Disparity in Wealth Accumulation — A Financial Market Approach [PDF]

Financial Market Approach. October 26, 2014. (Preliminary and Incomplete Version). Raphaele Chappe, The New School For S

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Disparity in Wealth Accumulation — A Financial Market Approach October 26, 2014 (Preliminary and Incomplete Version) Raphaele Chappe, The New School For Social Research Willi Semmler, The New School For Social Research Abstract Disparity of wealth seems to be more severe than the disparity in income. In this paper we study to what extent the financial market has contributed to wealth disparities. We assess current empirical work on this issue and explore, in a dynamic asset accumulation model with heterogeneous investors, the role of informational differences, risk aversion, saving rates and leveraging in their contribution to wealth disparities. As shown, though those results are obtained in a stochastic approach, the outcomes are less related to stochastic shocks but rather to some feedback and scale effects operating in favor of some investors in the financial market.

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Introduction

Disparities and inequality are rising in most developed economies — with respect to income, but more so with respect to wealth. In a recent opinion published with the Financial Times, Robert Reich, the former Secretary of State for Labor for the Clinton administration, points out that: “Since the start of the recession, the share of total U.S. national income going to profits has risen even as the share going to labour has plunged. Profits in the U.S. corporate sector are now at a 45-year high.” (Reich, 2012). Corporate earnings now represent the largest share of the gross domestic product (and wages the smallest share) than at any time in recorded history, leading Reich to conclude that 2013 has been the year of “the great redistribution” (Reich, 2014). In other words, from a distributional perspective the fraction of a smaller group of citizens accumulate a larger share of income and wealth. Roughly speaking, we may ask whether this a result of rising disparity in labor income or capital income. This paper studies the role of the financial market for the secularly rising disparity in wealth holdings. 1

Of course disparity and inequality are multi-faceted, with different components, and cannot be summarized by one single cause, measure or determinant. There is income inequality and wealth inequality. Income can be decomposed between, roughly speaking, labor income and capital income (and possibly an in-between category of entrepreneurial income for self-employed entrepreneurs). Labor income and capital income each have, of course, their own distribution. We can understand total income inequality in terms of the distribution of labor income on the one hand, the distribution of capital income on the other (itself dependent on capital ownership), and the share of each source of income in terms of accounting for total income. Top income shares in the U.S. are now higher than before World War II (Piketty and Saez, 2003). After the war, the share of the top decile income (excluding capital gains) fluctuated between 31 and 33 percent until the 1970s. By 1998 it had risen to 44 percent in the U.S. Today it is as much as 50 percent of total income, with the top 1 percent alone getting 20 percent (Piketty and Saez, 2003, Wolff, 2010). Income inequality is worse in the U.S. than in other Western countries, as this compares with 35 (10) percent and 25 (7) percent going to the top decile (centile) in Europe and Scandinavia respectively – see Table 7.3 from Piketty (2013, p. 392) which summarizes the current (as of 2010) distribution of income for the U.S. as well as countries with lower inequality levels. Studying the evolution of the composition of income over the reference period 1913-1998, Piketty and Saez (2003) find a steady decline in top capital incomes (dividend, interest, rents, royalties, capital gains) since the 1960s, and a significant increase of the share of wage income since 1929, for all income groups. This leads Piketty and Saez (2003) to conclude that there has been a change in how high income earners derive their income. They argue that “the working rich have now replaced the coupon-clipping rentiers.” (Piketty & Saez, 2003, p. 3). This could suggest that inequality today is mainly driven by factors that affect top wage income. One hypothesis is that the wage distribution itself may have worsened through factors that shape the supply and demand of skilled and unskilled labor, such as technological and institutional change, globalization and outsourcing, labor laws and job protection, union membership, etc. Regarding top labor income specifically, Piketty expresses some reservations as to whether the standard theory of the marginal productivity of labor can properly account for the explosion of very high salaries for the top one percent (and especially 0.1 percent) earners (Piketty 2013, p.529). Yet, this is not to say, of course, that capital income does not play an important role in explaining rising levels of inequality. The financial market seems to have significantly contributed to wealth disparity, and capital income tends to play an increasingly important role relative to labor income as one climbs up the social ladder to top income earners (specifically within the top one percent). The top one percent is characterized by a combination of both top capital income earners and top labor income earners, rather than the complete replacement of one by the other (Piketty, 2013, p. 475; Wolff & Zacharias, 2009). Capital income exceeds labor income as a share of total income for the top 0.1 percent of top income earners. On average, since the 1980s, the wealth of 2

high net worth individuals has grown faster than that of average investors, and faster than world GDP (see Table 12.1 in Piketty, 2013). There are now $13.7 million of high net worth individuals (having investable assets of $1 million or more), holding collectively $52.62 trillion as of 2013 (Capgemini & RBC Wealth Management, 2013). It is well known that the wealth disparity is even greater than income inequality. There are long swings in wealth inequality, declining with the rise of income tax in the prewar until the post War II period and then again secularly rising again in the last few decades, in particular in the US. The fall in top capital incomes was for most countries concentrated around key macroeconomic and fiscal shocks (World War I, the Great Depression, and World War II). Piketty and Saez (2003) explain the decline in top capital incomes in terms of the inability of large fortunes to recover from such shocks, leading to a decreased concentration of capital income (rather than a decline in the share of aggregate capital income in the economy, which is relatively steady in the long run at around 25-30 percent). At the beginning of the century capital/income ratios were about 6-7 in Europe, and 4-5 in the U.S. They dropped significantly due to the financial and physical destruction of capital during the Great Depression and the two world wars (though Europe was more affected than the U.S.). These shocks to the capital/income ratio (and capital income) are largely responsible for the decline of top income shares in the first half of the century (Piketty & Saez, 2003). As concerning recent decades, studies show that historically wealth distribution has again become very concentrated in the U.S., since the end of the 1970s (See Wolff 1996 and 2010), this in part due to the gradual rise in capital/income ratios in recent decades (Piketty, 2013). Wealth inequality has increased more than income inequality since the late 1980s. In the U.S., the wealthiest 5 percent of American households held 54 percent of all wealth reported in the 1989 Survey of Consumer Finance; this share has now reached 63 percent as of 2013 (Yellen, 2014). The rise in top wealth share in the U.S. is well documented (Wolff, 2006), as well as fat tails for the wealth distribution (Nirei & Souma, 2007). The top of the wealth distribution (people in the Forbes 400 list) exhibits a power law distribution (Klass, Biham, Levy, Malcai, & Solomon, 2007). In Europe, the top 10 percent of wealthiest households own 50.4 percent of total net wealth (European Central Bank, 2013). The distribution of financial assets is even more concentrated than the distribution of total wealth. In the U.S. the wealthiest 5 percent of households held nearly two-thirds of all financial assets in 2013, and the bottom half of households hold as little as 2 percent (Yellen, 2014). Since the 2007/2008 financial crisis, there has been a drop in the wealth (networth) of households. However, the median household was affected more than the top 1 percent of households (36.1 percent drop in wealth compared with 11.1 percent) so that the wealth distribution is even more unequal now than before the crisis (see Wolff, 2010).1 At the peak of the housing bubble in 2007, 1 The

findings in Wolff (2004) and Wolff (2010) are primarily based on the Survey of Con-

