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Given a vast concern about high income inequality in Thailand as opposed to empirical findings around the world showing people's preference for fair income inequality over unfair income equality, it is therefore important to examine whether inequality in income distribution in Thailand over the past three decades is fair, and what fair inequality in income distribution in Thailand should be. To quantitatively measure fair income distribution, this study employs the fairness benchmarks that are derived from the distributions of athletes' salaries in professional sports which satisfy the concepts of distributive justice and procedural justice, the no-envy principle of fair allocation, and the general consensus or the international norm criterion of a meaningful benchmark. By using the data on quintile income shares and the income Gini index of Thailand from the National Social and Economic Development Council, this study finds that, throughout the period from 1988 to 2021, the Thai income earners in the bottom 20%, the second 20%, and the top 20% receive income shares more than the fair shares whereas those in the third 20% and the fourth 20% receive income shares less than the fair shares. Provided that there are infinite combinations of quintile income shares that can have the same value of income Gini index but only one of them is regarded as fair, this study demonstrates the use of fairness benchmarks as a practical guideline for designing policies with an aim to achieve fair income distribution in Thailand. Moreover, a comparative analysis is conducted by employing the method for estimating optimal (fair) income distribution representing feasible income equality in order to provide an alternative recommendation on what optimal (fair) income distribution characterizing feasible income equality in Thailand should be., Comment: 20 pages, 6 figures, 3 tables

Forecasts for key macroeconomic variables are almost always made simultaneously by the same organizations, presented together, and used together in policy analyses and decision-makings. It is therefore important to know whether the forecasters are skillful enough to forecast the future values of those variables. Here a method for joint evaluation of skill in directional forecasts of multiple variables is introduced. The method is simple to use and does not rely on complicated assumptions required by the conventional statistical methods for measuring accuracy of directional forecast. The data on GDP growth and inflation forecasts of three organizations from Thailand, namely, the Bank of Thailand, the Fiscal Policy Office, and the Office of the National Economic and Social Development Council as well as the actual data on GDP growth and inflation of Thailand between 2001 and 2021 are employed in order to demonstrate how the method could be used to evaluate the skills of forecasters in practice. The overall results indicate that these three organizations are somewhat skillful in forecasting the direction-of-changes of GDP growth and inflation when no band and a band of +/- 1 standard deviation of the forecasted outcome are considered. However, when a band of +/- 0.5% of the forecasted outcome is introduced, the skills in forecasting the direction-of-changes of GDP growth and inflation of these three organizations are, at best, little better than intelligent guess work., Comment: 10 pages, 8 tables

This study examines whether income distribution in Thailand has a property of scale invariance or self-similarity across years. By using the data on income shares by quintile and by decile of Thailand from 1988 to 2021, the results from 306-pairwise Kolmogorov-Smirnov tests indicate that income distribution in Thailand is statistically scale-invariant or self-similar across years with p-values ranging between 0.988 and 1.000. Based on these empirical findings, this study would like to propose that, in order to change income distribution in Thailand whose pattern had persisted for over three decades, the change itself cannot be gradual but has to be like a phase transition of substance in physics., Comment: 9 pages, 2 figures, 3 tables

Given that the existing parametric functional forms for the Lorenz curve do not fit all possible size distributions, a universal parametric functional form is introduced. By using the empirical data from different scientific disciplines and also the hypothetical data, this study shows that, the proposed model fits not only the data whose actual Lorenz plots have a typical convex segment but also the data whose actual Lorenz plots have both horizontal and convex segments practically well. It also perfectly fits the data whose observation is larger in size while the rest of observations are smaller and equal in size as characterized by 2 positive-slope linear segments. In addition, the proposed model has a closed-form expression for the Gini index, making it computationally convenient to calculate. Considering that the Lorenz curve and the Gini index are widely used in various disciplines of sciences, the proposed model and the closed-form expression for the Gini index could be used as alternative tools to analyze size distributions of non-negative quantities and examine their inequalities or unevennesses., Comment: 10 pages, 3 figures, 6 tables

A good prediction is very important for scientific, economic, and administrative purposes. It is therefore necessary to know whether a predictor is skillful enough to predict the future. Given the increased reliance on predictions in various disciplines, prediction skill index (PSI) is devised. Twenty-four numerical examples are used to demonstrate how the PSI method works. The results show that the PSI awards not only the same score for random prediction and always predicting the same value but also nontrivial scores for correct prediction of rare or extreme events. Moreover, the PSI can distinguish the difference between the perfect forecast of rare or extreme events and that of random events by awarding different skill scores while other conventional methods cannot and award the same score. The data on growth of real gross domestic product forecast of the Bank of Thailand between 2000 and 2019 are also used to demonstrate how the PSI evaluates skill of the forecaster in practice., Comment: 22 pages, 1 figure, 8 tables

