Simulation Analysis of Universal and Selective Welfare

Simulation, Sociology

Date: 2023.06.13 ~ 2023.06.22

Writer: 9tailwolf

Caution:

  • Every codes and images are made by 9tailwolf. For personal use only.
  • Every datas are made by Matplotlib in Python.
  • This simulation will not be precised. You should pay attention to amount of change.


Summary

  1. I analyzed universal welfare and selective welfare in terms of inequality improvement.
  2. The smaller the amount of welfare, the higher the inequality, the closer the application percentage was to 100%, and the larger the selective cost, the more effective the universal welfare was.
  3. It is important to choosing welfare policy by the situation.


Introduction

After COVID-19 pandemic, controversy of welfare became hot topic. Jaemyung Lee(DP leader, Korea 20th presidential candidate) consist that policy about universal basic income since 2017, and the Basic Income Party, which aims to realize basic income, was also created. However, this debate continues in Korea.

In this page, I simulated with selective welfare and universal welfare with some coefficients to analyze. One thing to note I am not claiming anything based on this simulation.


Model Setting

Income Model is consist of polynomial function \(y = bx^{a}, (a \geq 1)\) with [0,1] domain. \(x\) is percent of income class. \(y\) is cumulative sum of the income. By this way, I can set inequality environment and make Lorenz Curve1 to calculate Gini coefficient. Gini coefficient is indicator that evaluate inequality, 1 is the worst state(most inequality) and 0 is best state(equality).

Following is a application of Income Model with 0.4 gini coefficient.


Selective Welfare Model is consist of application percentage, selective cost, and cost. In this model, standard is determined by application percentage. And welfare is determined by a normal distribution probability according to the distance from the criterion. It is a selection error. And the cost is decreased by selective cost.

Universal Welfare Model is simple. It is consist of just cost. In this model, every people can get same cost.

And I try to test with selective welfare and universal welfare. Following is a result of test above models.


Analizing the above simulation, the improvement of inequality in selective welfare at the same cost is most effective in the lower class selection. In addition, as the application range is expanded, the improvement of gini coefficient effect is decreasing, and at some becomes less than that of universal welfare.


Crossing of Selective and Universal Welfare by amount of welfare

First, I simulated to find crossing with selective and universal welfare. It is to qualitatively analyze which policy is more effective according to welfare size. And the simulation follows below condition.

  • 1000 people with average income 1000
  • 0.4 Gini coefficient
  • 5 fixed selective cost

And below is a result of simulation.


Analyzing the qualitative results, the smaller the amount of welfare, the more favorable the universal welfare. However, this effect is not absolute because it simply represents a crossing. In other words, the smaller amount of welfare is effective at selection of small range or universal.


Comparison of Selective and Universal Welfare by Gini Coefficient

It is also important to find out which welfare applies to which income inequality. I simulated 9 different conditions to see difference. Conditions are combination with amount of welfare(10%, 5%, 3% of the average income) and application percentage (30%, 50%, 90%). Other conditions follow below.

  • 1000 people with average income 1000
  • 5 fixed selective cost

I briefly do a qualitative analysis.

Simulation of Selection (30%) and Universal Welfare(10%)



Since 10% of welfare amount is too large, selective welfare is effective at most case except a state of extreme equality.


Simulation of Selection (50%) and Universal Welfare(10%)



Since 10% of welfare amount is too large, selective welfare is effective at most case except a state of extreme equality and extreme inequlity.


Simulation of Selection (90%) and Universal Welfare(10%)



Since 10% of welfare amount is too large, selective welfare is effective at most case except a state of extreme equality. But the difference is smaller than other(30%, 50% of the application percentage) cases.


Simulation of Selection (30%) and Universal Welfare(5%)



It is simmilar as 30%-10% model case because 5% is large too.


Simulation of Selection (50%) and Universal Welfare(5%)



It is also simmilar as 50%-10% model case because 5% is large too.