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the richest 1 percent held 34.6 percent of wealth – now they own 37.1 percent (Wolff, 2010). This result is somewhat surprising given that stock prices were affected by the financial crisis even more than housing prices. Yet the middle class took a bigger hit from the decline in home prices than wealthy investors took from the decline in stock prices because houses were a larger share of the gross assets of the middle class than stocks were for the wealthy (Wolff, 2010). The major asset of the middle class in the U.S. is their home. In the euro area, 60.1 percent of households own their main residence (European Central Bank, 2013). In this paper we explore the forces causing disparities and inequalities that are greatly coming from financial market. Running away of some “top labor income” and “super star” incomes, may end up there, but important effects for rising wealth disparities seem to stem from forces in the financial markets. Though there is no clear evidence regarding the link between standard monetary policy and economic inequality, in a recent keynote address, Yves Mersch (member of the Executive Board of the European Central Bank) highlighted that monetary policy could have an impact on wealth inequality precisely because of households’ connection to financial markets. Expansionary monetary shocks could increase inequality by redistributing wealth to those households more connected to markets, as well as not benefit low income households who hold more cash and risk-free assets than high income households, see Mersch (2014). For the rise of wealth in the last few decades – real and financial wealth as Piketty defines it – there might have been several factors at work: 1) rising superstar income enlarged through the financial market, 2) higher saving rates of certain groups of wealth holders, (consumption may have upper constraints, so that saving rates can rise), 3) higher returns of certain groups of wealth holders on the higher end of the distribution relative to average investors and low income earners, and 4) the possibility of leveraging up investments using larger assets and net worth as collaterals. These are the forces we want to explore in our paper. The history of economic theory provides us with some deeper explanations of the distribution of income and wealth. Those explanations start with the classical economists (Smith, Ricardo, Marx) on the laws governing the allocation of income between wages, rent and profit. The modern theory of income distribution beginning after World War II (the works of Kaldor, Kuznets, Kalecki) mainly explored the issue of whether a country’s level of economic prosperity and stage of development has implications for income inequality. Kaldor (1956, 1961) proposed a Keynesian model of economic growth, distribution and inequality arising from different saving rates of workers and owners of capital. Kuznets (1955) studied the relation between income distribution and a country’s state of development. Kuznet’s hypothesis was that the distribution of income is more unequal in early stages of development (economic inequality first increases while a country is developing), but that this trend is reversed after a certain income sumer Finances (SCF) conducted by the Federal Reserve Board.

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threshold is reached – the famous inverted U-shape function (the Kuznet curve) relating inequality to the level of GDP. As the human-capital-led growth theory made progress, the role played by education and human capital formation on inequality was explored. The endogenous growth literature further explored the issue of the exact causal relation between the factors of economic growth and income distribution, in particular which ways it goes: inequality as an obstacle to growth or a factor of growth2 . Based on a unique data collection covering 20 countries and spanning (for some) three centuries, Thomas Piketty’s recent book Capital in the Twenty-First Century defies traditional economic thinking by suggesting that the trend of increasing inequality is the natural result of free-market dynamics. His position is arguably closer to the gloomy views of Karl Marx than to the standard growth model where income differentials just arise from the marginal contributions of the factors of production3 , or the optimistic hypothesis advanced by Kuznets in the 1950s and 1960s (market forces will ultimately reduce inequality as a country experiences industrialization and economic growth). The success of Piketty’s book has placed distributional issues and inequality at the forefront of the public economic debate. 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 a reasonable consideration if the returns on assets for certain groups of wealth holders are greater than the growth rate of income of the rest of the population. It of course also assumes that the consumption fraction of income of the first group does not erode the asset accumulation of that group. As such, as he then argues, the prosperous decades that followed the Great Depression and World War II (two major external shocks that reduced inequality) were more the exception than the rule in terms of making wealth inequality declining, a period somewhat unique and unlikely to be repeated. The recent development, as many argue, is not without significance for the political system. While most of the literature is focused on understanding disparities and inequality in terms of income from labor, we here propose to study wealth inequality and the process of wealth accumulation from a microeconomic perspective focusing on the financial market. A particular emphasis here is the fact that high net worth individuals are growing their wealth largely on the strength of the strong performance of global financial markets and with the help of large scale wealth management firms. Through their individual retirement accounts (401k, pension funds, etc.), average investors are likely to also be exposed to financial markets either directly or indirectly (e.g. via mutual funds) – the share of households with indirect ownership of stocks increased from 23.5 percent in 1989 to 47.7 percent in 2001 (Wolff, 2010). Yet their performance in terms of wealth accumulation may show different results than for high net worth individuals. As to personal investment and savings, low income investors usually invest in low return assets – in risk free deposits in thrift organizations and 2 See

Greiner et al. (2005, ch 8) one must admit that the Solow growth model would in fact also permit disparity of income per capita in the long run, if one allows for differential saving rates. 3 Although

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commercial banks. They also typically cannot easily leverage up when higher returns are expected. We may then study the problem of wealth inequality by asking what characteristics of the wealth distribution can be obtained from the dynamic behavior of heterogeneous investors over time. In order to study the process of wealth accumulation and distribution, we turn to a recurring and classic problem in financial economics, the accumulation and allocation of funds into different types of assets, following different investment conditions and features. This leads us to a dynamic portfolio theory using a stochastic dynamic model of wealth accumulation with preferences, saving and consumption, difference risk behavior, and heterogeneity between investors. The rest of the paper is organized as follows. In Section 2, we review the main body of related literature. Section 3 outlines the stylized facts we wish to study. Section 4 introduces a stochastic dynamic model of wealth accumulation. Section 5 presents our main results and simulations. Section 6 concludes the paper.

