 So, this is our third lecture on the issue of modeling, I know that with your background in sociology, you will not be very comfortable with the issues in modeling, but you must know at least what the models are and if you ever see any discussion of a model in any paper on population processes, you must understand what the author is trying to achieve by using modeling. So, in the first lecture, I talked about what is model, importance of model, what kind of questions can be answered with the help of models and in the second lecture, I showed some examples of models in fertility and mortality. Now, I will go to some other issues in modeling, to some other areas and to some examples of models which have been in use in population literature in the recent times and issues in modeling like how to build a model, how to estimate parameters, validation and estimation. So, let me begin with modeling in the field of migration. So, far much of modeling in population studies has been done in the field of fertility and mortality and the reason was that earlier we did not have estimates of them and models were required to estimate birth and death rates with help of partial data from census and surveys. Now, in the field of migration, I will show you one simple, but interesting model of migration. This all started in 1885, when Ravistine published an article in the journal of the statistical society about patterns of migration based on data on migration in western countries which were available to him at that time. He said that the great body of migrants travel short distances, women out number men in short distance migration. So, interestingly some of these observations of Ravistine can be found to be valid even today and in the context of India too. If you analyze data on migration based on place of birth or place of last residence, all these things come true that the great body of migrants travel short distances within district or within state as compared to between states and in short distance migration say between districts women out number men. Then migrants move from agricultural areas followed by migration. Migrants move from agricultural areas to industrial cities means rural to urban migration followed by migration from centers of industrial cities to suburban areas. So, there are two types of migration patterns he is talking about simultaneously rural to urban and within urban areas from heart of city to peri urban villages or peri urban wards in the city. Then each migration current has a counter current with similar characteristics and the major causes of migration are economic. Now, in census we have lots of data on causes of migration also and we can see that in India too today in 2010 the major cause of migration is economic especially rural to urban migration or migration from heart of city to peri urban area. Four years later in 1889 Ravistine published another article in journal of Royal statistical society and this article was based on the experience of North America and Europe. In this article he said that people travel long distances to occupy unsaturated land. Nearly hundred years later in 1940 Samuel Stouffer published an article in American sociological review and he showed that the number of migrants from place i to place j is inversely proportional to intervening opportunities. The model was confirmed in 1975 by Badiqi who found that it to be quite an accurate description of migration. Actually it is quite interest to see how in the field of sociology some people have used some basic ideas of modeling and in case of migration whenever we discuss anything about modeling of migration we always remember Jeff. Jeff in 1946 developed and validated what is called a gravity model of migration to represent that volume of migration between two cities m i j migration between place i and place j it directly proportional to populations of the cities i and j that means p i and p j and inversely proportional to distance separating the two cities d i j. You can use Stouffer's theory of migration of intervening opportunities also and that fits quite well with this model of migration d the distance between two places interacts with intervening opportunities and you can combine Jeff's model of migration with Stouffer's model of migration. Now, Jeff assume that income and unemployment are uniformly distributed over the areas. So, this model will be if employment and income are uniformly distributed. You see that later on when this migration was improvised researchers included explicitly the variables of income and employment wage rate income employment labor force size to develop this model further that should not be seen as rejecting the model of Jeff because Jeff is saying that assuming income and unemployment are uniformly distributed over the areas then this happens. Other models of migration should simply be seen as more complex models or depiction of more complex aspects of migration rather than rejection of Jeff's model. Here k is a constant of proportionality that can be found from the empirical data. So, the model can be fitted to empirical data for a number of countries and k can be estimated. To some sociologies the model may look funny or absurd, but Jeff found that the model fitted very well for all modes of transportation that is the interesting part of it. At the end I have given you references of all these things. So, you find that Jeff is publishing his article this model of migration not in any mathematical or statistical journal, but in the top journal of sociology. And later on in 1975 using a similar argument Dorigo and Tobler in 1983 express m i j migration again between i and j two places place i and place j as k constant of proportionality u i here u stands for unemployment rate w stands for wage rate. So, u i w i divided by u j w j into l i l j here l represents the size of labor force. So, l i is size of labor force at place i and l j is size of labor force at place j divided by d i j which is the distance separating the