknown. Several methods exist that obtain valid complete correlation matrices from incomplete correlation matrices. In view of non-unique solutions admissible to the problem of completing the correlation matrix, some authors have suggested numerical methods that provide ranges to different unknown elements. However, they are limited to very small matrices up to order 4.

Our objective in this paper is to suggest a method (and provide a Fortran program) that completes a given incomplete correlation matrix of an arbitrary order. The method proposed here has an advantage over other algorithms due to its ability to present a scenario of valid correlation matrices that might be obtained from a given incomplete matrix of an arbitrary order. The analyst may choose some particular matrices, most suitable to his purpose, from among those output matrices. Further, unlike other methods, it has no restriction on the distribution of holes over the entire matrix, nor the analyst has to interactively feed elements of the matrix sequentially, which might be quite inconvenient for larger matrices. It is flexible and by merely choosing larger population size one might obtain a more exhaustive scenario of valid matrices.

Incomplete, complete, correlation matrix, valid, semi-definite, eigenvalues, Differential Evolution, global optimization, computer program, Fortran, financial economics, arbitrary order

Abstract:
In the extant literature a suggestion has been made to solve the nearest correlation matrix problem by a modified von Neumann approximation. In this paper it has been shown that obtaining the nearest positive semi-definite matrix from a given non-positive-semi-definite correlation matrix by such method is either infeasible or suboptimal. First, if a given matrix is already positive semi-definite, there is no need to obtain any other positive semi-definite matrix closest to it. When the given matrix is non-positive-semi-definite (Q), then only we seek a positive semi-definite matrix closest to it. Then the proposed procedure fails as we cannot find log(Q). But, if we replace negative eigenvalues of Q by a zero/near-zero values, we obtain a positive semi-definite matrix, but it is not nearest to the Q matrix; there are indeed other procedures to obtain better approximation. However, the modified von Neumann approximation method yields results (although sub-optimal) and is, perhaps, one of the fastest method most suitable to dealing with larger matrices. Yet, we provide an alternative algorithm (and a Fortran program) to obtain a positive (semi-)definite matrix that performs (speed as well as accuracy-wise) much better.

Nearest correlation matrix problem, positive semidefinite, non-positive-semi-definite, von Neumann divergence, Bergman divergence

Abstract:
In this paper Sato's two-level CES production function has been estimated by nonlinear regression carried out through five different methods of optimization, namely, the Hooke-Jeeves Pattern Moves (HJPM), the Hooke-Jeeves-Quasi-Newton (HJQN), the Rosenbrock-Quasi-Newton (RQN), the Differential Evolution (DE) and the Repulsive Particle Swarm methods (RPS). The last two methods are particularly suited to optimization of extremely nonlinear (often multimodal) objective functions.

While data may be containing outliers, the method of least squares has a clear disadvantage as it may be pulled by extremely small or large errors. The absolute deviation estimation of parameters is more suitable in such cases. This paper has made an attempt to estimation of parameters of Sato's two-level CES production function by minimizing the sum of absolute errors. While the HJPM and the HJQN perform poorly at minimizing the sum of absolute deviations, the RQN performs much better. The DE and the RPS perform very well in estimating the parameters. We also estimate the parameters of a production function in which the output is determined by capital, labour and energy. The model is in the family of the Linear exponentials (LINEX) type. To estimate this model, we use German Sector "Market-determined Services" data for the years 1960-1989. Using the same data, we also estimate Sato's function with constant as well as variable returns to scale. Estimation has been done by minimization of the absolute deviations. Minimization has been done by Particle Swarm and Differential Evolution methods. The models fit extremely well to the data.

Sato's productions function, CES, constant elasticity of substitution, two-level, Linear exponential, LINEX, Hooke Jeeves, Quasi-Newton, Rosenbrock, Repulsive Particle swarm, Differential Evolution, Global Optimization, Outliers, Least absolute deviation, Service Production function, German Data

Abstract:
Human Development Index (HDI) is a composite index obtained by a weighted aggregation of other three indices, each measuring one aspect, namely life expectancy, education and real per capita income. Intra-country equality in income distribution, however, is very important with regard to quality of life and, thus, human development. This paper is concerned with the question that if the measure of income equality also were included in construction of the HDI, then what would be the relative weights of different indices. One method could be to assign equal weights to all the four, but it is too pragmatic. Alternatively, the principal component analysis (PCA) may be applied to derive weights. But, again, the PCA is an overly elitist method that undermines the poorly correlated set of variables, which might be very important in their own right, in favor of highly correlated set of variables. We propose an alternative method that maximizes the sum of absolute coefficients of correlation of the composite index with the constituent indices. Such an index is inclusive in nature and gives proper representation to weakly correlated variables also. The method has been applied to data of 125 countries and the HDI so constructed has been compared with the PCA HDI and HDR (UNDP) HDI. We find substantial ups and downs in the HDI ranks of different countries.

Human development index, HDI, income distribution, equality, relative weights, representation, inclusive, elitist, principal component, alternative method, UNDP, correlation, absolute, International comparison, countries

Abstract:
In the economics of joint production one often distinguishes between the two cases: the one in which a firm produces multiple products each produced under separate production process, and the other "true joint production" where a number of outputs are produced from a single production process, where each product shares common inputs. In the econometric practice the first case has often been dealt with by aggregation of individual production functions into a macro production function. The second case has often called for estimation of an implicit aggregate production function.

Most of the studies relating to estimation of joint production functions have noted two difficulties: first that allocation of inputs to different outputs are not known, and the second that a method of estimation (such as the Least Squares) cannot have more than one dependent variable. Construction of a composite (macro) output function is at least partly motivated by the inability of the estimation methods to deal with multiple dependent variables and different forms of production function for different outputs.

This study has conducted some simulation experiments on joint estimation of the CES, the Transcendental and the Nerlove-Ringstad functions. Allocation parameters (of inputs) across the products have been introduced. Estimation has been done jointly, but without constructing a composite macro production function or an output transformation function. We use nonlinear least squares based on the Differential Evolution method of global optimization that permits fitting multiple production functions simultaneously.

Joint production, multiple output, allocation parameters, nonlinear least squares, Differential Evolution, Nerlove-Ringstad, Transcendental, CES, macro, implicit, composite production function, transformation function, canonical correlation, multiple dependent variables

Abstract:
A production possibility surface is the frontier surface determined by the available resources in an economy and the technology applied for production. The surface is in the non-negative orthant, meaning thereby that neither the resources nor the quantity produces may take on a negative value. Mathematically, the shape of the surface is ellipsoidal.

It is interesting to fit a production possibility surface to empirical data on two counts: first, it is an example of a nonlinear surface fitting that cannot appreciably be approximated by a simple linearization method, and second, that it is an example of the surface that cannot ordinarily be fitted by most of the conventional non-linear regression algorithms. These algorithms fail mostly because they approach the best fitting surface from both sides, interior and exterior of the surface, and thereby land themselves into the problem of finding square root of a negative quantity.

