RURAL OUT MIGRATION AT THE HOUSEHOLD LEVEL

Transcription

1 International Journal of Scientific and Research Publications, Volue 7, Issue 6, June ISSN RURAL OUT MIGRATION AT THE HOUSEHOLD LEVEL Raj Kuar Yadav*and Upendra Kuar Departent of Statistics,UdaiPratap Autonoous College, Varanasi,Uttar Pradesh,India ABSTRACT: Migration, conventionally, being an iportant part of deography, is least studied as copared to fertility and ortality. Due to decreasing birth and death rate, igration (internal or international) has becoe a ore iportant concern for deographers and other social scientists.since probability odels provide concise and clear representations of extensive data sets in a better way (Aryal, 010),in recent years increased attention has been paid to the proposition and derivation of probability odels for the oveent of huan population at icro level. The ai of the paper is to study the pattern of rural out igration with the help of a probability odel. The data for the study have taken fro two different places. The study shows that the logarithic series distribution is a well approxiation for the rural out igration in the given area. Key-Words: Rural out igration, logarithic series distribution, axiu likelihood estiation. INTRODUCTION: Migration, conventionally, being an iportant part of deography, is least studied as copared to fertility and ortality. Due to decreasing birth and death rate, igration (internal or international) has becoe a ore iportant concern for deographers and other social scientists. Most of the studies in past (Greenwood 1971; Isbell 1944; Lee 1966; Singh et.al., 01; Singh 1986; Stouffer 1940,1960 and Ziff 1946 ), depending upon the conceptualization of igration process and the scale of investigations, used acro approach by operating on highly aggregate data for countries, districts, states and the nation as a whole. These types of studies are unable to provide sufficient explanation for the treendous regional and local heterogeneity. They also ignore the decision aking process of igrating individuals (Singh and Yadava 1981). Thus a study of environent in which igration takes place and the igration decision process at the icro-level is ore iportant. Studies of igration at the icro-level i.e. at the levels of individuals, failies or householdshave iportant iplications for housing policies and also for the developent of other sociological odels related to failiesandcounities(pryor,1975;rossi,1955). It is seen that a igrant household (with one or ore persons involved in the process of igration in relation to do soe job outside the village) ay have different socio-econoic and cultural characteristics through reittances besides ideas, awareness and environents than a non-igrant household. It is worth entioning here that rural-urban igration in India is of chain type at least in the beginning of the igration process before finally they settled in the urban areas or returned back to the villages. A useful way of addressing the diversity of igration syste is to treat the ajor conteporary cases in a general coparative frae work (Sions &Piche, 00). There is need to put ore ephasis on using odels to analyse and explain iportant deographic issues and to predict deographic futures (Singh et. al., 016). One of the iportant property of icro level odels is that a researcher can introduce individual heterogeneity- easured (accounting different rates for individual with different characteristics such as age, sex, social class, cohort, etc.) and uneasured (choosing for each individual an adjusting factor each being the transition rate).