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Related Literature

2.1

Standard Approach to Income Inequality

One research trend is how do we explain the recent trend of high inequality of labor income in the U.S. specifically? The traditional theory is that wages are equal to the marginal productivity of labor, which in turn depends on a worker’s skills and qualifications, as well as the supply and demand for such qualifications in a given society. The demand for labor is dependent upon the technology used to produce goods and services (technically captured by the concept of a production function), and its supply is dependent on the educational system (Piketty, 2013, pp. 482-483). From the 1960s to 1980s, the development of human-capital-led growth theory further studied the role played by education and human capital formation in inequality. See Becker and Tomes (1979) for an approach taking into account the characteristics of the community individuals find themselves in. See also Becker (1962), Stiglitz (1975), Riley (1976). Bowles and Gintis (2002) emphasize the role of inherited wealth in the persistence of inequalities. See also Brock and Durlauf (2006) for the role played by social environment for socio-economic outcomes, focusing on social-interaction dynamics.4 Consistent with the standard theory that wages are equal to the marginal productivity of labor, which in turn depends on supply and demand for skills, one theory is that the increase of labor income inequality in the U.S. in the past three decades can be explained in terms of insufficient investments in higher education (Goldin & Katz, 2008). Another theory is that the main cause of the declining demand for unskilled workers and the corresponding deterioration of their relative wage is international trade (rather than technological improvement). As production shifts to high-skill production, we can expect the wage 4 See

also Barsington, Kato and Semmler (2010).

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differential between skilled and unskilled workers to increase. Richardson (1995) proposes a basic model in which trade and technology are exogenous, and shows that international trade might result in an increase in wage inequality due to dislocations and the difficulties of adjustment in the labor market.5 A third line of this research explores the relation between technical progress and inequality – how technology influences relative wages.6 We will note here in passing that the standard model encounters difficulties to properly account for the disproportional increase in the top salaries for the 1 percent and 0.1 percent. As Piketty observes, there is a very sharp discontinuity of salaries between the top 1 percent of wage earners and the remaining top 9 percent. This cannot be easily explained in terms of qualifications or professional experience, as one would have expected a gradual increase in salaries (Piketty, 2013, p. 498). Piketty’s recent hypothesis is that the main driver of inequality is the tendency of returns on capital (note that Piketty uses “capital” interchangeably with wealth) to exceed the rate of economic growth. This is Piketty’s key inequality relationship r > g which in principle is obvious, following classical growth theory (since part of those returns on assets is consumed and cannot make the economy growing). If, as above mentioned we give this the interpretation that the returns on assets for certain groups of wealth holders are greater than the growth rate of income of the rest of the population, this is plausible. This naturally holds, if the consumption rate of the former group is smaller – a pattern we will explore further in our model variants below. Piketty derives this rising share share of total national income flowing to capital income (α) as equal to the rate of return on capital (r) multiplied by the capital/income ratios (β). In the long run, β is determined by the saving rate and the growth rate, with β = s/g (which Piketty labels the “second fundamental law of capitalism”). Piketty argues that recent low growth rates 5 Yet, we should also expect, in the long run, the ratio of skilled to unskilled employment to decline, as employment shifts to skilled labor. Krugman (1994) argues that international trade cannot be the main driver of wage inequality since this shift of employment to skilledintensive industries has not been observed empirically. Krugman finds that some common factor affecting all sectors must be the cause of the wage differential. 6 Building on the Romer (1990) growth model, Murphy, Riddell, and Romer (1998) use the movement in relative wages as indicators of changes in the demand for different types of labor, which in turn is related to technological change. The concept of skill-biased technological change can help explain why wages for skilled workers have grown significantly more than wages for unskilled workers in spite of the fact that the number of high skilled workers has sharply increased in many countries. Under a supply / demand framework, we would expect relative wages for skilled labor to decrease. Yet if technology is complementary to skills, the demand for skilled labor increases as technology grows. Further, if there is a large supply of skilled-workers, new technologies will be skill-based and skill-complementary to the extent the increased supply of skilled workers will make it profitable. Based on these ideas, Rubart, Greiner and Semmler (2004) develop a growth model of the Romer type to explore the forces generating skill-based wage inequalities. In the model, innovation is based on technical change, there are positive externalities, the structure of the productive sector is similar to Romer (1990), labor is divided into two groups (high skilled and low skilled), and there are substitution effects among the groups. See also Greiner, Semmler and Gong (2005) ch. 7 for a similar model. Aghion (2002) attempts to model endogenous technical change with quality improving innovation with wage dynamics.

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(in part due to small population growth) have led to a rise in β in advanced economies (though less so in the U.S. than in Europe and Japan). Piketty observes the historical data that shows that the return on capital is generally pretty stable at around 4-5 percent in the long run and concludes that, short of policy changes that might perturb the continued stability of this rate, or higher economic growth than anticipated (due potentially to technological progress), the share of income flowing to capital will increase.

2.2

Dynamic Portfolio Approach to Wealth Accumulation and Distribution

Most of this literature has focused on understanding inequality in terms of income. However, there are many reasons as to why wealth would be a more relevant measure of inequality. Arguably, wealth is more representative of one’s ability to consume (assets can be converte into cash) and overall economic wellbeing (the availability of financial assets can provide liquidity, a sense of security, and affect household behavior beyond mere income).7 Further, wealth distribution is also relevant to the distribution of power in a representative democracy. The principal concept of networth used in most studies is that of the marketable value of assets (such as real estate, stocks, bonds, 401(k) plans), not including consumer goods not held for resale (such as cars), less liabilities (mortgage debt, consumer debt, etc.).8 In addition, economists also use the concept of financial wealth (i.e. wealth that is not tied to the value of one’s home), which can be defined as networth minus net equity in owner-occupied housing. The process of wealth accumulation can be approached from a microeconomic perspective, but it has considerable externalities. We may study the problem of wealth inequality by asking what characteristics of the wealth distribution can be obtained from the dynamic behavior of individual households over time. This approach differs from the human capital model (the marginal productivity of labor) in that it explores the possibility that inequality may result from behavior in financial markets, in connection with certain structural parameters of the economy (market risk, taxation, cost of asset management, availability of leverage, etc.), investor characteristics (saving rates, discount rates, preferences and risk aversion), as well as luck and stochastic forces (income shocks, or even simple features of capital markets that inherently produce winners and losers), and not merely from the distribution of abilities, investment in human capital, or demand for specific skills. Power-law dynamics can emerge from simple features of capital markets, such as the idiosyncratic risk component associated with the realization of capital income, independently of any portfolio optimization problem and optimal decisions about how much to save or consume. This idiosyncratic component is not a standard assumption in most macroeconomic models, but see for instance Angeletos (2007), who introduces it in order to study aggregate savings 7 See 8 See

Conley (1999), Spilerman (2000). for example Woolf (2004).

