Entrepreneurs, Chance, and the DCoW

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PLOS ONE: Entrepreneurs, Chance, and the Deterministic Concentration of Wealth

Abstract

In many economies, wealth is strikingly concentrated. Entrepreneurs–individuals with ownership in for-profit enterprises–comprise a large portion of the wealthiest individuals, and their behavior may help explain patterns in the national distribution of wealth. Entrepreneurs are less diversified and more heavily invested in their own companies than is commonly assumed in economic models. We present an intentionally simplified individual-based model of wealth generation among entrepreneurs to assess the role of chance and determinism in the distribution of wealth. We demonstrate that chance alone, combined with the deterministic effects of compounding returns, can lead to unlimited concentration of wealth, such that the percentage of all wealth owned by a few entrepreneurs eventually approaches 100%. Specifically, concentration of wealth results when the rate of return on investment varies by entrepreneur and by time. This result is robust to inclusion of realities such as differing skill among entrepreneurs. The most likely overall growth rate of the economy decreases as businesses become less diverse, suggesting that high concentrations of wealth may adversely affect a country's economic growth. We show that a tax on large inherited fortunes, applied to a small portion of the most fortunate in the population, can efficiently arrest the concentration of wealth at intermediate levels.


Introduction

The distribution of wealth is a fundamental property of how society is structured and has myriad economic, political, and social implications. The right to keep a large part of what one earns is one of the basic tenets of democratic capitalism, which provides incentives to invest and contribute to the productivity of the economy. However, large concentrations of wealth raise equity issues and may be incompatible with democracy itself; as put bluntly by U.S. Supreme Court Justice Louis Brandeis: “We can either have democracy in this country or we can have great wealth concentrated in the hands of a few, but we cannot have both.”

Models of the wealth distribution [1]–[5] have failed to capture the empirically observed large concentration of wealth in the top few percentiles, predicting too even a wealth distribution [6]. A range of explanations have been offered for this discrepancy. Some observers attribute the concentration of wealth to political factors [7] or to inherent properties of human nature such as differences in human capital (reviewed in [8]). In addition, even though empirical patterns show that savings rates increase with household earnings [9]–[11], many models of savings assume that individuals save to buffer against earnings shocks so that savings rates decline when an individual accumulates sufficient wealth [6], [12], [13].

Recent work has identified the importance of entrepreneurship in generating high concentrations of wealth [11], [14], [15]. Entrepreneurs differ in their investment strategies from those assumed by most economic models. Rather than being diversified (as assumed by Capital Asset Pricing Models, e.g. [16]), successful entrepreneurs often retain a majority of their wealth in ownership of businesses they lead (e.g. [17], [18]). There may be a variety of cultural reasons for this. For example, entrepreneurs may by nature be more confident in their ability to produce wealth through their own businesses than through the stock market, or may feel the need to retain ownership to signal confidence in their business or to retain decision making power, prestige, or other non-pecuniary benefits [17], [18]. Entrepreneurship is quite frequent–about 1 in 9 people in the United States is self-employed, and this rate of entrepreneurship has held steady over at least the past two decades [19].


Analysis

We analyze whether a simple individual-based stochastic model that includes compounding returns can generate the highly concentrated wealth distribution observed among entrepreneurs in real populations. Before considering more complicated explanations, we believe it is useful to understand whether wealth concentration could occur due to the effects of chance alone. The effects of chance on wealth distribution may be revealed in models that track the wealth of individual entrepreneurs and include stochasticity, as opposed to more commonly used aggregate general equilibrium models, which do not allow for effects of stochastic variation among individuals. We isolate the role of chance by starting with assumptions that favor equality of wealth and exclude other factors that could lead to the concentration of wealth. We assume that all individuals have equal talent and begin with the same amount of capital. We also assume that business success in one year is not correlated with future business success. After exploring the implications of these assumptions, we test whether our conclusions are robust to variations in assumptions.

[YMix]

Clean-up executed on Aisle 5.

Let's start over with this thread.

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Thank you Ymix.


"We assume all entrepreneurs begin with equal capital, set to 1 unit of wealth. In each time period () each entrepreneur () invests their capital and earns a return rate, , that is randomly drawn from a normal distribution with mean and variance . In reality, variance in return rate could be due to many factors, however the goal of our model is to assess the influence of chance alone. We investigate this by assuming all entrepreneurs are equal in all factors that could affect return rate, except for the effects of chance. Because returns are independent random draws for each individual for each period, in our simplest model we avoid (1) temporal autocorrelation, i.e., a successful entrepreneur in one period does not have an increased chance of getting a high rate of return in subsequent periods, (2) correlation across individuals in the same time period, i.e., all years have a constant average rate of return, and (3) differences among individuals in the chance of getting high or low returns. The number of individuals in this simplest model does not change, nor is there any explicit treatment of death. Thus, this version of the model describes the wealth of individual entrepreneurial families in a society where accumulated wealth is passed seamlessly to the next generation.

This simple model demonstrates that, with passing time, the proportion of wealth held by an arbitrarily small fraction of entrepreneurs asymptotically approaches 1– that is, a small proportion of entrepreneurs come to possess essentially all of the wealth."



"In this simplest model, the concentration of wealth occurs merely because some individuals are lucky by randomly receiving a series of high growth rates, and once they are ahead with exponentially growing capital, they tend to stay ahead. Because the variance in the sum of return rates is additive, over time the individuals with interest rates at the right tail of the ever-widening normal distribution come to dominate the wealth. Recall that it is the exponents that are normally distributed, not the amount of wealth, so that individuals at the high end of the distribution achieve exponentially greater fortunes. Because of the law of large numbers, our results are robust to changes in the assumption that returns on investment are drawn from a normal distribution. Annual returns drawn from any distribution that obeys the central limit theorem will give exponents whose sum approaches a normal distribution. Note that wage income, because it does not grow exponentially, is not expected to have similar wealth-concentrating effects"

[Skin Job]

I hope it is OK for me to drag this exchange over from Hell, I believe it is topical and within the rules:

The University has spoken, and everyone knows simulations are 100% above reproach. Just ask climatologists.

Yes Yes. Whatever it takes to avoid the substance. These guys are obviously hacks no matter what the numbers do.

Just because you uncritically accept their numbers doesn't necessarily mean I uncritically reject them. I merely point out that simulations are far from infallible (duh).

That's not entirely correct. You attempt to judge my critical skills and find them wanting. This is usually an error. You also attempt to impugn the source of the math like it had something to do with the math. The math is not at all abstract.

If you're going to knock the paper, you're going to have to take more than a halfassed cut at it.

I didn't intend to judge your critical skills per se, but you have posted the paper without any of your own critical analysis, indeed with virtually no commentary at all. I'll freely admit I'm not qualified to judge the study, which is why I rely on those more qualified to break it down. Basically I am extremely skeptical of simulations in general, and specifically of "scientific" studies that correlate so closely with an ideological point of view.

If you're not going to comment on the substance of the paper, perhaps due diligence would impel you to post links to some peer reviews of it?