2 International Journal of Scientific and Research Publications, Volue 7, Issue 6, June ISSN Many Studies have been done to apply and/or forulate probability odels in natural as well as social sciences (Afsar, 1995; Aryal, 003; Wintle, 199).Since probability odels provide concise and clear representations of extensive data sets in a better way,in recent years increased attention has been paid to the proposition and derivation of probability odels for the oveent of huan population at icro level (Yadava, 1977). Singh and yadava (1981) have introduced the negative binoial distribution to study the pattern of rural-out igration at household level. Shara (1984) applied this odel on a different data set and found that this odel is not suitable for the total nuber of igrants (including feales and children) fro a household. Since igrated feales are ore likely to affect the socio-cultural characteristics of households in coparison to other feales of household, it is iportant to study the pattern of total nuber of igrants fro a household. Shara (1984) proposed a probability odel under the assuption that (i) the nuber of ale igrants aged 15 years and above follows negative binoial distribution and (ii) the distribution of alive children to a couple be known. However, the distribution of alive children to a couple has not yet been derived theoretically; the prior knowledge about these two distributions is difficult. Singh (1985) proposed a probability odel under the assuption that there are two types of households first in which only ale aged 15 years and above igrate and second in which the ale igrate with their wives and children. Several authors have proposed odels in the sae line to describe the distribution of household according to the total nuber of igrants including wife and children (Singh et. al., 014, 015; Yadava and Yadava, 1988; Yadava et. al., 1989, 1991). The ai of the paper is to study trends in rural-out igration at the household level through soe probabilistic odels and also to do soe odification in the exiting estiation procedure. DATA: The above discussed odel is verified by the data set collected in a priary survey entitled Migration and its Ipact in Rural Varanasi has been conducted during Septeber -October 015 in four villages of two blocks of Varanasi District by the Departent ofstatistics, U. P. Autonoous College, Varanasi. Apart fro this the data set collected during October 009 to June 010 in Northeastern Bihar. A PROBABILITY MODELS FOR RURAL OUT MIGRANTS A probability odel for describing the variation in the nuber of rural out-igrant households has been derived on the basis of following assuptions: (i) At the survey point, the household is either exposed to the risk of igration or it is not exposed to the igration risk. Let α and (1-α ) be the respective probabilities. (ii) The probability of igrating one ale fro a household is greater than the probability of igrating two ales, and probability of two ales igrating is greater than that of three ales fro a household and so on. Thus, the pattern of igration fro a household is a decreasing function and follows a logarithic series distribution with paraeterλ. Let x represent the nuber of rural out-igrants fro a household, then under the assuptions (i) and (ii), the probability function of x is given by P(x = k) = 1 α, for k = 0 λ k... (1.1) = α for k = 1,,3,...; 0 < λ < 1; 0 < α < 1 k ln (1 The log-series distribution has a long positive tail and the shape of the tail is siilar to that of geoetric distribution for large values of k. However, the log-series distribution has the advantage that it has only one paraeter instead of two paraeters of Negative Binoial Distribution.

3 International Journal of Scientific and Research Publications, Volue 7, Issue 6, June ISSN Estiation Consider a saple consisting of n observations of the rando variable x with probability function given by expression (1.1). Suppose that n k (k = 0, 1,,, ) represents the nuber of observations of k th cell and nk = n. The likelihood function for the given saple (x 1, x,, x n ) can be expressed as : k = 0 n L (x, x,..., x = (1 - ) n -λ k k 0 [ α, λ )] α α 1 n... (1.) k = 1 k log( 1 = n0 n n nk xk 0 k = 1 ( 1 α ) ( α ) λ Π x n [ log( 1 n n k k ] k = (1.3) where x k represents the value of k. Taking logariths of (1.3) and differentiating with respect to α and λ respectively and equating to zero gives the following equations: log L no n no = + = 0... (1.4) α 1 α α nk xk log L k = 1 n n0 = + = 0... (1.5) λ λ ( 1 log( 1 The equation (1.4) yields the estiator of α as α = n n 0 n The estiating equation for λ is obtained by solving equation (1.5) as: (1- log (1- k = 1 n k x k +(n - n 0 )λ =0... (1.6) This equation can be solved nuerically and the nuerical solution of (1.6) is the desired axiu likelihood estiate for λ. Using the fact that E (n 0 ) = n (1-α), E(n-n 0 ) = nα E (x k ) = αλ nαλ and E nkxk = ( 1 log( 1 ( 1 log ( 1 k =1 The expected values of second partial derivatives are obtained as log L E( n0) E( n n0) n E = = = ϕ α ( 1 α) α α( 1 α) 11 (say)... (1.7)

4 International Journal of Scientific and Research Publications, Volue 7, Issue 6, June ISSN E E nk xk log k = 1 log( ) ( n0) = + λ L ( λ ) [ 1+ 1 λ ] E n [( 1 log ( 1 ] 1 = - n α + λ( 1 log( 1 1+ log( 1 [( 1 log( 1 ] = φ (say)... (1.8) The covariance between α and λ is zero since E log L = 0 and hence the variance of α and λ can be α λ obtained as v( α) = 1 and v( = 1 φ φ 11 Conclusion: The Study indicates that the present odel is a reasonable approxiation to describe the distribution of households for the rural out igrants and at least at the icro-level. Both the data set shows that the odel used describes the phenoenon satisfactorily well. The exact variance and covariance of the estiator for the odelhave also been coputed. Table-1. Distribution of observed and expected frequency of nuber of households according to the nuber of rural out igrants (Varanasi district data 015) Nuber of observed Expected χ Migration 0.05 (d.f. =3) Total 649 α 0.39 p 0.53 λ 0.6 var(α) Var(l) Fig.1. Expected and Observed Frequency of Nuber of Migrants (Varanasi district data 015)