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and growth (see also Benhabib and Zhu, 2008). This analytical development suggests that inequality can result from luck and stochastic forces, rather than the distribution of abilities and investment in human capital. For example, Klass et al. (2007) find that a simple stochastic multiplicative model whereby variations in the market value of an investment portfolio are characterized by random noise and no investor can consistently “beat the market” (markets are efficient) can reproduce the Pareto wealth distribution for the 400 wealthiest individuals based on the Forbes 400 data.9 Note however that empirically, lower wealth percentiles follow an exponential rather than power-law distribution. The authors suggest that this may be explained lower percentiles of the population being less affected by financial market fluctuations to the extent they make fewer transactions in the stock market. Similar dynamic models might account for both the power-law and exponential distributions at higher and lower percentiles respectively. A model which combines a multiplicative asset accumulation process with an additive wage process can successfully reproduce both exponential and power-law distributions – see for instance Nirei and Souma (2007), finding the Pareto exponent for the power-law tail distribution a function of the ratio of savings from labor income to asset income. Recent research reaches similar conclusions regarding the wealth distribution by modeling households’ optimal decisions about how much to consume or save from their labor and investment income. For instance, Fernholz and Fernholz (2014) consider a set-up in which identical and infinitely-lived households have equal investment opportunities (equal expected returns) but face idiosyncratic investment risk (with luck alone affecting the evolution of wealth in the form of higher returns due the realizations of independent Brownian motions). They find that in the absence of any redistributive mechanisms (broadly defined as any process that proportionately affects wealthy households and poor households differently, including both direct and indirect transfers), the equilibrium distribution of wealth is not stationary and over time becomes increasingly right-skewed (at the limit wealth tends be entirely concentrated at the top). The major factor affecting the distribution of wealth is the idiosyncratic risk (the standard deviation of the independent Brownian motions). Accumulation with the wealthiest households increases with individual households’ exposure to idiosyncratic risk. Importantly, the set up disregards differences in investor characteristics: households are identical in terms of their abilities to earn labor 9 At each period, a randomly chosen wealth for one investor is multiplied by a factor λ drawn from a given distribution p (λ). Starting from a homogeneous distribution of wealth for 400 investors, Klass et al. (2007) find that this process evolves towards a power-law distribution with an exponent varying between 1 and 2 (a simulation done for 10,000 investors yields the same result). A crucial assumption in Klass et al. (2007) is that the same distribution p (λ) be used for all the investors, as an implementation of the efficient market hypothesis (no investor can consistently obtain a return distribution that is better than that of other investors). Though the short time gain/loss distribution is similar for all investors, differences between more successful and less successful investors are magnified by the multiplicative dynamics in the system (the impact of random stock price fluctuations on each investor being proportional to the investor’s wealth).

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incomes, expected returns of risky asset, and preferences for consumption over time (discount rates and risk aversion). In addition to idiosyncratic risk, a stochastic labor endowment process can also conceivably generate skewness in the wealth distribution. There is a large literature exploring the so-called “Bewley economies”, in which agents solve an infinite horizon consumption problem with incomplete markets, investing in a risk-free bond, and facing a stochastic process for labor earnings. Standard Bewley models cannot generate heavy tails in wealth (Aiyagari, 1994; Huggett, 1993). To generate heavy tails some authors introduce features such as preferences for bequest and entrepreneurial talent (Cagetti & De Nardi, 2008; Quadrini, 1999, 2000) and heterogeneous discount rates (Krusell & Smith Jr, 1998). It can be shown that the Pareto distribution of the right tail is driven by capital income risk rather than labor earnings (Benhabib, Bisin, & Zhu, 2011, 2014). Wealth inequality increases with the capital income risk that households face. Cagetti and De Nardi (2006) also give a comprehensive overview of the standard intertemporal economic models and the standard causes for the increase in wealth. Their intergenerational model shows that more restrictive borrowing constraints generate less inequality in wealth holdings, but also reduce average firm size, the amount of entrepreneurial activities, and aggregate capital accumulation.

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Stylized Facts and our Set-up

Overall, why might the assets of some asset holders grow faster than the assets of others? In general we could imagine three types of scale effects: First, investors have more or better information about expected returns than others. Though it is commonly assumed that markets are efficient and no money is to be made by forecasting (all information is already built into asset prices and returns), industry, firm and product knowledge, as well as knowledge on innovations, product development, and future market share are likely to give rise to better information and higher expected returns.10 Information flux could include insider information obtained through informal networks. There are economies of scale associated with the size of the portfolio, meaning that wealthier investors can afford more sophisticated asset managers, thereby securing higher returns. Studying university endowments as a case study, Piketty finds that the rate of return depends on the size of the endowment (see Table 12.2 in Piketty, 2013). Further, for average investors there can also be restrictions on the types of investments made, and on the corresponding associated expected returns. For example, though 401k funds invest in equities, most pension funds of unions, firms and the public sector have constraints such that they should invest a large portion in risk free assets (Treasury bills and Treasury bonds). 10 This has often been the case in industry developments such as the oil boom, before World War I, the boom in the auto industry after World War I, the boom in the steel industry, during and after World War I, the high tech boom in the 1990s, the commodity price boom after 1995, the real estate boom after 2001, and the recent banking and finance industry boom.

