Modeling Immigration

Modeling Immigration Similar to Thermal Systems Models

By Som Karamchetty

Modeling Concept:

     Immigration is usually discussed and described as the number of people moving to a country. But, immigration is much more than people moving. People bring or take with them a number of attributes. They carry wealth, education, knowledge and skill capabilities, innovative abilities, behaviors, and so on. Therefore, it is important to consider them in a mathematical model.

     In engineering, thermal systems are modeled in terms of mass and energy balance. Mass transfer is accounted for in mass balance or the law of conservation of mass. Energy transfer is accounted for in energy balance or the First Law of Thermodynamics. It may further be noted that energy comes in many forms and various forms of energy are considered as applicable to a situation.

     In the case of immigration, we may account for people in a balance similar to mass balance. Wealth transfer may be considered in a manner similar to energy balance. Like energy, wealth also comes in many forms as explained in the formulation of the model in the following sections.

     In thermodynamic systems, when energy transfer takes place from one form to another, the conversion may not take place at one hundred percent efficiency. This is explained in terms of the Second Law of Thermodynamics. In the case of wealth transfer from one form to another, certain conditions may prevent the one hundred percent conversion.

     Here is a suggested model of immigration patterned after the systems modeling approach normally used in thermal systems modeling. As in the case of the thermal systems models, we use a modeling approach that uses a system and surroundings.

Immigration Model:

     Following the thermal systems analogy, we take a country as the System and the rest of the world as Surroundings with immigrants and emigrants as shown in Figure 1.

Figure 1: System and Surroundings - with People Balance

   First, we apply a relationship similar to the law of conservation of mass or the mass balance. It is also called the mass flow equation in thermodynamic (or fluid flow) systems. In case of immigration, let us take into account the number of people in a country before and after a certain number of people enter as immigrants and another group of people leave as emigrants during a certain period.

    Suppose a country A has Nci number of citizens.  Now, if n_1, number of people immigrate from the rest of the world to country A, and if n₂, number of people emigrate from the country A to the rest of the world, country A will have N_cf number of citizens and residents, the following equation applies.

N_ci + n₁ - n₂  = N_cf     (1)

Where,

N_ci is the Number of Citizens or people in the country initially,

n₁ is the number of immigrants that entered the country,

n₂ is the number emigrants that left the country, and

N_cf is the number of citizens or people in the country finally.

    Suppose that the net wealth of each citizen (or resident) of country A is hi and the people immigrating (entering a country) have a net individual wealth of h1 and the people emigrating (leaving the country) A have a net individual wealth of h2, then the net wealth of each citizen of the country A changes to hf and the following equation applies to the wealth of the country.

N_{ci *} h_i + n_{1 *} h₁ - n_{2 *} h₂  = N_{cf *}  h_{f                            (2)}

This equation is similar to the Energy Equation or the Law of Conservation of Energy or the First Law of Thermodynamics.

     Country A may receive a certain amount of wealth from another country in the world or give some wealth away to other countries in the world without any people carrying that wealth.

     Suppose the country A receives an amount of wealth W_in from the rest of the world, and gives away an amount of wealth, equal to W_out, to the rest of the world, then the following equation applies. This is shown in Figure 2.

N_{ci *} h_i + n_{1 *} h₁ - n_{2 *} h₂ + W_in – W_out = N_{cf *}  h_{f                            (3)}

_{Equation (3) has units of wealth, dollars.}

Figure 2: Wealth Balance with Immigration and Emigration

    When people move across countries’ borders, they bring with them their capabilities like education, innovative capability, and so on. These capabilities are similar to chemical energy, catalytic capability, and so on in a material. In order to take these capabilities into consideration, we can apply various enhancements to this basic equation (3) showing wealth balance.

     Suppose the country A has an average individual education level e_i and the arriving immigrants have an average education level of e₁ and the emigrants have an average education level of e₂, then the average education level of country A changes to e_f and the following equation applies.

N_{ci *} e_i + n_{1 *} e₁ - n_{2 *} e₂ = N_{cf *}  e_{f                          (4)}

_{Equation (4) has units of education.}

     After immigrants arrive in the country A and a certain time lapses, they will use their educational qualifications to create wealth. It will be somewhat like a chemical reaction occurring and generating thermal or other energy. In that sense, education level will be like chemical energy in a material. Using such an analogy, we can use the wealth equivalent for education and write Equation 5, below.

N_{ci *} h_ei + n_{1 *} h_e1 - n_{2 *} h_e2 = N_{cf *} h_{ef                         (5)}

     By combining the Equations 3 and 5, we get the combined wealth and education balance shown in Equation 6.