Statistical fitting of ellipse (or ellipsoid) to empirical data remained unattractive for a long time. However, in the last two decades or so, it attracted many researchers especially to solve the pattern recognition problems. Bookstein (1979), Sampson (1982), Taubin (1991), Rosin (1993), Gander et al. (1994), Kanatani (1994), Pilu (1996) and Matei and Meer (2000) are some of the important works on this problem.

In this paper we propose a new, simple iterative method for our limited purpose at hand. For an illustration, we estimate the parameters of the ellipse by fitting the parametric equations to the simulated data. A computer program (FORTRAN) implementing the proposed method is given.

Ellipse, ellipsoid, production possibility surface, conic fitting, empirical data, computer program, FORTRAN, Least squares, LAD estimation

Abstract:
The enterprise of running private schools has of late assumed the nature of an industry in India. Ever-increasing population, a race for providing education to ones children, degenerating quality of education in govt.-run schools, unlimited supply of educated youths ready to work at the lowest salary and the possibilities of earning huge profits for a modest investment together have contributed to the viability of this industry.

In Kohima, the capital city of Nagaland (India), which is our study area, there are 31 private high/higher secondary schools against only 3 govt. run schools. These private schools enroll some 25 thousand pupils while the enrolment in the govt.-run schools is barely 1.6 thousand students. These private schools employ 766 teachers and pay them an average salary which is only one third of what the govt.-run schools pay. According to the ILO (1996) definition of subsistence wages (the hourly wage sufficient to buy one kg. of the lowest priced staple cereal), the employees of these schools barely earn a subsistence wage. Nevertheless, these schools generate a revenue of Rs. 88 million of which Rs. 3.7 million is the net profit.

Our analysis shows that private schooling industry in Kohima operates in a monopolistic competition market - bordering on oligopoly. There is price leadership in determining the fees to be charged by the schools making this industry.

Private schooling industry, oligopoly, monopolistic competition, subsistence wages, Kohima, Nagaland, microeconomics of education

Abstract:
Logarithmic spirals are abundantly observed in nature. Gastropods/cephalopods (such as nautilus, cowie, grove snail, thatcher, etc.) in the mollusca phylum have spiral shells, mostly exhibiting logarithmic spirals vividly. Spider webs show a similar pattern. The low-pressure area over Iceland and the Whirlpool Galaxy resemble logarithmic spirals.Many materials develop spiral cracks either due to imposed torsion (twist), as in the spiral fracture of the tibia, or due to geometric constraints, as in the fracture of pipes. Spiral cracks may, however, arise in situations where no obvious twisting is applied; the symmetry is broken spontaneously. It has been found that the rank size pattern of the cities of USA approximately follows logarithmic spiral.

The usual procedure of curve-fitting fails miserably in fitting a spiral to empirical data. The difficulties in fitting a spiral to data become much more intensified when the observed points z = (x, y) are not measured from their origin (0, 0), but shifted away from the origin by (cx, cy). We intend in this paper to devise a method to fit a logarithmic spiral to empirical data measured with a displaced origin. The method is also be tested on numerical data.

It appears that our method is successful in estimating the parameters of a logarithmic spiral. However, it may be noted that the range specification is very important. We have observed that if ranges are guessed unduly large (in which the shift parameters lie), the efficiency of the method is marred. Moreover, estimated values of the parameters of a logarithmic spiral (a and b in r = a*exp(b(theta+2*pi*k) highly sensitive to the precision to which the shift parameters (cx and cy) are correctly estimated.

Logarithmic Spiral, Growth Spiral, Bernoulli Spiral, Equiangular Spiral, Cartesian Spiral, Empirical data, Shift in origin, change of origin, displaced pole, polar displacement, displaced origin, Curve Fitting, Spiral fitting, Box Algorithm, Non-linear Programming, multi-modality, Rank size rule

Abstract:
In this paper we compare the performance of the Barter method, a newly introduced population-based (stochastic) heuristic to search the global optimum of a (continuous) multi-modal function, with that of two other well-established and very powerful methods, namely, the Simulated Annealing (SA) and the Differential Evolution (DE) methods of global optimization.

In all, 87 benchmark functions have been optimized 89 times. The DE succeeds in 82 cases, the Barter succeeds in 63 cases, while the Simulated Annealing method succeeds for a modest number of 51 cases. The DE as well as Barter methods are unstable for stochastic functions (Yao-Liu and Fletcher-Powell functions). In particular, Bukin-6, Perm-2 and Mishra-2 functions have been hard for all the three methods.

Seen as such, the barter method is much inferior to the DE, but it performs better than SA. A comparison of the Barter method with the Repulsive Particle Swarm method has indicated elsewhere that they are more or less comparable.

The convergence rate of the Barter method is slower than the DE as well as the SA. This is because of the difficulty of 'double coincidence' in bartering. Barter activity takes place successfully in less than one percent trials.

It may be noted that the DE and the SA have a longer history behind them and they have been improved many times. In the present exercise, the DE version used here employs the latest (available) schemes of crossover, mutation and recombination. In comparison to this, the Barter method is a nascent one. We need a thorough investigation into the nature and performance of the Barter method. We have found that when the DE optimizes, the terminal population is homogenous while in case of the Barter method it is not so. This property of the Barter method has several implications with respect to the Agent-Based Computational Economics

Global optimization, Simulated Annealing, Differential Evolution, Barter, Pareto optimality, competitive process, Particle Swarm, Agent-Based Computational Economics, Experimental Economics, non-convex functions, Fortran, computer program, benchmark, test functions

Abstract:
This study deals with several issues relating to an investigation into conceptualization, definition, measurement, spatial and community-wise distribution, asymmetry, inequality and a few other related aspects of quality of life in a commercial township of a developing tribal-abundant state located in a less developed, hilly and frontier region of India. Unlike many studies on the assessment of quality of life at a macro level wherein certain gross indicators (mortality rates, per capita income or literacy rate, etc. at the national or the regional level) have conventionally been used to measure QOL, in this investigation we measure QOL by means of 135 micro-level indicators - at the household and his neighbourhood level. Four facets of QOL are visualized - those related to housing, economic aspects and high consumption, which are singularly dominant and positive. They together contribute over 97 percent to the Composite Index of QOL. The fourth facet relates to accessibility. It contributes but only a little to the Index. The distribution of sample households according to the value of the Composite Index of QOL is asymmetric around the mean value. Overall, the sample households are closer to the Hell point and farther from the Bliss point. Asymmetry is the least in sector 3 followed by sector 4, and the most in sector 5 followed by the sectors 2 and 1. Average Quality of Life improves as one moves away from the core of the city, attains it peak at the medial sector and sharply declines afterwards. There are a number of destitute households in the sample. Most of them are in the rural outskirts of Dimapur, but scarcely a few in the sectors 2 and 3, where average quality of life is better. Perhaps, a residence in sector 2 or 3 is economically inaccessible to them.