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In Europe the most prevalent financial assets for assets are deposits (sight or saving accounts), which are owned by 96.4 percent of households, and voluntary private pensions/whole life insurance (held by 33 percent of households) (European Central Bank, 2013). All other financial assets are owned by less than 15 percent of households. Second, for large investors there are scale advantages, not only with respect to information but also with respect to leveraging. Investment opportunities can be explored more extensively with greater access to and lower cost of credit. Larger assets and larger net worth means larger collaterals, and availability of funding may rise and the cost of funding falls. Levering, and over-leveraging has become one of the most common and well known strategies to harvest large gains from traditional as well as new financial instruments in the recent past.11 Third, one might reasonably assume that larger income will imply lower consumption rates and higher saving rates. This will result in a higher proportion of funds being reinvested. Numerous studies in the literature have used this assumption showing that the wealth will be build up faster with higher saving ratios. The faster build up of wealth is an expected outcome of this strategy. There is lots of evidence that higher income leads to higher saving rates.12 Among households with heads aged 40 to 49, median saving rates on current income range from -23 percent in the lowest income quintile to 46 percent in the highest on the basis of Consumer Expenditure Survey (CEX), the best available data on household consumption (Dynan et al., 2004, p. 416).13 Saving rates estimated on the basis of the Survey of Consumer Finances (SCF) range from 1 percent in the lowest income quintile to 24 percent in the highest, with estimates for households in the 95th and 99th percentile of the income distribution of 37 and 51 percent respectively (Dynan et al., 2004, p. 416).14 Saving rates vary for different age groups, and are lower for ages 30-39 and 50-59. In order to study the process of wealth accumulation and distribution, we introduce a stochastic dynamic portfolio model of wealth accumulation with preferences and consumption. The choice of a portfolio is a recurring and classic problem in financial economics. We wish to study the evolution of wealth 11 There is this well-known Banker’s Paradox pointing to those scale effects: “The people who most need the money are worst credits risks and thus cannot get a loan, whereas people who least need the money are best credit risks and thus once again the rich get richer” (Tooby and Cosmides, 1996) 12 Early contributions include Fisher (1930), Keynes (1936), Vickrey (1947), Duesenberry (1949), Hicks (1950), Pigou (1951), Friedman (1957), Friend and Kravis (1957), and Modigliani and Ando (1960). For more recent work, see for example Saltz (1999), Dynan, Skinner and Zeldes (2004), and Chakrabarty, Katayama and Moslen (2008). 13 Dynan et al. (2004) define the saving rate for a CEX household as the difference between consumption and after-tax income divided by after-tax income. Consumption equals total household expenditures plus imputed rent for home owners minus mortgage payments, expenditures on home capital improvements, life insurance payments, and spending on new and used vehicles. 14 The saving rate variable used for the SCF calculations is equal to the change in real net worth between 1983 and 1989 divided by six times the average of 1982 and 1989 divided by six times the average of 1982 and 1988 total real household income. As such, it is computed over several years and is likely to be a less noisy measure of average savings.

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Figure 1:

simulations for three classes of investors, conservative, moderate and aggressive. We assume that such classes correspond, roughly, to investors belonging to the social classes identified by Piketty for thinking about distributional matters, mainly the working class (bottom 50 percent), the middle class (middle 40 percent), and the upper class (upper 10 percent) respectively. Unlike Fernholz and Fernholz (2014) who use a relative risk aversion parameter for all investors, we use different risk aversion parameters for three investor classes, as calibrated below. Using an algorithm for nonlinear model predictive control developed by (Grüne & Pannek, 2011), made suitable for economic issues with discounting in Grune et al (2013), we can run two sets of simulations. This algorithm allows to solve the model for a finite decision horizon, which we have set at twelve periods. In the first set of simulations, all investors face identical market conditions and do not bear individual idiosyncratic risk (in short, all investors are taken to face identical investment products and market conditions, such as the S&P500 or other well-diversified index), so as to isolate the impact of investor characteristics (risk aversion, leverage, saving rate) on the wealth distribution. In the second set of simulations (forthcoming), investors do bear idiosyncratic risk with respect to the stock index, as in Klass, Biham, Levy, Malcai, and Solomon (2007), Nirei and Souma (2007), and Fernholz and Fernholz (2014). In all scenarios we study the end wealth distribution and test for the robustness of the results by varying initial conditions slightly. We will test specifically for the isolated impact of investor level characteristics (risk aversion, leverage, saving rate) between the three classes of investors. All investors begin with the same initial wealth ($50,000), and the same initial wage income of $30,000 (close to the median wage, see Figure 1). We test for the impact on the end wealth distribution of risk aversion, leverage, saving rate.

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4 4.1

The Model A Stochastic Model

We use a dynamic portfolio approach resembling Campbell and Viceira (2002), which includes a wealth equation as well as mean-reverting returns for the riskfree investment and for the risky-asset. Models with mean reversion in returns are now frequently used in the portfolio modeling literature. There are stochastic shocks to the returns that take on the form of a Brownian motion. The basics of such model are analytically treated in Semmler (2011) Ch. 17 and Campbell and Viceira (2002). Similar models can be found, in different forms, in Chiarella, Hsiao and Semmler (2007), Wachter (2002), Munk, Sørensen, and Nygaard Vinther (2004), Platen and Semmler (2009), and Brunnermeier and Sannikov (2009). Our model consists of N investors whose wealth is given at any moment in time by Wnt , where the index n = 1, ..., N represents each investor (for the ease of notation we drop the subscript n going forward with the understanding that it is implied). Wealth can be consumed or reinvested, with only reinvested wealth earning the portfolio return in the next time period, so that consumption today is achieved at the expense of reinvesting assets that may increase consumption in the future. So, a decrease in consumption will lead to greater savings and wealth accumulation. Each investor is maximizing the expected power utility15 of consumption over a finite horizon (T ), and is assumed to have a power utility function U (Ct ) = Ct1−γ /(1 − γ) with the risk-aversion parameter γ. Power utility implies that absolute risk aversion is declining in wealth, with relative risk aversion a constant. Each investor is also choosing the allocation of wealth in the portfolio (the fraction of assets invested in risky and risk-free assets). To explain the evolution of income and wealth we use four stochastic processes: First, a process for wealth, whereby the investor starts with an initial wealth, and is earning labor income in each period [equation (2)]. We add labor income to the wealth equation in order to properly account for the share of labor income being continually saved-up and invested during a person’s life (for instance funding an employee’s 401k during employment). From the perspective of financial economics labor income can be thought of as a dividend on an individual’s “human wealth”, the expected present discounted value of future labor earnings. However, to the extent human wealth is not a tradable financial asset (it is difficult to monetize or sell claims against future labor income, due to imperfect capital markets), investors cannot directly borrow against future labor income. A fraction (1 − αt ) of assets is invested in a risk-free investment (riskfree here means that the return is known over the holding period, earning the risk free interest rate rt ), and a fraction (αt ) is invested in risky assets (earning a risk-premium xt above the risk free rate). If αt > 1, there is leverage and the fraction “invested” in the risk-free asset is interpreted as the cost of borrowing. Note that for the time being we have disregarded the possibility that an investor 15 Note that we could take log utility here, in which case we would be back to a classical growth model.