two cities. They also decompose migration into two parts a factor of repulsiveness and a factor of attraction what in sociological language we call push and pull factors push factors which push away migrants from the place of origin and pull factors which draw migrants toward the place of destination. Analogous to equation for m i j you can also write equation for r i repulsiveness and e attractiveness or an equation showing r i minus e j repulsiveness minus n t sing or pull factors as k u i w j divided by u j w i l i l j. The constant of proportionality k again can be obtained by using empirical data on a number of countries for which this model is to be fitted. One can change the variables in the model delete or add some transform variables to mathematical or trigonometric form, but as long as the logic developed by jiff in suggesting gravity models is correct the above types of models will remain relevant. Other people have done subsequently after this 1983 article some people said that in place of u you can take u raised to power alpha or in place of d you can take d raised to powers some beta like that or labour force i l i l j you know in place of taking l i l j as such you can take their powers alpha beta gamma something. And then you have accordingly a model with three or more parameters and these parameters can be estimated again from empirical data. It is expected that more is the number of parameters or constants of the model better fit your model will show, but behind all these models of migration the basic idea of jiff is still holds that migration between two places is caused by pull factors at the place of destination push factors at the place of origin. It is inversely proportional to distance separating the two places or as is to first says intervening opportunities. If we go into literature on migration then there are many other factors some people will say that migration also depends on personality factors or psychological factors yes migration can depend on psychological factors. Accordingly you have sociological models and psychological model sociological model focuses on what is the reason that people from a certain place are moving towards another place psychological model will focus on what are the reasons that in the same situation from the same place to same place some people migrate others do not. So, what are the differences in personality variables say locus of control and need for power need for affiliation what is that in personality because of this some people migrate some do not. And there can be interaction of sociological and psychological variables this is the line that modeling in the field of migration adopts. There is another type of modeling in population studies which may be called economic demographic models. Cole and Hoover in 1958 pioneered this modeling in the context of developing countries and they developed this model for India through which they showed that the short term and long term effects of population growth on economic development can be positive or negative. And the distinguish between short term and long term it may happen that population growth is harmful in the short term, but it may be beneficial in the long term. Their model paved the way for large scale computer simulation models in population and development these models are developed on the basis of certain axioms empirical relationships and theoretical understanding of the issues involved. What Cole and Hoover thought they said that growth rate of income depends on investment, investment industry in directly productive items in capital goods and this investment depends on how much can be saved out of national income money value of goods and services produced in a country in a year how much can be saved and how much can be invested. Now, this saving part depends on consumption requirements and consumption requirements depend on two things consumption requirements of the existing population and consumption requirements of the additional population due to population growth. So, by decomposing national income into various components consumption and saving and by showing transformation of saving into investment Cole and Hoover were able to see what will be the rate of capital accumulation under different assumptions of population growth and what they found that in the beginning for some years to come rapid growth of population in India will be bad because you are increasing population you are increasing consumption you are increasing consumption of existing population you are increasing consumption requirement due to additional population. So, money left for investment is less, but in the long run say after 15 or 20 years when children born today join labor force and they start contributing to production at that time they can be useful for national economy. Right now my purpose is not to discuss the connection between economy and population studies I just wanted to say that here is another type of modeling in the field of population studies which relates issues of population growth to issues of economic development and Cole and Hoover's model developed in 1958 is still remain the classical the best model to illustrate this kind of connection and this was developed for India in particular. The variables of the system are connected through mathematical equations if you want to develop a model of this kind you have to identify your variables and you have to develop mathematical equations between these variables and the parameters of the equation are estimated using available data and appropriate estimation techniques. Predictions based on these models are correct to the extent that we have correct assumptions accurate data and appropriate estimation procedure error at any level may lead to error of unknown magnitude in the results. Now last time I said that as such because of availability of better demographic data from census, sample registration scheme, national family health survey, district level health surveys and youth surveys have