Backwards Retropolation of Unknown Migration and Exploitation of the - PDF document

Backwards Retropolation of Unknown Migration and Exploitation of the Lee-Carter Model to Modelling Migration Profile Ondrej Simpach 1 Abstract. During last two years, the European Union has experienced a significant immigration wave. Knowing the age-and-sex specific migration profile is important for social policy planning and decision making. European countries are classified as a “ transit ” and as a “target”. The methods of demographic projections address the issue of migration only rarely. Net migration balance is often determined by expert guesses and is used to correct the final form of the population development. There are currently not sufficient methods of the migration projections. Therefore, the aim of the contribution is to present the methodology of the projection of the age-and-sex specific net-migration profile on the case study of the Czech Republic and other Visegrad Four Countries (Slovakia, Poland, Hungary) (as the transit countries which the migration wave only passes through) in Middle Europe. The procedure is based on Lexis approach and stochastic modelling by Lee-Carter model. The principle of the method is based on the backward retropolation of the needed data and consequent application of the main component method. The projection horizon might vary depending on the available data. Results are largely universal and serve as the supplement to already used demographic models and expert guesses. Key words: immigration, Middle Europe, Visegrad Four Countries, Lexis diagram, Lee-Carter model, population projection JEL Classification: C22, C32, J11 1 Introduction Current immigration development to some countries of the European Union (EU) does not have the parallel in the history. Hence, the modelling and extrapolation is difficult. There are countries in Europe which in relation to migration wave serve as target and countries through which the migrants are passing. Regardless if it is a country of transit or of destination, analysis always encounters the problem of a solid database (Šimpach, Pechrová, 2016) . According to the Eurostat (2016) database it is clear, that many countries have started to consistently detect age-and-sex-specific numbers of immigrants only in year 2004. In the Visegrad Four Countries (Czech Republic, Slovakia, Poland, Hungary), which currently belong among the transit countries (i.e. immigrants assume that will only pass through the country to some western European country, where they have already their family or relatives) have been a good database gathered by the Eurostat since 2000. However, it is not sufficient to make quality analyses based on sophisticated quantitative methods. 1 University of Economics Prague, Faculty of Informatics and Statistics, Department of Statistics and probability. Winston Churchill sq. 4, 130 67 Prague, Czech Republic. Email: ondrej.simpach@vse.cz, tel.: +420 737 665 461. 1

Simpach, O. (2017). Backwards Retropolation of Unknown Migration and Exploitation of the Lee-Carter Model to Modelling Migration Profile. In: 28 th IUSSP International Population Conference , 29 th October – 4 th November 2017, Cape Town, South Africa, pp. 1 – 9. Demographic processes of mortality and fertility have one common denominator that currently allows the analysis of these processes and makes possible to perform their modelling. It is the existence of a quality database and of the statistics can be divided by the gender and age group that are crucial for modelling of any demographic process, including migration. Many statistical offices (including the Czech Statistical Office – CZSO) lacks a long-term database of the number of immigrants by gender and by age at time t ( I x,t = immigrants x -years old in time t ) and the number of emigrants by sex and age at time t ( E x,t = emigrants x -years old in time t ). These statistics began to be collected in the Czech Republic only after 2000, in Slovakia, Poland and Hungary after 2004. Until then, there were examined only aggregate numbers of immigrants and emigrants in a given year, specific maximally by the gender. This is not sufficient to use the approaches that are currently commonly applied on other demographic processes. Therefore, the aim of this contribution is to elaborate the methodology of the projection of the age-and-sex migration on the case study of the Czech Republic and other Visegrad Four Countries population. The method is based on stochastic modelling. 2 Literature and Motivation Demographic analyses and population projections are very important. “ On the basis of the data on the sex-and-age structure of the population it is possible to anticipate relatively well the long-term development and foresee the future requirements, for instance, in the fields of education, the health service, social services, etc.”, (Fiala, Langhamrová and Langhamrová, 2009). Similarly, Lassilla, Valkonen and Alho (2014) demonstrate “that, although demographic forecasts are uncertain, they contain enough information to be useful in forward-looking policy rules”. However, the models are typically made under the assumption that future demographic development is deterministic. Immigration crisis can represent serious distortions to the models. Also, the longer is the projection horizon, the less probable is that the assumptions of the models would hold (Hyndman, Shang, 2009). Therefore, the stochastic approach must be considered. Despite that it enables more precise projections of population, its assumptions might not hold in turbulent development of the reality. Migration is a very important demographic component and it cannot be ignored in models or cannot be considered as unchangeable in time (or at least not in case of the larger areas.) Currently the EU is contending with problems of immigration. The problem of possible datasets distortion should be discussed as many demographic models are not able to adequately explain the migration process. “Population migration involves the relocation of ind ividuals, households or moving groups between geographical locations” (Vitanov and Vitanov, 2016). Some of the population pressures might be relieved by immigration, but it must not be too high as “with growing disparities between the levels of material wealth in rich and poor countries, migration appears to be an attractive option for inhabitants of less developed count ries”, (Rowlands, 1999). The increased migration from countries affected by wars and poor economic situation has recently raise many concerns. Our contribution deals with immigration to European countries which are considered to be the transit for the immigrants from third countries. Particularly we examine the migration to Czech Republic, Slovakia, Poland and Hungary. 3 Methodology and Data One of the basic assumptions about the demographic processes is classical balance equation          M / F M / F M / F M / F M / F M / F S S B D I E , (1)  t t 1 t t t t (where M = males, F = females) that is sex-specific, but not age-specific. The difference in the number of live born and death is natural increase (decrease) of population while the difference 2

Simpach, O. (2017). Backwards Retropolation of Unknown Migration and Exploitation of the Lee-Carter Model to Modelling Migration Profile. In: 28 th IUSSP International Population Conference , 29 th October – 4 th November 2017, Cape Town, South Africa, pp. 1 – 9. in numbers of immigrants and emigrants is mechanical increase (decrease) of population, denoted as    M / F M / F M / F I E . (2) t t t Mechanical increase (decrease) of population has its interpretation as net migration balance, and the division of this balance by the average state of the population of particular sex in time t yields so-called net migration rate calculated as  M / F M / F I E     M / F M / F M / F t t i e . (3) t t t M / F S t ( S ͞ t is in this case the mid-state number of population in time t that is assumed to be at 1 st July of particular year). From above stated equations it is possible to define the cohort sex-specific form of balance equation as     M / F M / F M / F M / F . S S D (4)  x , t x , t 1 x , t x , t Using Lexis diagram (see Figure 1), Figure 1 Diagram for calculation of unknown number of net migrants by Lexis approach (Lexis, 1875). There is time on axis x and age on axis y . Marked area is divide d to 2 × 1/8 and 2 × 3/8 = 8/8. Source: own elaboration based on Lexis (1875) approach. knowing the initial, the middle and the final state of the demographic event and knowing completed ages, the Figure 1 is utilized where in the surface of the angles is 3 3 1 1     I , II , III and IV . (5) 8 8 8 8 Consequently, we express the new form of sex-specific cohort balance equation and include those angles from Lexis diagram as 3