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own equity in his or her home and potentially finance current consumption by borrowing against this equity (with for instance a home-equity line of credit). We are only considering financial wealth. Second, a process of a mean-reverting equity premium on risky assets (the stock index) described by an Ornstein-Uhlenbeck process, whereby the timevarying excess return is xt and the expected mean of the equity premium x [equation (3)]. λ is an adjustment coefficient, representing the adjustment speed of the equity premium towards the mean. All future trajectories of the equity premium will evolve around x, and will do so (in the long run) with a long-term variance of δx2 /2λ. Third, a process of a mean-reverting risk-free interest rate, described by a Cox-Ingersoll-Ross process, whereby the time-varying risk-free interest rate is rt and the mean interest rate θ [equation (4)]. The drift is exactly the same as in the Ornstein-Uhlenbeck process (ensuring mean reversion in the long run), with the adjustment coefficient κ. The level dependent volatility avoids the possibility of negative interest rates. All future trajectories of the risk-free rate will evolve around θ, and will do so (in the long run) with a long-term variance of δr2 /2κ. The dynamics described in equation (4) are for nominal interest rates. Our model does not take into account inflation uncertainty, whereby the real price of assets could be determined by deflating by the price index (the nominal price of the real consumption good in the economy, the dynamics of which could be determined by another system of differential equations, as in Munk et al. (2004), for example). Fourth, a process for the evolution of labor income. We model the process of labor income following Campbell and Viceira (2002) in Ch. 6. We assume that expected labor income growth is constant, and allowing for the possibility of transitory income shocks [equation (5)]. We also explore retirement horizon effects (by introducing a positive probability that the investor retires). For each investor, the continuous-time (with discount rate δ) optimal portfolio and consumption problem for agents is as follows: ˆ

T

e−δt

max α,C

t=0

Ct 1−γ dt 1−γ

(1)

s.t. dW = {[αt (rt + xt ) + (1 − αt )rt ]Wt + Lt − Ct }dt + σw Wt dz1t

(2)

dxt = λ(x − xt )dt + σx dz2t √ drt = κ(θ − rt )dt + rt σr dz3t

(3)

dLt = gLt dt + σL dz4t

(5)

14

(4)

Table 1: Capital market parameters from Munk et al. (2004)

where Ct is the total amount consumed in the period, determined as a percentage of wealth, and T the finite investment horizon. Note that in our simulations capital income earned in one period is available for consumption in the next period, while labor income is immediately available for consumption in the current period. A stochastic shock is imposed on each dynamic equation, where the terms are the increments in the Brownian motions (Wiener processes). Each process has its own volatility parameter, with an excess return (equity premium) volatility parameter σx , an interest rate volatility σt , and a labor income volatility σL . Though the Wiener processes are possibly different for all four Brownian motions, we assume that the Wiener process in the wealth equation can be written as a function of the Wiener processes for the risky and risk-return, with the same framework as in Munk et al. (2004): σw Wt dz1t = −{αt σS dz2t + (1 − αt )σB dz3t }

(6)

where σS is the stock return volatility, σB is the bond return volatility, with σB = σr when there is no interest rate premium and the duration of a bond is 1. The expected excess return and the stock return processes are instantaneously perfectly negatively correlated, as are the short interest rate and the return on the bond. We assume, as in Munk et al. (2004) that the two basic Wiener processes that generate the dynamics of the excess stock return and the nominal interest rate (dz2t and dz3t ) are correlated with a constant correlation coefficient ρxr . The correlation between the stock index and the nominal interest rate is −ρxr .

4.2

Calibration of the Model

We assume T = 12. To calibrate the model to U.S. data, we assume capital market parameters (Table 1) and investor level parameters (Table 2) empirically estimated in Munk et al. (2004): For purposes of setting limits on the maximum consumption, we refer to the following saving rates estimates (Table 3) from Dynan et al. (2004). Using the estimates prepared on the basis of the SCF, we cap consumption to reflect the following saving rates for our different investor group (using the 15

Table 2: Investor level parameters from Munk et al. (2004)

Table 3: Saving rates estimates from Dynan et al. (2004)

data of a specific quintile as a representative of the investor class, though this is somewhat imperfect because the quintile categories do not perfectly match out distributional categories): 0 percent for the bottom 50 percent (the second quintile), 17 percent for the middle 40 percent (the fourth quintile), and 23 percent for the top 10 percent (the fifth quintile). Regarding labor income, we assume a yearly growth rate of 2 percent, as consistent with the past 5 years, and a labor volatility σL = 0.1. If αt > 1, there is leverage and the fraction “invested” in the risk-free asset is interpreted as the cost of borrowing. We assume that only aggressive investors (the upper decile) have access to leverage. Average investors typically do not use borrowed funds to invest in the stock market, and investment products available to average investors (e.g. through a pension fund or a 401k) typically do not include leverage. In the mutual fund industry, for instance, the use of leverage is restricted by Section 18(f) of the Investment Company Act of 1940. This is not the case for alternative investments and other products offered by sophisticated asset managers, which are typically less regulated. The hedge fund industry is unrestricted in terms of leverage both in the U.S. and the EU.16 In our simulations we set the maximum leverage to αt = 2.17

5

Simulations

We consider the wealth distribution after 30 periods for a population of N = 1, 000 and study the impact of risk aversion, leverage, and saving rate. For now we use a step size of one (so that 30 periods are equivalent to 30 years). As mentioned before, when we run simulations with leverage, we assume that 16 Neither Dodd-Frank nor the Alternative Investment Fund Managers Directive seem to provide for concrete limits on leverage, only disclosure. 17 On average at the fund level, the hedge fund industry has a 1.5 to 1 debt to equity ratio.

16

leverage is capped at αt ≤ 2, but only made available to the top 10% of investors. In all simulations we assume as a starting point a risk-free rate of 1% and a risk premium of 5%. As mentioned above, in all simulations and results below, 50 percent of investors are taken to belong to the lower class and invest conservatively (saving rate cannot be lower than 17%, and the risk aversion parameter γ = 4.177). The top 10 percent of investors are taken to invest as aggressive investors (saving rate cannot be lower than 23%, and the risk aversion parameter γ = 2.198). In the first set of simulations, all investors face identical market conditions and do not bear individual idiosyncratic market risk. Further, we retain the same random shocks in all simulations, so as to test for the impact of other variables. When investors do earn labor income, we assume that each investor bears individual idiosyncratic risk with respect to labor income, due to personal circumstances and career path (hence in our figures below, the indication that there is no idiosyncratic risk refers to market risk only). We also explore retirement horizon effects (by introducing a positive probability that the investor retires) - we beging with a small probability that the investor retire in the next period (2%). This probability increases by 2% in each forecasted period in the investor’s investment horizon (12 periods) T , as well as at the beginning of each period in the overall simulation (30 periods). Figure 2a shows the evolution of the risk-free interest rate and the risk premium throughout the simulation (30 periods) as driven by Brownian motions. Figure 2b shows the shocks to the stock index. These are taken to be identical for all investors, since we do not consider idiosyncratic risk for this first set of simulations. All investors begin with the same initial wealth (we test for the robustness of the results by varying initial conditions slightly and consider both initial wealth of $10,000 and $50,000 – we can assume any currency at this stage, though for convenience sake we use US Dollars). We run simulations with and without labor income (given the same initial wage income of $30,000 for all investors, close to the median wage in the U.S., see Figure 1). To show what the details of any given simulation might look like, Figure 3a shows for a given investor the evolution of wealth through the simulation (30 periods), and the consumption ratio (as a percentage of the sum of financial wealth at the start of period and income earned in the current period – including both labor income and capital gains/dividends earned with respect to investments made in the prior period). Figure 3b shows the path of labor income given the process in equation (5) for one specific investor (with his or her own idiosyncratic to labor income) in a simulation over 30 periods where investors begin with $10,000 in the first period. In forthcoming work, we ultimately intend to test the robustness of our results by running Monte-Carlo simulations for each investors (i.e. running simulations for many possible market processes, given different shock paths, with again the possibility of investors bearing individual idiosyncratic risk).