met our requirements of finding estimates of birth rate, death rate, age specific fertility rate, life expectancy or age of marriage or related issues. So, for these things we do not depend on models like stable population in the last lecture I talked about stable population and cosi stable population. We do not depend on stable or cosi stable population for estimation of projections, but we still need modeling for what purpose do we need modeling I will show one or two questions which can better be answered by using mathematical models. Now, the issues are no more estimation and prediction of demographic rates and issues. There are other issues aging and health at the older ages then timing of the end of world population growth. We all know that we are moving towards stabilization of population, but when will this happen? When will world population stabilize? When will China's population stabilize? When will India's population stabilize? When will US population stabilize? Are some populations going to decline? What will be their effect on world population stabilization? The causes behind them determinants of the timings of stabilization of population then determinants of neonatal mortality, perinatal mortality, determinants of child mortality and trends in HIV 8. These are some new issues in which modeling is required. Lot of modeling is going on in the field of HIV 8. Aim is to understand the process by which HIV virus spreads from a small number of cases to larger population. How much time it takes in some country? I think in the last lecture I gave you the example of Africa that only 20 years ago, very few persons, a handful of persons actually were affected by HIV virus there. And in 20 years time in some countries as many as 20 percent, 25 percent, 30 percent of all the adult population is suffering from HIV virus. So, what is the process of diffusion or progress or growth or transmission from one part of population to other parts or from high risk group to general population? That can be understood with the help of modeling of HIV 8. So, these are some new issues, new concerns. Models are still therefore, useful in certain areas, economic and demographic planning, policy experimentation. Policy experimentation if I want to know we are able to raise our couple protection rate from the current level to 60 percent. What will be its impact on birth rate? If we are able to raise couple protection rate to 80 percent, what will be its impact on total fertility rate? Or if we are able to reduce deaths due to AIDS by 30 percent, what will be its impact on life expectancy and so on? That is policy experimentation. Then evaluation of programs, evaluation of family planning program, there are very specific models on the line of models of nuptiality or marriages, which can be used for studying impact of family planning program on birth rate. Imagine that you have to find out what is the impact of family planning program? Merely statistics of how many people are using family planning methods is not enough. You must also know for how much period they use them, means what are the rates of continuation and you must know how effective those methods are. And for estimating continuation rates, one can very well use live table or stationary population model. Then for simulation of word systems, connecting polity, environment, agriculture, industry, education, food, you can build word system models. Then understanding processes of epidemics such as HIV and flu in India, ICMR is particularly interested these days in transmission of flu virus, swine flu, H1N1, HIV. How are they spreading? If somebody, these are the models which government of India needs today very much and not much is known in this field. Then analyzing employment situation also requires modeling. It may be said that models may be used in any field of demographic interest. What one needs to apply modeling is to have clarity of objectives. If you are to build models, then the first thing is that you must be clear about objectives. What you want to achieve? Model can be simple, model can be complex. GIF's model of migration is an example of very simple model. But subsequent developments in the field of modeling of migration in which lot more variables have been added apart from population, size of labor force is added, wage rate is added, unemployment rate is added. In some models, I have seen social distance between cities is also added, linguistic differences are added. So, the model become more and more complex. More aspects of reality you want to represent through your models, more complex your models will become. Depending on your need, depending on your objectives you can go for simple or complex models. Then appropriate measurement of the variables of the system, this is another requirement. How will you major wage rate? How will you major, you know there can be several wage rates or how will you major attractiveness of a city or repulsiveness of a city or how will you major unemployment rate. Measuring, even defining unemployment is a big problem and measurement of unemployment are going to affect estimation of your parameters variables. Then you require a theory, theory that links the various variables of the model directly or indirectly. What are independent variables? What are dependent variables? What are mediator variables? Proximate variables? What are moderator variables? You must have a clear understanding of different variables involved in the system. Then you require mathematical equations to describe the above relationships. Then adequate data of high reliability, adequate computing facilities. If you have simple model, maybe you can do manual calculations, but if you are going for word system simulation or you are going for Monte Carlo simulation method. Then you require high speed computers and then instruments to measure the fitness of the model. Finally, you have to check whether the model, you can fit all kinds of models to all kinds of data, but you must also know whether