inequality

Introduction: A quiz

What causes inequality? Let’s start our inquiry with a quiz:

The first impression would be, given that both the initial endowment and the opportunity of obtaining the new income are perfectly equal, the final distribution must resemble the initial (uniform) distribution with no substantial inequality. However, computer simulation shows that the final distribution is asymptotically normal (see the graph below).

So, the correct answer to the quiz is (B). It is somewhat astounding that inequality exists even if there is absolute equality in the initial endowment and interim opportunity. We call this inequality as the natural rate of inequality given that the inequality is generated when everything is equal. More interestingly, if you are more or less convinced by this simple "thought experiment" that there is a natural rate of inequality, then this approach surely has a potential to answer other causality-type of questions related to inequality and mobility, where empirical data are limited. 

Research Questions

Wealth inequality has increased in major economies over the last decades. Specifically, the wealth Gini and the top 10% wealth share in the US reached record levels, remarkably higher than its G7 peers, especially during the COVID-19 pandemic. Meanwhile, inequality in China had worsened dramatically. There is a huge literature on the effect of inequality on welfare, trust, and growth and therefore on the optimal inequality. Instead, this paper focuses on the upstream of the issue—what are the factors that cause wealth inequality? 

Wealth inequality is inextricably intertwined with social mobility in public choices. Inequality takes a static snapshot of the distribution of wealth at a point in time, and social mobility describes the dynamic evolution of the distribution. Arguably and ideally, a social system with high concentration of wealth (“inequality of outcome”) can only be economically efficient and politically acceptable if the social mobility (“equality of opportunity”) is high. However, empirical evidence suggests a negative correlation between wealth inequality and inter-generational social mobility (known as the “Great Gatsby curve”), which seems to negate the Utopian hope. To resolve this disjunction, we attempt to simultaneously address a closely related question—what are the factors that cause social mobility?

METHODOLOGY

Unfortunately, data on social mobility are extremely scanty and most empirical studies are on inter- rather than intra-generational mobility. Only a few longitudinal surveys are available for a specific period and a specific country. In fact, data availability on wealth inequality is not much better due to the lack of observations on the richest. Any inductive reasoning is ultimately restricted by observable evidence, but can we say anything about the factors that affect wealth inequality and social mobility without a complete dataset of empirical observations? In other words, can we discuss causality when data-demanding econometrics is not feasible? We propose simulation-based thought experiments or Agent-Based Models (ABMs) to provide some novel insights into causality-type questions in a deductive reasoning tradition. This new approach allows us to establish the causalities and evaluate the relative importance of the factors based on controlled thought experiments.

In economics, most theoretical models are developed in the neoclassical tradition and most empirical models are assessed by econometric regressions, ignoring that there may well be other conceptual tools at hand. We have learned many things from physics, such as comparative statics, statistical modelling, and even controlled experiment. However, thought experiments (e.g., “chasing a beam of light” in Einstein’s theory of relativity and “Schrodinger’s cat” in quantum mechanics) seem less appealing to contemporary economics. Economists are usually optimistic about finding a succinct but comprehensive story (the model) to match the reality (the data or stylized facts). There are good reasons for this Posi-tivistic stance, but the original purposes of many economic studies may not be so ambitious. We may just want to answer simple causality questions such as “whether X (e.g., growth) affects Y (e.g., inequality) ceteris paribus”, so sometimes deductive rather than inductive reasoning is enough to serve the purpose. In this case, data-fitting econometric models are a sledgehammer to crack a nut—yet they still often fail thanks to omitted variables, measure-ment errors and model misspecifications that stand between the model and the data. If we can, for now, downplay the ambition of data-fitting induction and divert the purpose to question-answering deduction, it will open the door for new methodological possibilities.

Thought experiment is one choice. In fact, suppositional reasoning with the help of thought experiments has been widely used in philosophy (e.g., “the pleasure machine” by Robert Nozick), political science (e.g., “the veil of ignorance” by John Rawls) and early economists (e.g., “the five pounds miracle” by David Hume). Like controlled experiments in behavioral economics, carefully designed thought experiments can avoid complications in the data, so we can focus on the key causality. Nowadays, deductive reasoning in thought experiments can be harnessed by computational simulations—the ABMs. 

The essence of ABMs is to build a bottom-up model based on individual-level microdata evidence. The agents’ be-havior is dependent on each other’s and the local environment, making it a complex system with sophisticated interactions, dynamics, nonlinearities and heterogeneities. Macroscopic patterns “emerge” out of the interactions and dynamics at the microscopic level. In other words, the aggregate is not equal to the sum—a fundamental divergence from the representative agent paradigm where interactions are basically assumed away. However, an observed macroscopic measure of the system (e.g., Gini coefficient or Shorrocks index) can correspond to a myriad of possible microscopic states (e.g., different decision rules and interaction rules of the agents). The level of our ignorance on the mi-crostates for a given macrostate is usually measured by Shannon information entropy. In practice, we can pin down most of the model uncertainties by calibrations using microeco-nomic evidence. This is a more realistic “micro-foundation” than the theoretical micro-foundation (i.e., optimization of representative agents) adopted in New Classical and New Keynesian models. Any left-over uncertainties in the microstates of the model can then be estimated by minimizing the gap between the observed and the simulated macrostates.

Results

We design some simple thought experiments to evaluate the contributions of the four literature-backed factors to wealth inequality. It is found that, ceteris paribus, (a) an income tax reduces inequality, (b) a higher growth reduces inequality, (c) a higher dispersion of human capital raises inequality, and (d) capital ownership raises inequality.

In addition, we can quantify the effects of various factors on wealth inequality and social mobility in the following table. It is shown that ownership of physical capital is the most powerful contributor of inequality and immobility. No wonder Karl Marx criticised the raw form of Capitalism and doomed it to collapse.

In our paper, we also develop an empirical ABM with rich realistic features, which can quantitatively capture empirical stylised facts of the G7 countries and China (G7+C). Based on the estimated ABM, we can then simulate many interesting data which are not observable in reality. Among others, we can simulate an important social mobility measure, the Shorrocks Index (SI). With the measures of inequality (Gini coefficient) and mobility (Shorrocks Index), we can then plot the intra-generational Great Gatsby Curve for the first time (see the figure below).

Conclusion

Here is a take-home summary of our findings on inequality and mobility, based on the novel method of thought experiment:

Based on our deductive and inductive results, we have implied the following two policies to promote equality and mobility:

Please read our published paper in the Journal of Economic Behavior & Organization. Data, codes, and supplementary materials can be found on the journal website.