17

Figure 2: Risk free rate (%, in blue), risk premium (%, in red), and stock market (index) shocks, over 30 periods (b) Shocks to stock index

(a) Risk free rate and risk premium

Figure 3: Evolution of wealth (in ’ooo, in blue) and consumption ratio (as a % of both starting wealth and income for the period), over 30 periods

(a) Evolution of wealth and consumption ratio

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(b) Evolution of labor income

Figure 4: Wealth distribution (without labor income) at the end of 30 periods, without leverage (αt ≤ 1), no idiosyncratic shocks (b) Starting wealth 50k

(a) Starting wealth 10k

Figures 4a and 4b show the wealth distribution (histogram) at the end of simulation period, where all investors start with $10,000 (Figure 3a) and $50,000 (Figure 3b), and earn no labor income throughout the simulation. The only difference between investors is the minimum saving rate and risk aversion, assigned on the basis on of the investor category (50 percent of investors are assumed to be conservative, 40 percent are assumed to be moderate, and 10 percent are assumed to be aggressive). Since all investors begin with the same wealth, at this stage, these categories do not correspond to the bottom, middle and upper distributional percentiles, but are still helpful to understand the impact of investor characteristics on the wealth distribution. We find that investors belonging to any given investor class (conservative, moderate or aggressive) end up with the same amount of wealth at the end of the simulation as all other investors belong to the same class, since all investors in a given class are essentially identical at that stage (and there is no idiosyncratic risk). Hence the end wealth distribution has three single separate peaks. Interestingly, the characteristics of aggressive investors in terms of risk aversion (γ = 2.198 as opposed to γ = 4.177 and γ = 8.689 for moderate and conservative investors respectively), and saving rate (a minimum of 23% of current year income for aggressive investors, as opposed to 17% and 0% for moderate and conservative investors respectively) already create a fatter distributional tail.

Figures 5a and 5b show the wealth distribution for the exact same simulations, but for the fact that leverage is allowed for the agressive investors. For a starting wealth of $10,000, aggressive investors end up with $25,000 as opposed to $6,500 (Figure 5a vs. Figure 4a). For a starting wealth of $50,000, they end with $120,000 as opposed to $33,000 (Figure 5b vs. Figure 4b). We can see that the availability of leverage (αt ≤ 2 ) for 10 percent of investors (aggressive) 19

Figure 5: Wealth distribution (without labor income) at the end of 30 periods, with leverage (αt ≤ 2), no idiosyncratic shocks

(a) Starting wealth 10k

(b) Starting wealth 50k

creates a fat tail – investors with leverage opportunities end up almost six times wealthier at the end of the simulation (compare $25,000 for aggressive investors relative to $5,000 for the others in Figure 5a, and $120,000 relative to $25,000 in Figure 5b).

Figures 6a and 6b show the wealth distribution when investors earn labor income (initial wage of $30,000), without any leverage, while Figures 7a and 7b show the wealth distribution when investors earn labor income with leverage. We find that the presence of idiosyncratic labor income risk means that there is more dispersion in the end wealth distribution, which looks like a normal distribution skewed to the right. When investors start with $10,000, availability of leverage for aggressive investors results in an added $500,000 in wealth at the end of the simulation. When investors begin with $50,000, leverage results in as much as an added $1,000,000 for the fat tail of the distribution. Hence, we also find that leverage creates fatter tails. In a second set of simulations, we intend to model the results when investors do bear idiosyncratic risk with respect to the stock index, as in Klass, Biham, Levy, Malcai, and Solomon (2007), Nirei and Souma (2007), and Fernholz and Fernholz (2014) [forthcoming]. We also run a set of simulations where we impose the constraint that αt ≤ 0.1 to reflect the fact that the lower wealth group mainly invests in low risk assets: deposits of banks, Treasury bills and Treasury bonds. Pension fund rules also impose similar conservative requirements. We find that this restriction results in a severe double peak distribution, with the lower class on the lower end of the wealth distribution (Figure 8a and 9a show the end wealth distribution without

20

Figure 6: Wealth distribution (with labor income) at the end of 30 periods, without leverage (αt ≤ 1), no idiosyncratic shocks (b) Starting wealth 50k

(a) Starting wealth 10k

leverage, both without and with labor income). As before, the presence of idiosyncratic risk for labor income results in a more dispersed wealth distribution. Leverage further intensifies the problem, both without and with labor income (Figure 8b and 9b respectively). In Figure 8b, we see quite well the impact of leverage as allowing the wealth of the top 10 percent to really take off as compared with the rest of investors.

6

Conclusion

In order to study the process of wealth accumulation and distribution, we introduce a stochastic dynamic portfolio model of wealth accumulation with preferences and consumption. In our simulations, investors decide on how to allocate financial assets (between a risk free asset and a risky asset) as well as how much to consume (as a percentage of both current period income and wealth available at the beginning of each period). We study the problem of wealth inequality by asking what characteristics of the wealth distribution can be obtained from the dynamic behavior of heterogeneous investors over time. For this purpose, we distinguish between three groups of investors that we assume roughly correspond to investors belonging to the social classes identified by Piketty for thinking about distributional matters, mainly the bottom 50 percent (conservative), the middle 40 percent (moderate), and the upper 10 percent (aggressive). Each investor category has different saving rates and risk aversion parameters. For the time being we assume away the existence of idiosyncratic risk for investors, 21

Figure 7: Wealth distribution (with labor income) at the end of 30 periods, with leverage (αt ≤ 2), no idiosyncratic shocks (a) Starting wealth 10k

(b) Starting wealth 50k

Figure 8: Wealth distribution (without labor income) at the end of 30 periods, lower investors constrained to αt ≤ 0.1, no idiosyncratic shocks (b) Starting wealth 10k, with leverage (αt ≤ 2) for top 10% investors

(a) Starting wealth 10k, without leverage (αt ≤ 1) for other investors

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Figure 9: Wealth distribution (with labor income) at the end of 30 periods, lower investors constrained to αt ≤ 0.1, no idiosyncratic shocks (b) Starting wealth 10k, with leverage (αt ≤ 2) for top 10% investors