the models that you have fitted are actually appropriate models or they serve the purpose, they fit well, they help you in achieving your objectives and for that purpose some test of goodness of fit would be required. As time passed and demographers took interest in new areas, several new domains of modeling have developed in literature. The area of modeling is going to expand further. There are lots of journals, population studies, demography, among international journals, studies of family planning. Then in India, you have journals, demography, India, journal of health and family welfare, which have been publishing articles based on modeling. Models have provided insights into causes of change in the demographic variables. For example, so models are used not only for representing reality or for estimation of future, but they have also been used in developing insights into causes of change in the demographic variables. For example, using the simple multivariate regression model with total fertility rate as dependent variable and GTP means gross domestic product per capita, life expectancy and gross primary and secondary school enrollment rate, percent urban and agriculture as percent of GDP as independent variables. Brand drew the following conclusion. This article was published in a recent issue of population and development review. The model was simple, multiple regression analysis and the dependent variable GTP, dependent variable is total fertility rate. And GTP, life expectancy, school enrollment rates, percent urban, agriculture as percent of GDP, they appear as independent variables. A model is fitted. Actually, variants of that model were fitted. On the basis of his study of data with help of this multiple regression analysis, he drew the following conclusions. One, that fertility decline in countries with lowest course on development means in developing countries cannot be explained by socio-economic theory. So, demographic transition theory, which explains changes in fertility and mortality in terms of economic variables, industrialization, urbanization, economic development did not explain demographic transition in the less developed countries or developing countries. This was one conclusion. The relationship between development indicator, these are all development indicators, life expectancy, life expectancy, GDP, percent, these are all socio-economic or development indicators. The relationship between these development indicators and fertility is weaker in developing countries than was the case with developed countries. Under the AC sub demographic transition theory was what we learned about relationship between fertility and socio-economic variables. The relationship was not found to be that is strong in less developed country. What does that mean? If socio-economic development factors are not, suppose the model shows and his model showed this, what does it mean? If the socio-economic factors do not explain demographic factors or the relationship between socio-economic factors and demographic factors is rather weak. And also third very interesting conclusion that the relationship between development indicators and fertility has shifted over time. So, what does that mean? That means that there are factors other than socio-economic factors, which explain transition infertility in less developed countries. And this model then favors the family planning theory or sociological theory of modernization and westernization that behind transition infertility in the less developed countries are family planning programs and also the change in values caused by modernization and westernization. It is not simply socio-economic development. So, some of the above conclusions would not be possible to make if the appropriate data did not exist or if the technique of multivariate regression analysis was not known. In an interesting article using data on homicide rates, Cole and Gramocio in 2009, this article was also published in population and development review showed that as female education increases, the homicide rates also increase. Something interesting, sometimes models come up with interesting and unexpected answers. Actually, in my class in introductory sociology, I give this example of Cole and Gramocio's model to show what positive is or what comparative sociology will mean in our time. Cole and Gramocio are using exactly the same methodology which long back Dukheim used for studying suicide. Here in place of suicide, they are studying homicide and in place of variables like marriage or religion or change in income, they have their own variables. Now, one of the interesting findings of this is that homicide rates increase with female education. Normally, we will think that with education and development, more awareness, more legal consciousness, humanitarianism, modernization, westernization, homicide rates would come down. Now, it was found that with improvement in literacy and education among males, homicide rate comes down, but with improvement in education among women, homicide rate goes up. It was an unexpected finding and sociologists then were required to explain. They have their own reasons and then they pose it a number of factors that explain this unexpected relationship, but this has opened a new area of research in which sociologists can now work and explain why is it that you find a negative relationship between decline in homicide rates and women's education. Another very interesting research in which modeling has been used is the research by bone guards. This was also published in population and development review. The theme of this research was like this, that it has been a matter of great interest to establish how much gain in life expectancy is ever possible. There is lot of debate on this. There was a time and not in distant past only 100 years ago, when life expectancy was as low as 20 years. Today, life expectancy in some of the developed countries at least for females has reached the level 82 years. In our