Construction of the facet indices as well as the composite index based on full matrix of inter-correlation among the indicators of QOL yields better results than if the indices are constructed by using block-diagonal partial information. A perusal of the table containing loadings of pooled object variables (indicators) suggests that about one-fourth of the loadings (absolute value) are less than 0.10. Exclusion of such variables from the object set would not affect the composite index of QOL adversely, but only add to the parsimony. However, retaining them does not have any undesirable affect. We avoid pruning them out. An advice to exclude such 'weaklings' from the set of object variables in order to enhance the explanatory power of the index is rather usual. We hold that such an advice is naive and its practice illusive. An inference based on partial information can never outperform the inference based on full information.

Quality of life, Dimapur, Nagaland,Principal component analysis, Bliss point, Hell point, destitute households

Abstract:
The objective of this paper is to introduce a new population-based (stochastic) heuristic to search the global optimum of a (continuous) multi-modal function and to assess its performance (on a fairly large number of benchmark functions) vis-a-vis that of two other well-established and very powerful methods, namely, the Particle Swarm (PS) and the Differential Evolution (DE) methods of global optimization. We will call this new method the Barter Method of global optimization.

This method is based on the well-known proposition in welfare economics that competitive equilibria, under fairly general conditions, tend to be Pareto optimal In its simplest version, implementation of this proposition may be outlined as follows:

Let there be a fairly large number of individuals in a population and let each individual own (or draw from the environment) an m-element real vector of resources, x = (x1, x2, …, xm). For every xi there is a (single-valued) function f(x) that may be used as a measure of the worth of xi that the individual would like to optimize. The optimand function f(.) is unique and common to all the individuals. Now, let the individuals in the (given) population enter into a barter of their resources with the condition that (i) a transaction is feasible across different persons and different resources only, and (ii) the resources will change hands (materialize) only if such a transaction is beneficial to (more desired by) both the parties (in the barter). The choice of the individuals, (i, k) and the resources, (j, l) in every transaction and the quantum of transaction would be stochastic in nature. If such transactions are allowed for a large number of times, then at the end of the session: (a) every individual would be better off than what he was at the initial position, and (b) at least one individual would reach the global optimum.

We have used 75 test functions. The DE succeeds in 70 cases, the RPS succeeds in 60 cases, while the Barter method succeeds for a modest number of 52 cases. The DE as well as Barter methods are unstable for stochastic functions (Yao-Liu#7 and Fletcher-Powell functions). In eight cases, the Barter method could not converge in 10000 iterations (due to slow convergence rate), while in 4 cases the MRPS could not converge. Seen as such, the barter method is inferior to the other two methods. Additionally, the convergence rate of the Barter method is slower than the DE as well as the MRPS. However, the DE and the RPS have a history of a full decade behind them and they have been improved many times. In the present exercise, the RPS is a modified version (MRPS) that has an extra ability for local search. The DE version used here uses the latest (available) schemes of crossover, mutation and recombination. In comparison to this, the Barter method is a nascent one. We need a thorough investigation into the nature and performance of the Barter method. It has interesting implications as to the Agent-Based Computational Economics.

Agent-Based Computational Economics, Barter method, Differential Evolution, Repulsive Particle Swarm, Global optimization, non-convex functions, local optima, Fortran, computer program, benchmark, test functions

Abstract:
In this paper an attempt has been made to fit the Gielis curves (modified by various functions) to simulated data. The estimation has been done by two methods - the Classical Simulated Annealing (CSA) and the Particle Swarm (PS) methods - of global optimization. The Repulsive Particle Swarm optimization algorithm has been used. It has been found that both methods are quite successful in fitting the modified Gielis curves to the data. However, the lack of uniqueness of Gielis parameters to data (from which they are estimated) is corroborated.

Gielis super-formula, supershapes, Simulated annealing, Particle Swarm method, Repulsive Particle Swarm method of Global optimization, nonlinear programming, multiple sub-optimum, global, local optima, fit, data, empirical, estimation, parameters, curve fitting, Shape Recovery

Abstract:
The IDEAS publishes every month the rankings of economists (and departments of economics including research institutions working in the related areas) in different countries. These rankings are based on a large number of measures. It is observed that economists of some countries participate more vigorously in academic and professional activities. This paper investigates into the factors responsible for variations in participation of economists of different countries in academic and professional activities reflected in their intellectual output.

Economist, participation, rankings, IDEAS; RePEc, intellectual output, human development, less developed countries, journal articles, working papers, SSRN

Abstract:
This essay draws attention to the fundamental axioms of human nature which the socio-economic policies of India bank upon and analyses why in spite of elaborate planning for development well over a span of fifty years the core economy of the country remains unchanged with widespread poverty, poor wage rates, child labour and hunger.

Conceited socialism, covert individualism, uncritical idealism, politics as a profession, criminalization of politics, politicization of crime, modernized attitudes.

Abstract:
Ricardo Chacón generalized Johan Gielis's superformula by introducing elliptic functions in place of trigonometric functions. In this paper an attempt has been made to fit the Chacón-Gielis curves (modified by various functions) to simulated data. Estimation has been done by the Particle Swarm (PS) methods of global optimization. The Repulsive Particle Swarm optimization algorithm has been used. It has been found that although the curve-fitting exercise may be satisfactory, a lack of uniqueness of Chacón-Gielis parameters to data (from which they are estimated) poses an insurmountable difficulty to interpretation of findings.

Ricardo Chacón, Jacobian Elliptic functions, Weierstrass , Gielis super-formula, supershapes, Particle Swarm method, Repulsive Particle Swarm method of Global optimization, nonlinear programming, multiple sub-optimum, global, local optima, fit, empirical, estimation, cellular automata, fractals

Abstract:
Johan Gielis showed that all closed curves might be considered as some sort of deformed ellipses. He gave a superformula to parameterize such shapes. In this study an attempt has been made to estimate the parameters of Gielis' superformula from empirical data. We use an optimum search algorithm on multi-modal surfaces - the Genetic Algorithm- to find the best fit. Randomly scattered starting points have been used for the search of an optimum solution. Some examples are based on simulated data, while the solution of a real problem also may be attempted. It has also been shown that the parameters of the superformula are not uniquely related to the data from which they are estimated. This lack of uniqueness may pose the problems of interpretation of parameters.