Concern about income inequality has become prominent in public discourse around the world. However, studies in behavioral economics and psychology have consistently shown that people prefer not equal but fair income distributions. Thus, finding a benchmark that could be used to measure fair income distribution across countries is a theoretical and practical challenge. Here a method for benchmarking fair income distribution is introduced. The benchmark is constructed based on the concepts of procedural justice, distributive justice, and authority's power in professional sports where it is widely agreed as an international norm that the allocations of athlete's salary are outcomes of fair rules, individual and/or team performance, and luck in line with no-envy principle of fair allocation. Using the World Bank data, this study demonstrates how the benchmark could be used to quantitatively gauge whether, for a given value of the Gini index, the income shares by quintile of a country are the fair shares or not, and if not, what fair income shares by quintile of that country should be. Knowing this could be useful for those involved in setting targets for the Gini index and the fair income shares that are appropriate for the context of each country before formulating policies toward achieving the Sustainable Development Goal 10 and other SDGs., Comment: version 1, 56 pages, 7 figures, 6 tables

The pursuit of having an appropriate level of income inequality should be viewed as one of the biggest challenges facing academic scholars as well as policy makers. Unfortunately, research on this issue is currently lacking. This study is the first to introduce the theoretical concept of targeted level of income inequality for a given size of population. By employing the World Bank's data on population size and Gini coefficient from sixty-nine countries in 2012, this study finds that the relationship between Gini coefficient and natural logarithm of population size is nonlinear in the form of a second-degree polynomial function. The estimated results using regression analysis show that the majority of countries in the sample have Gini coefficients either too high or too low compared to their appropriate values. These findings could be used as a guideline for policy makers before designing and implementing public policies in order to achieve the targeted level of income inequality., Comment: 2 tables, 3 figures

This paper discusses serious drawbacks of existing knowledge in macroeconomics and finance in explaining and predicting economic and financial phenomena. Complexity science is proposed as an alternative approach to be used in order to better understand how economy and financial market work. This paper argues that understanding characteristics of complex system could greatly benefit financial analysts, financial regulators, as well as macroeconomic policy makers., Comment: 37 pages

Given many popular functional forms for the Lorenz curve do not have a closed-form expression for the Gini index and no study has utilized the observed Gini index to estimate parameter(s) associated with the corresponding parametric functional form, a simple method for estimating the Lorenz curve is introduced. It utilizes 3 indicators, namely, the Gini index and the income shares of the bottom and the top in order to calculate the values of parameters associated with the specified functional form which has a closed-form expression for the Gini index. No error minimization technique is required in order to estimate the Lorenz curve. The data on the Gini index and the income shares of 4 countries that have different level of income inequality, economic, sociological, and regional backgrounds from the United Nations University-World Income Inequality Database are used to illustrate how the simple method works. The overall results indicate that the estimated Lorenz curves fit the actual observations practically well. This simple method could be useful in the situation where the availability of data on income distribution is low. However, if more data on income distribution are available, this study shows that the specified functional form could be used to directly estimate the Lorenz curve. Moreover, the estimated values of the Gini index calculated based on the specified functional form are virtually identical to their actual observations., Comment: 9 pages, 10 tables, 1 figure

To simultaneously overcome the limitation of the Gini index in that it is less sensitive to inequality at the tails of income distribution and the limitation of the inter-decile ratios that ignore inequality in the middle of income distribution, an inequality index is introduced. It comprises three indicators, namely, the Gini index, the income share held by the top 10%, and the income share held by the bottom 10%. The data from the World Bank database and the Organization for Economic Co-operation and Development Income Distribution Database between 2005 and 2015 are used to demonstrate how the inequality index works. The results show that it can distinguish income inequality among countries that share the same Gini index but have different income gaps between the top 10% and the bottom 10%. It could also distinguish income inequality among countries that have the same ratio of income share held by the top 10% to income share held by the bottom 10% but differ in the values of the Gini index. In addition, the inequality index could capture the dynamics where the Gini index of a country is stable over time but the ratio of income share of the top 10% to income share of the bottom 10% is increasing. Furthermore, the inequality index could be applied to other scientific disciplines as a measure of statistical heterogeneity and for size distributions of any non-negative quantities., Comment: 9 pages, 2 tables, 7 figures