Modeling Immigration in Spain: Causes, Size and Consequences
Round 1
Reviewer 1 Report
Although I believe that this paper has a very good potential, I am rather sceptical about the manuscript in its present form, for the following reasons:
- In section 2, the authors attempt to approximate the available data by a nonlinear function. They show that, with an appropriate choice of parameters, the approximation works quite well. However, my concern here is that their nonlinear function has not only has a quite specific pre-defined structure (as in Eq.3) but also have many parameters. Surely, it is not surprising that one can approximate 22 data points by a specially chosen function with five free parameters. Thus, I don't see much value in this result - but tell me if I am wrong.
- Section 3 (where the model is introduced and some simulations are done) seems to be quite detached from Section 2 that deals with the data. This is not good.
- The conclusions section is far too short! In a well-written paper, this should be the main section. to explain what are the important findings (if any), how the authors addressed their specific research question, and what it the particular take-home message. A section as short as this, sadly, gives an idea that the authors are not themselves sure what to do with their own results... Please improve.
Author Response
Attending the suggestion 2, we have included the entire old Section 3 as a subsection 2.3 of the new Section 2. Attending comment 3, we have extended the conclusion section.
The first question by referee #1 is sound if one deals with an abstract case where we have not additional information. The problem is not like she/he states: having data 22 points to approximate by a nonlinear function. This is not the case, but we know the way as the data arrive and the reasons why the data arrive. The matter is not how to approximate a function with 22 data points, ignoring how the data arrive.
Reviewer 2 Report
A problem of immigration in Spain are investigated in this paper. The discrete mathematical model for dynamics of immigration processes is constructed on base of data from 1999 to 2020 years. The special sub populations of irregular immigrants, unaccompanied minor immigrants, and regular immigrants are studied. The dynamics of groups of unaccompanied minor immigrants is investigated in detail. The results of this paper are interest as an information.
Major remarks
The content of this manuscript corresponds better to a Journal of Demography for example.
There are simple mathematical methods in this paper. The mathematical investigation is absent.
What is a meaning of formulas (3), (6)? These formulas haven’t a new information.
Minor remarks
Line 3 – Article: Probable, this is “an irregular”.
Line 5 – What is “emisor”? This term is not clear.
Line 113 – Typo: The function L(n) must be here instead function R(n). The function R(n) is absent in other places.
After Line 147 - Figure 2 is surplus. Fig 3 is enough for this text.
Author Response
We have corrected all the minor remarks.
With respect to the major remarks, the first suggestion of referee #2 about the convenience of submission to a Journal of Demography, apart from the fact that the paper fills in the scope of the special issue, and referee #4 explicitly comment this fact, let us respect the freedom to the authors where they wish submit the paper.
With respect to comment 2, the referee is not aware that the paper deals with mathematical modelling, not general mathematics. This means that the challenge is the transformation of the real problem of immigration in mathematical terms. The research is not the investigation of a new mathematical problem.
With respect to the third query, formula (3) provides the proposed parametric function f(x) to fit the irregular immigration flow data where x denotes the time variable in years from 1999 until 2020. Formula (6) provides the extended matching function F(x) where the time variable includes now the period 2021-2025. The values of F(x) are used in the model (13)-(16) for valuation of the incoming irregular immigration B(n). This fact is now included in page 7, line 185 for the sake of clarity.
Reviewer 3 Report
Report: Modeling inmigration in Spain
This paper deals with the construction of a mathematical model to quantify the expected size of the immigrant population in Spain, both regular, and regular, taking into account economic, political and regulatory factors. The immigrant population is split in three subpopulations unaccompanied minors immigrants, irregular and regular immigrants. The model is discrete, described by a linear system of difference equations, the period of transit is six monthly, and taking into account the factors and historic data for each subpopulation, the change per semester of each subpopulation is analyzed, achieving a system of difference equations. Since some coefficients are difficult to estimate, the sensibility of the model under the change of these parameters is also treated. The period of study is short (decided by the authors) in order to make realistic the hypotheses, mainly the economic ones linked the regular immigration, linked to the unemployment rate. The computation of the expected size of each subpopulation allows the estimation of the budget of the Spanish Ministry of Inclusion, Social Security and Migration for the years of the study. The model is potentially exportable to other regions or countries by adapting the particular issues and characteristics of the country.
By the importance of the results, in my opinion, this paper should be accepted for publication.
Author Response
We thank the referee's comments.
Reviewer 4 Report
Report on the paper "Modeling immigration in Spain: Causes, Size and Consequences" by Sheila Torres, Rafael Company, Lucas Jódar
1. The aim of this paper is to estimate the expected size of the immigration population in a finite short period of time in Spain. First, the incoming irregular immigration behavior is described by a matching function. Moreover, the linear correspondence between ‘unemployment rate’ and ‘net legal migration balance” is established, and, consequently, a prevision of incoming irregular immigration is obtained. Then, splitting the population in three interest subpopulations, a discrete dynamic population model is proposed. The same type of model was used in other papers (see, e.g., [23] De la Poza, Elena, Lucas Jódar, and Lucía Ramírez. "Modelling bullying propagation in Spain: a quantitative and qualitative approach." Quality & Quantity 52.4 (2018): 1627-1642). Using the behavior of each subpopulation from the past, the coefficients of the model are deduced. Some numerical simulations are performed.
2. a) The manuscript’s strengths. The paper is well written and fits to Special Issue “Mathematical Models and Methods in Engineering and Social Sciences”.
In fact, the paper deals to a linear mathematical model in Sociology; and this is one of the aims of this Special Issue.
Overall Recommendation: Accept in present form.
Author Response
We thank the referee's comments.
Round 2
Reviewer 1 Report
The authors have made reasonable changes to address my concerns, I believe that the paper is ready for publication now.
Reviewer 2 Report
The text hasn't any significant corrections.