Johan Gielis, Genetic algorithm, Nelder-Mead method, Super formula, closed curves, non-linear programming, optimization, curve fitting, empirical data, sub-polygons, super-polygons, shape parameters, estimation, direct search algorithm, Local global optimum, multi-modal surfaces

Abstract:
Keane's bump function is considered as a standard benchmark for nonlinear constrained optimization. It is highly multi-modal and its optimum is located at the non-linear constrained boundary. The true minimum of this function is, perhaps, unknown. We intend in this paper to optimize Keane's function of different dimensions (2 to 100) by the Repulsive Particle Swarm (RPS) and the Differential Evolution (DE) methods of global optimization. The DE optimization program has gone a long way to obtain the optimum (if so!) results. Application of the RPS program has clearly failed to minimize the Keane's function of any considerable size. Then we have conjectured that the values of the decision variables (of Keane function) diminish with the increasing index values and they form two distinct clusters with almost equal number of members. These regularities indicate whether the function could attain a minimum or (at least) has reached close to the minimum. Incorporating our conjecture into computation, in each iteration we arrange the variable values in a descending order and then evaluate the function. This modification has improved the RPS performance greatly. The performance of DE also is significantly enhanced. Our results are comparable with the best results available in the literature on optimization of Keane function. Our two findings are notable: (i) Keane's envisaged min(f) = -0.835 for 50-dimensional problem is realizable by the RPS and the DE; (ii) Liu-Lewis' min(f) = -0.84421 for 200-dimensional problem is grossly sub-optimal. Computer programs (written by us in Fortran) are available on request.

Nonlinear, constrained, global optimization, repulsive particle swarm, differential evolution, Fortran, computer program, Hybrid, Genetic algorithms

Abstract:
The Two-Stage Least Squares (2-SLS) is a well known econometric technique used to estimate the parameters of a multi-equation (or simultaneous equations) econometric model when errors across the equations are not correlated and the equation(s) concerned is (are) over-identified or exactly identified. However, in presence of outliers in the data matrix, the classical 2-SLS has a very poor performance. In this study a method has been proposed to conveniently generalize the 2-SLS to the weighted 2-SLS (W2-SLS), which is robust to the effects of outliers and perturbations in the data matrix. Monte Carlo experiments have been conducted to demonstrate the performance of the proposed method. It has been found that robustness of the proposed method is not much destabilized by the magnitude of outliers, but it is sensitive to the number of outliers/perturbations in the data matrix. The breakdown point of the method is quite high, somewhere between 45 to 50 percent of the number of points in the data matrix.

Two-Stage Least Squares, multi-equation econometric model, simultaneous equations, outliers, robust, weighted least squares, Monte Carlo experiments, unbiasedness, efficiency, breakdown point, perturbation, structural parameters, reduced form

Abstract:
In this paper an attempt has been made to estimate the parameters of Gielis superformula (modified by various functions). Simulated data have been used for this purpose. The estimation has been done by the method of simulated annealing. It has been found that the simulated annealing method is quite successful in fitting the modified Gielis curves to observed data. However, lack of empirical uniqueness of Gielis parameters has been corroborated. Due to this, it is quite unlikely to succeed at an estimation of the true parameters of Gielis superformula, more so when it is modified by an unknown function, and seek a scientific explanation behind them.

Gielis super-formula, supershapes, Simulated annealing, nonlinear programming, multiple sub-optimum, global, local optima, genetic algorithm, Box's algorithm, Nelder-Mead, fit, data, empirical, estimation, parameters, curve fitting

Abstract:
This paper has elaborated upon the deleterious effects of outliers and corruption of dataset on estimation of linear regression coefficients by the Ordinary Least Squares method. Motivated to ameliorate the estimation procedure, we have introduced the robust regression estimators based on Campbell's robust covariance estimation method. We have investigated into two possibilities: first, when the weights are obtained strictly as suggested by Campbell and secondly, when weights are assigned in view of the Hampel's median absolute deviation measure of dispersion. Both types of weights are obtained iteratively. Using these two types of weights, two different types of weighted least squares procedures have been proposed. These procedures are applied to detect outliers in and estimate regression coefficients from some widely used datasets such as stackloss, water salinity, Hawkins-Bradu-Kass, Hertzsprung-Russell Star and pilot-point datasets. It has been observed that Campbell-II in particular detects the outlier data points quite well. Subsequently, some Monte Carlo experiments have been carried out to assess the properties of these estimators. Findings of these experiments indicate that for larger number and size of outliers, the Campbell-II procedure outperforms the Campbell-I procedure. Unless perturbations introduced to the dataset are numerous and very large in magnitude, the estimated coefficients are also nearly unbiased.

Abstract:
In this paper we construct thirteen different types of composite indices by linear combination of indicator variables (with and without outliers/data corruption). Weights of different indicator variables are obtained by maximization of the sum of squared (and, alternatively, absolute) correlation coefficients of the composite indices with the constituent indicator variables. Seven different types of correlation are used: Karl Pearson, Spearman, Signum, Bradley, Shevlyakov, Campbell and modified Campbell. Composite indices have also been constructed by maximization of the minimal correlation. We find that performance of indices based on robust measures of correlation such as modified Campbell and Spearman, as well as that of the maxi-min based method, is excellent. Using these methods we obtain composite indices that are autochthonously sensitive and allochthonously robust. This paper also justifies simple mean-based composite indices, often used in construction of human development index.

Composite index, linear aggregation, principal components, robust correlation, Signum, Bradley, absolute correlation, Shevlyakov, Campbell, Hampel, outliers, mutilation of data

Abstract:
Subjugation of women in certain spheres of life is very common in the patriarchal societies and it has a long history. In India, women have little social or economic independence. They are treated inequitably at home as much as at the workplace outside. Perhaps, it is so for the Indian society is predominantly patriarchal. However, Meghlaya, a state in North East India, presents a case different than what the rest of the country (except Kerala) does. A very large majority of population in the state belongs to three tribes, Garo, Jaintia and Khasi, well known for their being matrilineal and matrifocal (whether effectively matriarchal or not). In this paper we investigate how women in Meghalaya perform, vis-à-vis men, in the socio-economic sphere. The investigation is based on Census of India-2001 data. Two sets of nine variables that measure socio-economic inclusion of people in development have been obtained, the first for men and the second for women, and from these variables a composite index has finally been constructed. In the interim, many methods of constructing a composite index are discussed and applied on the data for obtaining loadings on the variables. Analytic methods (e.g. principal component/factor analysis) and synthetic methods (MSAR, MEFAR and MMAR) have been compared empirically. We find that the synthetic methods perform better than the analytic methods.

Do matriarchal/matrifocal societies favour women in socio-economic sphere and achieve gender equality? We conclude that indeed they do so. The tribes of Meghalaya whose societies are organized on matrifocal/matrilineal principles have obtained much greater gender equality than the societies (e.g. Hindu and Muslim) that are organized on the patriarchal principles.