Simulation of Selection (90%) and Universal Welfare(5%)



But in this case, universal welfare was more effective when the Gini coefficient was approximately 0.4 or higher.


Simulation of Selection (30%) and Universal Welfare(3%)



Clearly, it can be seen that the difference in welfare size reduces the effect of mitigating the Gini coefficient. In addition, it can be seen that the shape of the model also resembles the 50%-10% model.


Simulation of Selection (50%) and Universal Welfare(3%)



It is simmilar as 50%-10% model case.


Simulation of Selection (90%) and Universal Welfare(3%)



In all cases, universal welfare is effective. Because the selection cost was high relatively, screening welfare was inefficient.

Overall, universal welfare was effective in mitigating the Gini coefficient in unequal conditions, but selective welfare was effective in mitigating the Gini coefficient in moderate levels of inequality. But This case is amount to welfare on a grand scale. In the case of a small amount of welfare, universal welfare tended to become more effective.


Crossing of Selective and Universal Welfare by Application Percentage

I simulated to find crossing with selective and universal welfare. It is to qualitatively analyze which policy is more effective according to application percentage. This allows us to find out which welfare is effective at which gini coefficient. And the simulation follows below condition.

  • 1000 people with average income 1000
  • 5 fixed selective cost
  • 3% of the amount of welfare (I choose 3% because it is more easy to analyze.

And below is a result of simulation.


  • At lower class selection, it is effective in most situation. But it is close to support for lower class.
  • At 30% ~ 70%, the welfare effect according to each Gini coefficient was different. Similar to the previous simulation results, in the more equal case, selective welfare is effective, otherwise, universal welfare is effective.
  • At over 80%, universal welfare has always been advantageous.


Comparison of Selective and Universal Welfare by Selective Cost

Selective cost is important element to affect welfare. In fact, in Korea, the issue of child allowance screening costs has become a reason for universal application of child allowance2.

Below is a result of simulation of selective welfare and universal welfare by selective cost. And the simulation satisfy following condition.

  • 1000 people with average income 1000
  • 0.4 gini coefficient
  • 3% of the amount of welfare



Clearly, the high selective cost and close to 100% application percentage less efficient than universal welfare.

And I simulated the crossing according to the selective cost. The simulation satisfy following condition.

  • 1000 people with average income 1000
  • 0.4 gini coefficient
  • 5% of the amount of welfare



Also, it can be seen that the crossing according to the selective cost monotonically decreases according to the selective cost.


Result

I analyzed the efficiency of welfare according to amount of welfare, application percentage, state of equality, and selection cost. Comprehensively the smaller the amount of welfare, the higher the inequality, the closer the application percentage was to 100%, and the larger the selective cost, the more effective the universal welfare was.

It will be important for divide case of welfare policies. In cases where support is essential (elderly, disabled, unemployed, etc.), selective welfare will be required, and if not, universal welfare will have to be applied.

Also, welfare policies cannot be evaluated by improving equality. Welfare can be assessed by a variety of factors(regressive, financial, social consent, etc.). I do not and cannot claim what welfare is necessary on the basis of my research.


Extra: Korea Fifth Round of Relief Analize

Korea fifth round of relief is a s an argument for universal welfare selective welfare that was in 20213. I ran a simulation on this. The contents of Korea fifth round of relief is Support of 250,000 won(200$) each to the 88% of people. The simulation was satisfy following conditions.

  • 1000 people with average income 345 (Korea GNI per month is 3,450,000 won)
  • 0.331 gini coefficient (Gini Coefficient of Korea4)
  • 0.6% of the income (250,000 won per month is 0.6% of income)
  • 3% of the selective cost (Estimated selective cost)



As a result, At the same cost, it was found that universal welfare was more effective at an application percentage of 70% or higher.


Reference

1: Investopia
2: 한겨례 신문
3: 한겨례 신문
4: KOSIS