N_{ci *} h_i + N_{ci *} h_ei + n_{1 *} h₁ + n_{1 *} h_e1 – n_{2 *} h₂ – n₂ * h_e2 + W_in – W_out  =

N_{cf *}   h_f   + N_{cf *} h_ef                      (6)

By substituting the following relationships,

h_e1 = K * e₁

h_e2= K * e₂

h_ei = K * e_i

h_ef = K * e_f , using k as a constant to convert the average education level to average wealth equivalent, into Equation (6), we get

N_{ci *} h_i + N_{ci *} K * e_i + n_{1 *} h₁ + n_{1 *} K * e₁ – n_{2 *} h₂ – n₂ * K * e₂ + W_in – W_out  = N_{cf *}   h_f   + N_{cf *} K * e_f                      (7)

     Some immigrants bring their capability to invent and innovate whether or not they possess wealth and education with them. Over time, their ability to innovate creates wealth. Let us say, I is the average innovative ability of a person.  Innovative ability is similar to catalysts. (Catalysts may not possess energy but can help release thermal energy from other materials.) But, in a country where there is wealth (to finance enterprises), educated people to create and manufacture products, innovators can convert their ability to innovate into wealth over time. Now, we can add this ability to innovate and rewrite the equation 7 as follows.

     I_i is the innovative ability of existing citizens in the country A, I₁ is the innovative ability of the immigrants, I₂ is the innovative ability of emigrants, and I_f is the innovative ability of the final citizens of country A.

     We use hI_i as the wealth equivalent of innovative ability of initial citizens, hI1 as the wealth equivalent of innovative ability of immigrating people, hI₂ as the wealth equivalent of innovative ability of emigrating people, and hI_f is the wealth equivalent of innovative ability of final citizens. We get

N_{ci *} h_i + N_{ci *} K * e_i + N_{ci *} hI_i + n_{1 *} h₁ + n_{1 *} K * e₁  + n_{1  *} hI₁    -  n_{2 *} h₂ – n₂ * K * e₂ - n_{2  *} hI₂     + W_in – W_out  = N_{cf *}   h_f   + N_{cf *} K * e_f    + N_{cf *} hI_f                 (8)

If q is a constant that denotes conversion of the ability to innovate in to wealth, we get  

hI₁  = q * I₁

hI₂  = q * I₂

hI_i  = q * I_i

hI_f  = q * I_f  , and substituting these equivalents into Equation 8, we get

N_{ci *} h_i + N_{ci *} K * e_i + N_{ci *} q * I_i + n_{1 *} h₁ + n_{1 *} K * e₁  + n_{1  *} q * I₁    -  n_{2 *} h₂ – n₂ * K * e₂ - n_{2  *} q * I₂    + W_in – W_out  

=   N_{cf *}   h_f   + N_{cf *} K * e_f    + N_{cf *} q * I_f                 (9)

     It may be noted that in the above equations, the average values for wealth of people, the education level, and the innovative ability are used. In order to get finer details, we can define the average values for each of these values for smaller segments and sum them up. Such modeling will follow the models used in multi-component, multiple types of energy systems in thermal modeling of chemical systems.

Conclusion:

     These simple equations allow us to calculate and quantify the merits and demerits of certain types of immigration to the wealth of a country. Such modeling and simulations would help countries as they develop immigration policies.

     If immigrants bring education level and/or wealth, and/or innovative ability greater than the average existing education level and/or wealth, and/or innovative ability in the country the country’s wealth increases over time.

     On the other hand, if immigrants bring education level and/or wealth, and/or innovative ability less than the average existing education level and/or wealth, and/or innovative ability in the country the country’s wealth decreases over time.

     More detailed analysis may show the linkage between the types of education and skills an immigrant brings to a country and helps in innovation using locally available resources.

     Adult immigrants that come with good education and skills gained in a low cost country would actually save educational costs as opposed to child immigrants as children normally do not have educational qualifications, or wealth, or innovative and catalytic abilities. However, children will contribute to future wealth as citizens and are likely to have little effect on the culture of the country A.

     Immigrants also consume products and services and thus create jobs and economic activity. It will be interesting to explore the effect of immigrants via the market on the creation of wealth in a country.

     Immigrants’ behavioral characteristics would also have a strong effect on the wealth of a country; it can be captured in the equations.

     The equations actually formulate simple relationships but by looking at them in this way, one can be inspired to develop the relationships and assist the decision makers.

     For example, such a model would provide an answer to a question, such as, ‘is it better to give money to a country rather than allowing its poor citizens and illiterate people to immigrate’ from the perspective of country A.

Tailpiece:

     Since I talked about the Thermodynamic system model in the analogy, one might be justified to ask if the Second Law of Thermodynamics can also be applied. The answer is a resounding ‘Yes.’ If a person with high educational and/or innovative ability is not allowed to excel, (by giving such a person a menial job as opposed to a deserving position), the inherent capability is not utilized by the country A.