Gender equality, Patriarchy, Matriarchy, Matrilineal, Meghalaya, India, Tribes, Khasi, Garo, Jaintia, composite index, principal component, factor analysis, rotation, inclusive, synthetic, analytic, indices, absolute correlation, entropy, matrifocal , maximin, Differential Evolution

Abstract:
Arnold Zellner and Nagesh Revankar in their well-known paper "Generalized Production Functions" [The Review of Economic Studies, 36(2), pp. 241-250, 1969] introduced a new generalized production function, which was illustrated by an example of fitting the generalized Cobb-Douglas function to the U.S. data for Transportation Equipment Industry. For estimating the parameters of their production function, they used a method in which one of the parameters (theta) is chosen at the trial basis and other parameters relating to elasticity and returns to scale are estimated so as to maximize the likelihood function. Repeated trials are made with different values of theta so as to obtain the global maximum of the likelihood function.

In this paper we show that the method suggested and used by Zellner and Revankar (ZR) may easily be caught into a local optimum trap. We also show that the estimated parameters reported by them are grossly sub-optimal.

Using the Differential Evolution (DE) and the Repulsive Particle Swarm (RPS) methods of global optimization, the present paper re-estimates the parameters of the ZR production function with the U.S. data used by ZR. We find that the DE and the RPS estimates of parameters are significantly different from (but much better than) those estimated by ZR. We also find that the returns to scale do not vary with the size of output as reported by ZR. A Fortran program for estimation of the ZR function with RPS and DE has also been appended

Zellner-Revankar production function, maximum likelihood, global optimization, Repulsive Particle Swarm, Differential Evolution, U.S. Data, Transport Equipment Industry, variable Returns to scale, sub-optimality, Fortran Program

Abstract:
In this paper an attempt has been made to fit the Gielis curves (modified by various functions) to simulated data. The estimation has been done by two methods of simulated annealing - the Classical Simulated Annealing (CSA) of Kirkpatrick et al. and the Generalized Simulated Annealing (GSA) of Tsallis and Stariolo. It has been found that the Classical simulated annealing method is quite successful in fitting the modified Gielis curves to the data and, at the problem at hand, it performs much better than the 'Generalized Simulated Annealing' method. KC Mundim's computer program has been used as the central procedure for optimization by GSA. It has also been found that Mundim's program falters at searching the global minimum of Levy No. 5 and Levy No. 8 functions (test problems for global optimization algorithms) when starting points are arbitrary.

Gielis super-formula, supershapes, Generalized, Simulated annealing, nonlinear programming, multiple sub-optimum, global, local optima, fit, data, empirical, estimation, parameters, curve fitting, Tsallis engine, Boltzmann-Gibbs, Cauchy

Abstract:
This paper demonstrates that if we intend to optimally rank order n objects (candidates) each of which has m rank-ordered attributes or rank scores awarded by m evaluators, then the overall ordinal ranking of objects by the conventional principal component based factor scores turns out to be suboptimal. Three numerical examples have been provided to show that principal component based rankings do not necessarily maximize the sum of squared correlation coefficients between the individual m rank scores arrays, X(n,m), and overall rank scores array, Z(n).

Rankings, sub-optimal, optimality, principal component, factor scores, Differential Evolution, global optimization

Abstract:
The objective of this study is to bring out the case of poverty, undernourishment and health conditions of casual labourers in Shillong, the capital city of Meghalaya, India. A large section of the unskilled labourers work as casual workers. Casual labourers are those workers who work for a very short duration (for a few hours, a day or at most a few days under a single contract) for an employer, and who are (usually) paid for their labour either at the end of the contract or at the end of a day. Casual workers are often unskilled or semi-skilled; they usually do not own any other factors of production (such as land, capital or implements needed to perform the job) except their labour power. Casual labourers earn their livelihood by selling their labour power and often regenerate their labour power by 'investing', so to say, a very large part of their wage earning on food articles. Thus, in case of a casual labourer, the dichotomy of consumption and investment collapses into a single category. Due to low level of consumption, casual labourers are often poor performers - their efficiency is low. The market forces often impose on them the vicious circle of inefficiency - low wage rates - deficient consumption - inefficiency.

The study is based on the primary data collected from 125 casual labourer households with 688 family members. Overall, it is found that casual labourer households in Shillong are poor; their per capita income (per month) is Rs. 516.6 on an average and they spend a meager amount (Rs. 252.9 only or 48.95 percent of income) on food articles yielding energy. Some 38.4 percent of these households are below poverty line (fixed at Rs. 396 per capita per month). Poorer households have larger family size. Consequently, some 46.5 percent persons in the sample households are below poverty line. The mean energy intake of these households is slightly less than 1600 calories per person per day. The average energy intake among the BPL households is a meager 1307.66 calories per person per day. Only 19 households have calorie intake larger than 2000, and of them only 14 get more than 2200 calories. Of 125 households, the majority (93) have no milk consumption.

Overall, carbohydrates supply 76.5 percent of the energy intake and the contribution of proteins to the calorie intake is ranging between 9.55 and 10.64 percent across different income and food habit groups with the mean value of 10.16 percent. Irrespective of the per capita income group that they belong to, the casual labourer households, without a single exception, eat diets deficient in proteins far below the prescribed norms.

Of the total number of 688 persons in 125 households, 72 (10.47 percent) are found chronically sick. Among the 72 sick persons, 56 (77.78 percent) are in the BPL income group, 34 (47.22 percent) are children in 0-14 years age group, and 23 (31.94 percent) are adult women. Among the sick, the overwhelming majority indicates nutritional deficiency. Children and women are hit most hard by the dietary imbalance in food. Logit analysis on incidence of sickness suggests that the probability of a person being sick is very high (0.5 or more) in the extremely poor households. The probability of finding a sick person at about per capita income of Rs. 600 per month is 0.10 and it declines sharply with an increase in income.

Poverty, malnutrition, nutrition, deficiency disease, Shillong, Meghalaya, India, primary data, calorie, carbohydrate, protein, fat, logit analysis

Abstract:
This paper presents our findings on the structural relationship between household income and consumption expenditure in the township of Kohima. It is based on the primary data collected from 209 households inhabiting 19 wards of the township. It is found that about 56 percent of households are in the per capita monthly income class below Rs. 4000. About 61 percent of the household income is drawn from salaries and pension while about 22 percent of the same is drawn from self-employment. About one third of the income is spent on food items and about one fifth of the income is spent on clothes, shoes and housing-related items. About 11 percent of income is spent on education. The average propensity to consume is about 63 percent of income. The marginal propensity to consume is about 0.55. Per capita income explains about 85 percent of variance in per capita consumption expenditure. Distribution of income and expenditure over the households is mildly unequal as the Gini coefficients for them are 0.367 and 0.312 respectively.