country also life expectancy has gone to 64. Then, demographers, epidemiologists, medical experts, biologists, they are asking the question how much more gain in life expectancy is possible. Some people think that 82 we have already reached. Perhaps, we are close to maximum life expectancy we can have or may be some people will say that it can be further extended to 84. Some believe that it is possible to go up to 100, but it is all a matter of belief. Bone guard for the first time using modeling gave us a method by which we can really argue based on hard facts whether it is possible to have further gains in life expectancy. What bone guards did they projected that in the future longevity improvements will be larger and population aging will be more rapid than many governments of high income countries expect. Aging has already become a problem for governments in high income countries. Bone guards is very optimistic that there will be more gains in life expectancy or longevity in developed countries in the future, but the negative aspect dark side of that is that there is going to be aging at much higher pace than if longevity is going to rise to 90 or 95. How can we say this to demonstrate this point it decompose life expectancy as defined by him the conventional life expectancy at any time equals senescent life expectancy minus the longevity reducing effects of background and juvenile mortality. Life expectancy j juvenile is the life expectancy without juvenile mortality which means mortality up to say age of 25. It equals the average age of death for a newborn if there is no chance of dying before 25. If you want to calculate juvenile life expectancy or life expectancy for India if there is no juvenile mortality then you have to find out what will be the life expectancy provided up to the age of 25 nobody dies means number of deaths up to the age of 25 is 0 chance of dying that means l 25 small l in the language of life table small l 25 is same as small l 0 or radix of life table or initial birth cohort. LES senescent is the life expectancy if some causes of death such as cardiovascular diseases cancer risk of which increase with age are removed background mortality by causes such as accidents violence infectious diseases is independent of age. Bone guards study changes in life expectancy life expectancy j juvenile means without juvenile mortality and life expectancy senescent b and j for 16 high income countries with records from 1850 to 2000. It is a very good thing that at least for the developed countries we have detailed data on causes of death rates age specific death rates and causes of death separately for males and females. So, it is possible for us to decompose life expectancy into several components like juvenile mortality background mortality or mortality due to specific causes. Now, you need if you do not have a background of mathematics or algebra you should not be frightened by these alpha and beta, but if you have the background it is good you can follow it better the what I am trying to say that if in order to estimate what will happen to life expectancy if certain causes of death are removed we can form a function mu at age a which is called force of mortality mathematical modeling of life table functions. This force of mortality at a is expressed in the form this equation alpha e raised power beta a divided by 1 plus alpha e raised to power beta a plus gamma you can see it is a kind of logistic function. In the above equation beta measure the rate of increase in mortality with age and gamma measures the background mortality. So, it is possible to decompose mortality for age is above 25 then he expressed life expectancy senescent at is at time t like this 25 plus integral 25 to infinity and to consider the effect of specific factors such as prevention of his ultimately his interest lied in studying the smoking smoking as the cause of mortality. He was able to compute that if smoking habits are controlled how much will be the gain in life expectancy in the future. So, he was able to say on the basis of detailed data available on causes of death separately for males and females for developed countries in the world that we have not reached the plateau it is still possible to raise life expectancy further and that means government should be worried about the problem of aging which is going to be much more in the future. And he was able to show that if percentage smoking is reduced by a certain percentage what will be its gain in terms of life expectancy and that he was able to do by decomposing life expectancy into two or three components. So, that effects of juvenile mortality and background factors accidents cancer and those factors which make people belonging to higher age groups more have more risk of dying those factors are explicitly taken into consideration. Another field of modeling in sociology is in the recent past we find that models based on advanced statistical techniques have become more popular than mathematical model yesterday I was saying that in the field of population studies there is more of mathematical modeling than statistical. Nowadays there in sociology at least statistical modeling is coming up and Poisson regression, logit regression and multiple classification analysis are increasingly used by social scientist. In one survey of literature in sociology somebody said that there is a great shift in sociology while sociology some 25, 30 years ago use more of multiple regression analysis today they use Poisson regression or logit regression. The advantage of logit regression is that it can take care of qualitative variables also. Now, what are the stages in modeling I thought that at the end I must tell you about what are the various steps in modeling more systematically. So, first part of modeling is specification of model then estimation of parameters then validation and forecasting specification means it is a process of expressing relationships between dependent and independent variables in the form of