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Inequality is rising in most developed economies. At the peak of the housing bubble in 2007, the richest 1% held 34.6% of wealth in the U.S. The drop in household wealth following the crisis affected the median household more than the top 1% so that the wealth distribution is now even more unequal. Further, since the start of the recession, the share of total U.S. national income going to labor has plunged, while profits in the U.S. corporate sector are now at a 45-year high. In 2012, the top 10 percent of U.S. earners took more than half of total income – the highest level recorded in a century. These developments, of course, are not without political significance, as the wealth and income distribution is deeply relevant to the distribution of power in a representative democracy.

 

Thomas Piketty’s new book Capital in the Twenty-First Century suggests that these trends are the natural result of free-market dynamics – with the prosperous decades that followed the Great Depression and World War II more the exception than the rule, unlikely to be repeated. Piketty’s hypothesis is that the main driver of inequality is the tendency of returns on capital to exceed the rate of economic growth (this is Piketty’s key inequality relationship r>g), producing high capital/income ratios. If r is to remain at its historical rate of 4-5% p.a., while advanced economies continue to experience low growth rates, we are headed back to the 19th Century in terms of inequality. Though the framework is not entirely deterministic (there are counteracting tendencies that may slow the process of capital accumulation, such as for instance the diffusion of knowledge and know-how), Piketty’s new theory places distributional issues at the forefront of the public debate among economists, highlighting the need for changes in policy to reduce inequality.

 

My current research goal is to take Piketty’s hypothesis seriously – to understand what type of policy issues we might face if he is right, and what other variables may drive inequality. Drawing on some the current portfolio literature in finance and economics, I am currently modeling the evolution of wealth for a given population, trying to study the impact of certain policy variables (or at least variables that can be impacted by policy) — such as tax rates (as we know the U.S. tax system is rigged in favor of wealth, with labor income taxed at a higher rate than capital gains and dividends), the cost of asset management, the cost and availability of leverage, on the wealth distribution. I also intend to explore the impact of labor income inequality on the total evolution of wealth inequality.

 

I consider investors who potentially start with inherited financial capital and are maximizing the expected power utility of consumption over a lifetime (consumption today is achieved at the expense of reinvesting assets so as to increase consumption in the future). I add labor income to the wealth equation in order to properly account for the share of earnings being continually saved-up and invested during a person’s life (for instance funding an employee’s 401k during employment). Investors are choosing their consumption path, as well as the allocation of wealth in the portfolio (the fraction of assets invested in risky and risk-free assets). Asset returns are stochastic and take on the form of a Brownian motion with mean reverting (I will run Monte-Carlo simulations to ensure robustness and significance of the results). The simulations are done in Matlab, using an algorithm to solve dynamic optimization problems for nonlinear model predictive control.

 

Piketty’s view differs from standard economic theory, according to which the wealth distribution results from earning differentials. It is also in sharp contrast to the optimistic hypothesis advanced by Kuznets that market forces will ultimately reduce inequality as a country experiences industrialization and economic growth (and arguably closer to the gloomy predictions of Karl Marx). Though Piketty does not explicitly address the question of emerging economies, one might speculate that they would be facing a similar predicament once convergence ends and their growth rates diminish.

 

From a methodological standpoint, I am linking micro and macro perspectives, trying to understand macro results (the wealth distribution) emerging from individual portfolio allocation decisions. Identifying causal relationships will also be key: I have to understand whether the drivers shaping a more unequal wealth distribution truly have to do with the particular policy variables I am using, rather than specific parameters I may be using (for instance the volatility of the stock market, which inherently produces winners and losers)

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