On the basis of income elasticity of consumption expenditure on different items it has been found that rented house is an inferior good. Most of the food items, clothing, fuel, electricity, toiletries and education are normal necessity goods. Addictive items, medicine, newspaper, telephone, cable TV, travel, etc. fall in the superior goods category. Attending to social obligations is a strongly superior item of expenditure. Increase in family size affects consumption of superior goods adversely. Family size and income are positively correlated.

To investigate into how the different components of per capita income (salaries, pension, wages, etc.) relate to the different components of consumption expenditure (on food grains, vegetables, etc.), not severally but jointly, we have gone in for the canonical correlation analysis. This analysis between income components and expenditure components indicates that income obtained from secure and stable streams such as salaries, pension, rentals and self-employment supports expenditure on necessities such as food items, housing, clothing, etc. A community-wise distribution of income and expenditure reveals that while Angami, Ao and Lotha communities among the Naga tribes are relatively better off, households belonging to other Naga communities and those migrated from other parts of the country are relatively worse off. Several factors obtained from canonical correlation analysis are strongly significant and point to much more complicated structure and divergent determinants of relationship between the components of income and consumption expenditure.

We have also gone in for discriminant analysis to investigate if increase in per capita income of the households brings about structural changes in the pattern of consumption expenditure. Our findings suggest that indeed it is so and such structural changes are statistically significant.

Income, expenditure, marginal propensity to consume, Lorenz curve, Engel's elasticity, Gini coefficient, Robust regression, Least Median Squares, canonical correlation, discriminant analysis, Nagaland, Kohima, India

Abstract:
Meghalaya, a state in the North Eastern India, is inhabited by over 2.3 million of population of which 70 percent are Christian, 13 percent are Hindus and a little over 4 percent are Muslims as obtained in the Census 2001. In this study we investigate if numerical dominance of a community leads to socio-economic dominance. We have constructed two composite indices of exclusion by weighted aggregation of 13 socio-economic indicators. The first composite index (I1) is obtained by maximization of the sum of absolute coefficients of correlation of the index with the indicator variables, while the second index (I2) is constructed by the principal components analysis that maximizes the sum of squared coefficients of correlation of the index with the indicator variables. In our judgment, the first index presents the reality more correctly, as a number of indicators undermined by I2 are given their due representation in I1. A perusal of the index (I1) reveals that while the Christian segment of population in the rural areas of Meghalaya is certainly better off than its Hindu or Muslim counterparts, it scores comparatively poorly in the urban areas of Meghalaya. In the urban areas, the Muslim segment of the population is in the most advantageous position, followed by the Hindus. The Christians segment of population is more intensively excluded from the benefits of development. Thus, numerical dominance of a particular religious community does not entail socio-economic advantages. The advantages of numerical dominance may well be absorbed by the intra-community inequalities in the command over resources and opportunities.

Religious communities, Hindu, Muslim, Christian, Meghalaya, exclusion, inequality, composite index, principal components, maximization, absolute, coefficient, correlation, North East, India

Abstract:
Logarithmic spirals are abundantly observed in nature. Gastropods/cephalopods (such as nautilus, cowie, grove snail, thatcher, etc.) in the mollusca phylum have spiral shells, mostly exhibiting logarithmic spirals vividly. Spider webs show a similar pattern. The low-pressure area over Iceland and the Whirlpool Galaxy resemble logarithmic spirals.Many materials develop spiral cracks either due to imposed torsion (twist), as in the spiral fracture of the tibia, or due to geometric constraints, as in the fracture of pipes. Spiral cracks may, however, arise in situations where no obvious twisting is applied; the symmetry is broken spontaneously. It has been found that the rank size pattern of the cities of USA approximately follows logarithmic spiral.

The usual procedure of curve-fitting fails miserably in fitting a spiral to empirical data. The difficulties in fitting a spiral to data become much more intensified when the observed points z = (x, y) are not measured from their origin (0, 0), but shifted away from the origin by (cx, cy). We intend in this paper to devise a method to fit a logarithmic spiral to empirical data measured with a displaced origin. The optimization has been done by the Differential Evolution method of Global Optimization. The method is also be tested on numerical data.

It appears that our method is successful in estimating the parameters of a logarithmic spiral. However, the estimated values of the parameters of a logarithmic spiral (a and b in r = a * exp (b (theta + 2 * pi * k) are highly sensitive to the precision to which the shift parameters (cx and cy) are correctly estimated. The method is also very sensitive to the errors of measurement in (x, y) data. The method falters when the errors of measurement of a large magnitude contaminate (x, y). A computer program (Fortran) is appended.

Logarithmic Spiral, Growth Spiral, Bernoulli Spiral, Equiangular Spiral, Cartesian Spiral, Empirical data, Shift in origin, change of origin, displaced pole, polar displacement, displaced origin, Curve Fitting, Spiral fitting, Box Algorithm, Differential Evolution method, Global optimization

Abstract:
This study is an investigation into the real wage rates of casual labourers in Shillong, the capital city of Meghalaya. First, trends in nominal wages during 1997-2000 have been studied. Then the consumption expenditure of casual labourers on wage goods is analysed and finally, changes in prices of wage goods and the cost of living have been investigated during the same period. Sources of data are the primary surveys conducted by the authors.

We have found that wage rate (of a general casual laborer) is about Rs. 60 per day, which in case of an unskilled laborer is about Rs. 47 only. With each of the two working members getting some job for 22.5 days in a month, an average casual labourer household earns Rs 2565 (Rs. 475 per capita per month). For an average unskilled casual laborer household these figures are Rs. 2000 and Rs. 372 (per capita). ILO (1996) defines subsistence wage as the hourly wage sufficient to buy one kilogram of the lowest-priced staple cereal. The price of 1kilogram of rice (the staple cereal in the study area) varied between Rs. 8.5 to Rs. 10.0 during 1996-1998. The range was Rs. 10 to 11.5 in 1998-2000. The upper limit of daily wage rates of unskilled casual workers was Rs. 50. Work hours (per day) were 7 to 8 hours. From these figures, the hourly wage rate works out to be Rs. 7.0 or less, which cannot buy 1 kilogram of rice. Thus, casual laborers in Shillong earn only a subsistence wage.

Rice and house rent are the first two major claimants, accounting for some 40 percent of the total expenditure on wage goods. Beef, fuel and pan (+betel nuts) are the next significant claimants accounting for an additional 24 percent of the total expenditure. Potatoes, onions and vegetables together claim for some 9 percent and sugar, tea and milk together account for about 7 percent of the total expenditure. Fish, beef, meat (includes pork and mutton), potatoes, onions, vegetables and mustard oil together claim for a little over 30 percent of the total expenditure.