mathematical. So, we specify a model then estimate parameter there are various techniques of estimation of parameters least square maximum likelihood method of moments those who will do mathematical modeling will read more on this matter and they will know all these techniques. Then there is validation once you have known the parameters you would like to see whether your model is ok or not. So, you predict the values of dependent variable on the basis of data for independent variables and see whether estimated actual values empirical values are close to each other this is done with the help of capital R square then if capital R square is good and your model is fitted then you can use the model for forecasting. Obviously, modeling has certain limitations the first and foremost is the limitation caused by lack of perfect measurements not everything can be measured this problem is a general problem of mathematical modeling in social sciences and is not unique to population studies. Regression models for different measures of fertility may provide very different results if your dependent variable is total fertility rate you have one result if your dependent variable is crude birth rate you may have another result. So, that is another problem then when the validation of the model is made on the basis of past data the huge length of historical period may also influence the results and a serious limitation of modeling in population studies that statistical data are not available on measures of socio economic changes used by sophisticated socio economic theory. Socio economic theories are going in one direction mathematical modeling is going in another direction and in socio economic theories sometime sociologists are using terms like mobility strategies opportunity cost of time spent with children non familial mode of production and so on and it is not an easy job to develop measurements of what sociological concepts are being developed to explain different things. So, at the end I can say that modeling in population studies has helped in answering questions which could not be answered due to lack of data or lack of possibility of observations and experimentation yet the models have certain limitations. The prediction based on models depend on various factors including state of art understanding in the field nature of models employed and accuracy of data. Modeling is a growing field of research and more and more advanced models have been developed in different branches of population to take care of advanced understanding of the subject and to benefit from richer data available from diverse sources. This is what I would like to say on the issue of modeling. Now I would like some of you to ask some questions. I know that some of this material could have been very heavy for you if you do not have the background of mathematics, but this at least tells you that there is an interesting and independent branch of population studies in which there is scope for mathematicians, statisticians, economists to develop predictive purposes or for policy experimentation. Yes, thank you. Yes sir, I have a question that you have talked about one thing, two questions. Number one is to talk something about that there is a use of modeling for simulation of world system. So, who just clarifies to what is that? And the second question is when we from your discussion what I was trying to study some of the models that you have put up like Dodaro's model and GIF Zip's model. Now I think that it uses a lot of criteria like unemployment or poverty or level of education which are seemingly secular variables. Now in a situation like India and all developing countries where I think that the predominance or the sway that non-secular variables like say communal riots or language problems would have on migration flows for example, do you I am just skeptic as to how far can we actually replicate modeling of population distribution which is wide based secular exercise in developed countries in Indian society or whether there are models which also can capture these developments. Thank you very much. Your first question is about simulating world system. This simulation in sociological language also we talk of relationship between human population, environment or destructive effects of population growth. In simulating long ago in limits to growth a group argued that it is not possible to sustain the present processes of development for various reasons. Now to say so they have to have a model in terms of which relationship between population growth, economic development, consumption, rising aspirations, changes in agriculture, industry, urbanization, density of population, transport, communication, congestion and all kinds of environmental impacts on nature and human society can be studied. So, in simulation model what is done we try to first represent all the relationships between all possible variables. That means first we make a list of all the relevant variables then we make a number of equations showing all possible relationships between these variables. Now in such systems you do not have one dependent and a number of independent variables it is not multiple regression analysis actually you go for similar there are lots of simulation languages available it is a if may be somewhere some of you may have seen solving simultaneous equation model. It is a kind of problem of solving simultaneous equation model in which you work at several variables simultaneously and simulation languages, simulation computer simulation packages can be used to simulate what will happen to the whole system means somewhere something increases say population growth increase, population growth rate increases how does it impact literacy, how does it impact industrialization, how does it impact agriculture, intensive, extensive agriculture, government policy all the variables that you can think of a between which you can build relationships which can be measured and between which algebraic equations can be developed