5 International Journal of Scientific and Research Publications, Volue 7, Issue 6, June ISSN observed Expected Table-. Distribution of observed and expected frequencyof nuber of households according to the nuber of rural out igrants (Data set of Northeastern Bihar) No of Migrants observed Expected(Model I) χ α p λ var(α)

6 International Journal of Scientific and Research Publications, Volue 7, Issue 6, June ISSN var( Fig.. Expected and Observed Frequency of Nuber of Migrants(Data set of Northeastern Bihar) References: Aryal, T. R. (010): A new technique to construct the feale arriage life-table, Nepali Matheatical Sciences Report, Vol. 30 (1&) pp Greenwood, M. J. (1971): A regression analysis of igration to urban areas of a less developed country: the case of India, Journal of Regional Sciences, Vol. 11, pp Isbell, E. C. (1944): Internal igration in Sweden and intervening opportunities, Aerican Sociological Review, Vol. 9, pp Lee, E. S. (1966): A theory of igration, Deography, Vol. 3, pp Singh, R. B. (1986): A study of igration pattern fro rural areas, unpublished Ph.D. thesis, Banaras Hindu University, India. Stouffer, S. A. (1940): Intervening opportunities: a theory relating obility and distance, Aerican Sociological Review, Vol. 5 (6), pp Stouffer, S. A. (1960): Intervening opportunities and copeting igrants, Journal of Regional Science, Vol., pp Zipf, G. (1946): The P 1 P /D hypothesis: On the intercity oveent of persons, Aerican Sociological Review, Vol. 11, pp Singh Niraj K., Singh B.P., Singh, Brijesh P. (01): Migration Expectancy in northeastern Bihar, International Journal of Current Research, Vol. 4, Issue 11, pp Singh, S. N. and Yadava, K. N. S. (1981): Trends in rural out-igration at household level, Rural Deography, Vol. VIII, No. 1. Rossi, P. H. (1955): Why failies ove: A study in the social psychology of urban residential obility, Free Glencoe Press, New York. Pryor, R. J. (1975): Conceptualizing igration behavior: A proble of icro-deographic analysis, In Kosinski, L. A. and Webb, J. W., New Zeland, pp

7 International Journal of Scientific and Research Publications, Volue 7, Issue 6, June ISSN Sions, Alan and Victor, Piché. (00): Teaching igration and globalization, Genus, LVIII, No. 304, pp Singh, Brijesh P. and Singh, Niraj K. (016): On the Distribution of Risk of Migration and Its Estiation, International Journal of Statistical Distributions and Applications, Vol. (4), pp Afsar, R. (1995): Rural-urban igration and its ipact on woen roles and status, epowerent, A Journal of Woen for Woen, Vol.. Bangladesh. Aryal, T. R. (003): Probability odels for the nuber of rural out-igrants at icro-level, The Nepali Matheatical Sciences Report, Vol. 1(1), pp Wintle, M. (199): Push-factors in eigration: the case of province of Zeeland in the nineteenth Century, Population Studies, Vol. 46, pp Yadava, K. N. S. (1977): Soe aspects of out-igration and its effects on fertility, unpublished Ph.D. thesis in statistics, Banaras Hindu University, India. Shara, L. (1984): A study of the pattern of out-igration fro rural areas, unpublished Ph.D. thesis, Banaras Hindu University, India. Singh, R. B. (1986): A study of igration pattern fro rural areas, unpublished Ph.D. thesis in statistics, Banaras Hindi University, India. Yadava, K. N. S., Singh, S. K. and Kuar, U. (1991): Soe probability odels for the pattern of rural outigration: a icro approach, Journal of Scientific Research, Banaras Hindu University, Vol. 41c, pp Yadava, K. N. S., and Yadava, G. S. (1988): On soe probability odels and their applications to the distribution of the nuber of igrants fro a household, Janasankhya, Vol. 6(), Yadava, K. N. S., Singh, S. K. and Kuar, U. (1989): A probability odel for the nuber of igrants, Janasakhya, Vol. 7(). Singh, Brijesh P., Singh Niraj K., Roy, Tapan K. (014): On the Pattern of Migration in the Household: An Explanation through Binoial Law, International Journal of Statistics and Systes, Vol.9, No., pp Singh, Brijesh P., Singh Niraj K., Dixit, Shweta (015): Estiation of Paraeters of Inflated Poisson-Lindley Distribution for Adult Out Migration, Journal of Institute of science & Technology, Vol. 0, Issue, pp