In the later half of our study period, wages of unskilled labourers have systematically lagged behind the increase in the cost of living index. Wage rates of unskilled labourers have increased by 11 to 12 percent while the cost of living has increased by 20 percent during the study period. Wage rates of skilled labourers, which increases by (about) 80 percent or so, succeeded at overpowering the increase in the cost of living. The unlimited supply of unskilled casual labourers from the rural Meghalaya, Nepal, Bihar, Bengal, Bangla Desh, Assam, etc to Shillong has kept up an excess supply of unskilled casual labourers. However, that is not the case with the skilled casual labourers. Additionally, urbanization, development and rise in secondary and tertiary sector activities in Shillong has created jobs for skilled casual labourers more in proportion than that for the unskilled casual labourers.

Real wages, casual labourers, cost of life index, Shillong, Meghalaya, wage goods, subsistence wage, consumption expenditure

Abstract:
Some signal waveforms are very fast dampening oscillatory time series composed of exponential functions. The regular least squares fitting techniques are often unstable when used to fit exponential functions to such signal waveforms since such functions are highly correlated. Of late, some attempts have been made to estimate the parameters of such functions by Monte Carlo based search/random walk algorithms. In this study we use the Differential Evaluation based method of least squares to fit the exponential functions and obtain much more accurate results.

Signal waveform, exponential functions, Differential Evolution, Global optimization, Nonlinear Least Squares, Monte Carlo, Curve fitting, parameter estimation, Random Walk, Search methods, Fortran

Abstract:
In this paper we have proposed a method to conduct the ordinal canonical correlation analysis (OCCA) that yields ordinal canonical variates and the coefficient of correlation between them, which is analogous to the rank correlation coefficient of Spearman. The ordinal canonical variates are themselves analogous to the canonical variates obtained by the conventional canonical correlation analysis (CCCA). Our proposed method is suitable to deal with the multivariable ordinal data arrays. Our examples have shown that in finding canonical rank scores and canonical correlation from an ordinal dataset, the CCCA is suboptimal. The OCCA suggested by us outperforms the conventional method. Moreover, our method can take care of any of the five different schemes of rank ordering. It uses the Particle Swarm Optimizer which is one of the recent and prized meta-heuristics for global optimization. The computer program developed by us is fast and accurate. It has worked very well to conduct the OCCA.

Abstract:
In this paper we report our findings as to the extent of poverty among the casual labourers of Shillong, the capital city of Meghalaya, India. Two views of poverty have been considered; first at the per capita (per month) income level and the second at the nutritional level. Nutritional level has been defined in terms of calorie, carbohydrate, protein and fat intakes of the casual labourer households. We find that income elasticites of calorie availability and carbohydrate availability move close to each other. Income elasticities of protein are always higher than carbohydrate (and calorie). Elasticities of fat are initially larger than others, but with an increase in per capita income they slide down others. At small income levels relatively high-fat-low-protein articles are consumed while with an increase in income relatively low-fat-high-protein articles are consumed. The contribution of carbohydrates to calorie intake decreases with an increase in per capita income. Our findings do not corroborate Behrman and Deolalikar (1987), who showed that the income elasticity of calorie intake was quite low, and not significantly different from zero in statistical terms. If the income elasticity were close to zero, its implication is that improvement in the income of the poor will have little impact on the extent of malnutrition. Then the developmental policies intended to improve nutrition will have to use policy instruments which attack malnutrition directly rather than relying simply on raising income. But that is not the case as shown by our study. However, our findings support Strauss and Thomas (1990), Ravallion (1990). Bouis and Haddad (1992), and Subramanian and Deaton (1996), who find that income elasticities of energy component of food, although small, are yet significantly different from and much larger than zero. Subramanian and Deaton (1996), based on the National Sample Survey data, estimated the expenditure elasticity of calorie intake to lie in the range of 0.3-0.5 and in any case statistically different from zero. In our study, we find that income elasticities of calorie availability (to casual labourers in Shillong) are close to 0.4, which corroborate Subramanian and Deaton. We also find that not only calories, but other nutritional ingredients of food such as carbohydrate, protein and fat availabilities (intakes) also have income elasticities significantly larger than zero and, therefore, raising income to Rs. 800 (per capita per month) or so we may overcome the mal-nutrition problem among the poor.

Poverty, Shillong, Meghalaya, India, Nutritional intakes, carbohydrate, protein, fat, calorie, income elasticity, malnutrition

Abstract:
Effects of outliers on mean, standard deviation and Pearson's correlation coefficient are well known. The Principal Components analysis uses Pearson's product moment correlation coefficients to construct composite indices from indicator variables and hence may be very sensitive to effects of outliers in data. Median, mean deviation and Bradley's coefficient of absolute correlation are less susceptible to effects of outliers. This paper proposes a method to obtain composite indices by maximization of the sum of absolute Bradley's correlation coefficients between the indicator variable and the derived composite index.

Composite index, Principal Components analysis, absolute, Bradleys correlation coefficient, outliers, median, mean deviation, Differential Evolution, global optimization

Abstract:
Kelvin Lancaster considered a commodity as a bundle of characteristics or a bunch of vectors. The demand for a commodity is therefore a demand for its characteristics. Those characteristics may include time (whether a commodity is old or new), place (its location), positional value (whether it is owned or used by many or only a few), brand name (whether produced by this or that manufacturer), and so on. This view of considering a commodity as a bundle of characteristics opens an immensely wide scope for properly dealing with the demand for a commodity not only as a substitute of but also as a complement to other commodity or commodities. In this paper we have shown how the demand for a multi-characteristics commodity such as house can be estimated by a method suggested by Stackelberg that transforms the measures of various characteristics into polar coordinates, and how this method may be useful in identifying the complementary and substitutive characteristics of the commodity concerned. We have not gone in for identification of the demand equation. We apply this method on the primary data collected from 109 households inhabiting Kohima, the capital city of Nagaland (India). An analysis of the data suggests that consumers of rented house consider floor area, water supply and power supply complementary to each other and other characteristics of house as substitutes of the floor area. It has also been found that in Kohima a rented house is possibly an inferior commodity and its income elasticity for the overall sample is negative, although statistically insignificant.

Hedonic demand, Kelvin Lancaster, Heinrich von Stackelberg, Characteristics, polar coordinates, direction vectors, rent, demand for house, income, family size, primary data, household, Kohima, Nagaland, India

Abstract:
Rank-ordering of individuals or objects on multiple criteria has many important practical applications. A reasonably representative composite rank ordering of multi-attribute objects/individuals or multi-dimensional points is often obtained by the Principal Component Analysis, although much inferior but computationally convenient methods also are frequently used. However, such rank ordering - even the one based on the Principal Component Analysis - may not be optimal. This has been demonstrated by several numerical examples. To solve this problem, the Ordinal Principal Component Analysis was suggested some time back. However, this approach cannot deal with various types of alternative schemes of rank ordering, mainly due to its dependence on the method of solution by the constrained integer programming. In this paper we propose an alternative method of solution, namely by the Particle Swarm Optimization. A computer program in FORTRAN to solve the problem has also been provided. The suggested method is notably versatile and can take care of various schemes of rank ordering, norms and types or measures of correlation. The versatility of the method and its capability to obtain the most representative composite rank ordering of multi-attribute objects or multi-dimensional points have been demonstrated by several numerical examples. It has also been found that rank ordering based on maximization of the sum of absolute values of the correlation coefficients of composite rank scores with its constituent variables has robustness, but it may have multiple optimal solutions. Thus, while it solves the one problem, it gives rise to the other problem. The overall ranking of objects by maximin correlation principle performs better if the composite rank scores are obtained by direct optimization with respect to the individual ranking scores.