that is simulating the word system model. But the second point is very interesting and quite challenging for social scientists can we incorporate qualitative variables, political variables, religious variables we know that in our country now in the field of internal migration identity is going to play a major factor, demand of sun of soil kind or rising linguistic consciousness and its effect on political decisions, government decisions, civil society decisions or repulsiveness or attractiveness of different factors is with which migrants from eastern UP districts could go to Bombay 20 years ago is no more there and in eastern UP villages people know that if you go to Bombay you can find employment wage rates are higher. But you will also face resistance from local workers from Maharashtra MNS and all these political divisions may put lot of resistance that is why in one study R C S Bose said that in case of India there is apart from push and pull factor there is also push back factors. So, many of these people may be push back from Bombay to their native place and they are aware of this now how to incorporate this factor in model broadly we can say that identity development of identities or linguistic consciousness or political consciousness of this type sun of soil demand will affect migration process. So, in the model for M I J somewhere on the right hand side some variable showing these cultural, political, linguistic identities must also appear. A model builder is more concerned with how to measure those things if you can measure these things in terms of acceptable variables then they can be incorporated and then the second question would be where will they appear in what algebraic form that is not such a big the most difficult question is how to operationalize some of these cultural, religious and political variable as long as you cannot find good operationalizations of these variables you cannot have them in models. But if you can somehow operationalize these sociolinguistic or political and religious factors and put them somewhere on the right hand side of the equation for M I J it is possible to incorporate them in migration model. It will be a fascinating area of research and if you if you can do so even simple addition to GIFS model by using these link not that linguistic or political things have not been incorporated in these model. But in case of India where these problems have a new complexion and which are going to affect our policies regarding migration and which are going to affect unity and integrity of the country. It will be a very good contribution if some some as if somehow you can operationalize some of these variables and include them in the migration model. Another interest which we found in your presentation was you cited somebody study which showed the linkages between seemingly non-related things like homicide and female education that reminded me of Durkheim study on suicide where he links up seemingly unrelated variables with the phenomena of suicide. Now what I am asking is don't we think that at times so suppose someone waywardly brings out such a correlations between seemingly wayward variables which do not should not have relation but suppose we are able to actually plot a regression or a correlation among such variables but they actually do not exist in real. So can't it be such that modeling of this sort can be misleading? I mean if I make my question clear. Yes your question is very clear and that takes our attention to the issue of pseudo correlations. Not all empirical correlations are real correlations you know to give you an example of how sometime behind unexpected correlation there may be a reason. Let me give an example of unexpected correlations having a reason we know that in economics according to economic theory the relationship between income and fertility should be positive. Those who have more income as they can buy more of all kinds of thing they can also buy more of children or they can afford to have more children but empirical relationship between fertility and children is negative. So how to reconcile this logic say that rich people should have more children and empirical relationship show that rich people has have less number of children. But here we have a plausible explanation and that is that apart from quantity of children parents also consider quality of children. So there is a trade off between quantity and quality and in place of producing large number of children of poor quality they want to produce a small number of children of high quality. So there is an explanation but you can also cite lots of examples of empirical correlations which are not valid for those types of correlations we have a term pseudo correlation. So that means in research important conclusions or inferences of research will be based not only on empirical findings but on the combination of theory and empirical findings. If empirical findings go against your theory they make you rethink about the theory perhaps there is a need to modify your theory somewhere if you think or other researches or other observations in other settings show that no theory so good so strong that it has worked in most situations it is only with respect to your data your research data that theory is not working then maybe you have to check your data. So there may be pseudo correlation or they or sometimes correlations which mean nothing may arise because of some fault in the data. So we have to be careful and we have to make a balance use of both theory that is why review of literature is an essential and the most important part of research. Otherwise though anybody will conduct a survey collect some data come up with empirical findings all survey researches and all empirical findings will not contribute to knowledge in the field. It is a balance between hypothesis developed on the basis of review of literature review of good literature not just literature review of good literature in diverse settings and empirical results. Thank you.