Rank ordering, standard, modified, competition, fractional, dense, ordinal, principal component, integer programming, repulsive particle swarm, maximin, absolute, correlation, FORTRAN, program

Abstract:
The Pearsonian coefficient of correlation as a measure of association between two variates is highly prone to the deleterious effects of outlier observations (in data). Statisticians have proposed a number of formulas to obtain robust measures of correlation that are considered to be less affected by errors of observation, perturbation or presence of outliers. Spearman’s rho, Blomqvist’s signum, Bradley’s absolute r and Shevlyakov’s median correlation are some of such robust measures of correlation. However, in many applications, correlation matrices that satisfy the criterion of positive semi-definiteness are required. Our investigation finds that while Spearman’s rho, Blomqvist’s signum and Bradley’s absolute r make positive semi-definite correlation matrices, Shevlyakov’s median correlation very often fails to do that. The use of correlation matrices based on Shevlyakov’s formula, therefore, is problematic.

Robust correlation, outliers, Spearman’s rho, Blomqvist’s signum, Bradley’s absolute correlation, Shevlyakov’s median correlation, positive semi-definite matrix

Abstract:
Based on the bibliographical data available with the RePEc (Research Papers in Economics), the Internet Documents in Economics Access Service (IDEAS) publishes every month the up-dated academic rankings of different geographic regions (countries/states in the US). This paper raises the question whether the method used by the IDEAS/RePEc to obtain academic rankings of different regions in terms of the academic performance of economists associated with them can be considered optimal. It devises five different types of ranking procedure based on the principles of representation of numerically large and varied types of ranking criteria by a single index of overall ranking scores. Empirically, it uses the data published by the IDEAS for the month of September 2008.

It is found that the overall ranking scores obtained by the IDEAS are almost optimal on the four (of the five) principles of representation. However, it is not so when the principle of representation is maximization of the minimal squared correlation of overall ranking scores with the constituent individual ranking scores. The overall ranking scores based on maximization of minimal squared correlation beget larger impact (weight) of a select few scientometric criteria such as h-index, download counts, and certain specific (co-authorship discounted) measures of impact-weighted citation and productivity of authors affiliated to the regions under consideration. As a consequence, it has some bias in favour of economically developed regions, while the overall ranking scores obtained by the IDEAS are slightly biased in favour of the economically less developed regions. The IDEAS rankings, therefore, have a tendency to discount for the disadvantages faced by the economists associated with the less privileged regions.

IDEAS, RePEc, Bibliometric, Scientometric, principles of representation, academic rankings, economics, impact factors, h-index, citation index, journal pages, global optimality, differential evolution

Abstract:
Is journal impact factor a good measure of research merit‘ This question has assumed a great importance after the notification of the University Grants Commission (Minimum Qualifications for Appointment of Teachers and other Academic Staff in Universities and Colleges and Measures for the Maintenance of Standards in Higher Education) Regulations, 2009 on September 23rd 2009. Now publication of research papers/articles in reputed journals has become an important factor in assessment of the academic performance of teachers in colleges and universities in India. One of the measures of reputation and academic standard (rank or importance) of a journal is the so-called ‘Impact Factor.’ This study makes a detailed statistical analysis of Journal Impact Factors across the disciplines. It finds that if journal impact factor is used to assess the academic performance of individuals (for the purpose of selection, promotion, etc) and it is not borne in mind that due to vast differences in the nature of distribution of impact factors across the disciplines they are not justifiably comparable, a below average scholar in the one discipline will rank higher and will be honored (and benefitted) more than another scholar in some other discipline (wherein the journal impact factor is adversely skewed). It may be noted that in the university departments there are specializations with low impact factor journals and other specializations with very high impact factor journals. But the teachers/researchers of different specializations in the departments compete with each other for promotion. In this milieu, the researchers with an unfortunate specialization (wherein the journal impact factor is mingy or adversely skewed) would receive injustice is plainly predetermined. Therefore, a measure such as the h-index which quantifies the quality as well as productivity of an individual author/scholar would be more appropriate than the journal impact factor. The h-index may be fine-tuned and hence the g-index or Tol’s index may be used. Nevertheless, even the h-index and the Tol’s index would not be appropriate to the purpose of inter-disciplinary or inter-specialization comparisons. A more informed and balanced judgment of the expert committee for selection, appointment and promotion purposes will continue to be extremely important.

Journal impact factor, University Grants Commission, regulation, India, UGC, Higher education, academic performance indicator, API, Hirsch, h-index, Tol, g index, skewness, service conditions, statistical analysis

Abstract:
Professor Narmadeshwar Jha was a noted scholar on History of Economic Thought - the thought that took its shape under the influence of Alfred Marshall. His widely referred book - The Age of Marshall: Aspects of British Economic Thought, 1890-1915 - was written under the supervision of Professor A.J. Brown of Leeds (UK) and published with a commendatory foreword written by Sir Dennis H. Robertson. Professor Jha devised a methodology to conduct research in the history of economic ideas. This brief paper presents Professor Jha as a teacher, economist and scholar.

History of Economic Thought, Bhagalpur University, Bihar, India, Alfred Marshall, Institutional Economics, Will to economize, Rabindranath Tagore, Dennis H Robertson, A. J. Brown, University of Leeds (UK)

Abstract:
Structural change which is inherent in an evolving economy refers to a long-term widespread transformation of the fundamental relationships among different parts and organic constituents of it, rather than micro scale or short-term change in output and employment. Short-term economic challenges that are managed with fiscal or monetary policies do not form part of the structural change. Structural change rather involves obsolescence of skills, vocations, and permanent changes in spending and production. In structural change, a subsistence economy is transformed into a manufacturing economy, or a regulated mixed economy is liberalized. Structural change is also initiated by policy decisions or through permanent changes in resources, population or the society. A current structural change in the world economy is globalization. The present paper in this regard is an attempt to have a close examination of the evolution of the concept by reviewing some of the important literatures and verify in the context of the state of Meghalaya whether there has been any such structural change. Although the study is severely constrained by availability of relevant data, it has been visualized that changes in population growth rate and its demographic attributes, economic participation and dependency ratios, sectoral distribution of income, infrastructural advancement, etc indicate to the structural change that is taking place in Meghalaya.

structure, structural change, Meghalaya