(a) Starting wealth 10k, without leverage (αt ≤ 1) for other investors

considering that there are no winners or losers in the stock market, but rather that all investors have access to identical investment opportunities. In a second set of simulations, we will specifically consider the impact of idiosyncratic capital market risk on the wealth distribution. We find that the differences in saving rates (capping consumption) and risk aversion alone are sufficient to impact the wealth distribution over time, and that the availability of leverage for some investors (the upper 10 percent) creates fatter tails. The presence of labor income does not change these results, though it does create a greater degree of dispersion with respect to the end wealth distribution (due to the presence of idiosyncratic shocks to labor income). We can also use this basic framework to test for the impact of higher expected returns available to some investors. For the time being, we have limited our simulations to the constraint that some investors on the lower end of the distribution are limited to investing in low risk assets with lower expected return. The simulations show the increase in wealth inequality resulting from this constraint. We can prolong this work by studying the impact of informational advantages that would allow investors on the higher end of the distribution to benefit from investment opportunities that may allow them to earn expected returns that are slightly higher, in the long run. Overall, using a dynamic model of asset accumulation with heterogeneous investors, we highlight the important role of informational differences, risk aversion, saving rates and leveraging in terms of their contribution to wealth disparities. As shown, though those results are obtained in stochastic approach the outcomes are less related to stochastic shocks but rather to some feedback and scale effects operating in favor of some investors in the financial market.

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References [1] Aghion, P. (2002). Schumpeterian Growth Theory and the Dynamics of Income Inequality, Econometrica, vol. 70, 3: 855-882 [2] Aiyagari, S. R. (1994). Uninsured idiosyncratic risk and aggregate saving. Quarterly Journal of Economics, 109(3), 659. [3] Angeletos, G. M. (2007). Uninsured idiosyncratic investment risk and aggregate saving. Review of Economic Dynamics, 10(1), 1-30. doi: 10.1016/j.red.2006.11.001 [4] Barsington, Kato and Semmler (2010). Transitioning out of Poverty. Metroeconomica, Vol. 61, No. 1: 68-95. [5] Becker, G.S. (1962). Investment in Human Capital, Journal of Political Economy, Vol. 70: S9-S49. [6] Becker, G. S., and Tomes, N. (1979). An equilibrium theory of the distribution of income and intergenerational mobility, Journal of Political Economy, 87 (6), pp. 1153–89. [7] Benhabib, J., & Zhu, S. (2008). Age, luck, and inheritance: Cambridge, Mass. [8] Benhabib, J., Bisin, A., & Zhu, S. (2011). The Distribution of Wealth and Fiscal Policy in Economies with Finitely Lived Agents. Econometrica, 79(1), 123-157. [9] Benhabib, J., Bisin, A., & Zhu, S. (2014). The Wealth Distribution in Bewley Models with Investment Risk. NBER Working Paper No. 20157. [10] Bowles, S., Gintis, H. (2002). The inheritance of inequality, Journal of Economic Perspectives, 16 (3), pp. 3–30. [11] Brock, A. W., Durlauf, S. N. (2006). Social interactions and macroeconomics, in Colander, D. (ed.): Post-Walrasian Macroeconomics: Beyond the Dynamic Stochastic General Equilibrium Model, Cambridge University Press, Cambridge. [12] Brunnermeier, M. and Y. Sannikov (2009). A Macroeconomic Model with a Financial Sector. Working Paper, Princeton University, Princenton, NJ. [13] Cagetti, M. and M. De Nardi (2006). Entrepreneurship, Frictions, and Wealth. Journal of Political Economy, October, 114(5): 835-870. [14] Cagetti, M., & De Nardi, M. (2008). Wealth Inequality: Data and Models. Macroeconomic dynamics, 12, 285-313. [15] Campbell, J. and L. Viceira (2002). Strategic Asset Allocation. Oxford University Press: Oxford, UK. 24

[16] Capgemini and RBC Wealth Management (2014). World Wealth Report [17] Carroll, C., J. Slacalek, J. and K. Tokuoka (2014). The Distribution of Wealth and the Marginal Propensity to Consume. European Central Bank, Working Paper Series, No. 1655 [18] Chakrabarty, H., H. Katayama, and H. Maslen (2008). Why Do the Rich Save More? A Thoery and Australian Evidence. Economic Record Sep2008 Supplement, 84: S32-S44. [19] Chiarella C., C. Hsiao and W. Semmler (2007). Intertemporal Investment Strategies under Inflation Risk, Research Paper Series 192, Quantitative Finance Research Centre, University of Technology, Sydney. [20] Conley, D. (1999). Being Black, Living in the Red: Race, Wealth and Social Policy in America. Berkeley and Los Angeles: University of California Press. [21] Duesenberry, J. (1949). Income, Saving, and the Theory of Consumer Behavior. Harvard University Press:Cambridge, MA. [22] Dynan, K., J. Skinner and S. Zeldes (2004). Do The Rich Save More? Journal of Political Economy, 112(2): 397-444. [23] European Central Bank (2013). The Eurosystem Household Finance and Consumption Survey Results: From the First Wage. Statistics Paper Series. No 2/April 2013. [24] Fernholz, R., & Fernholz, R. (2014). Instability and Concentration in the Distribution of Wealth. Journal of Economic Dynamics & Control, 44, 251269. [25] Fisher, I. (1930). The Theory of Interest. The Macmillan Company: New York, NY. [26] Friedman, M. (1953). Choice, Chance, and the Personal Distribution of Income. Journal of Political Economy August 42(4): 277-90. [27] Friend, I. and I. B. Kravis (1957). Consumption Patterns And Permanent Income. American Economic Review 47(2): 536-555. [28] Goldin, C. D., & Katz, L. (2008). The race between education and technology. Cambridge, Mass.: Belknap Press of Harvard University Press. [29] Greiner, A., Semmler, W., and Gong, G. (2005). The Forces of Economic Growth: A Time Series Perspective, Princeton University Press, Princeton, NJ. [30] Grüne, L., & Pannek, J. (2011). Nonlinear Model Predictive Control. Theory and Algorithms. London: Springer-Verlag.

25

[31] Hicks, J.R. (1950). A Contribution to the Theory of the Trade Cycle. Oxford University Press: London, UK. [32] Huggett, M. (1993). The risk-free rate in heterogeneous-agent incompleteinsurance economies. Journal of Economic Dynamics and Control, 17(5-6), 953-969. [33] Kaldor, N. (1956). Alternative Theories of Distribution. Review of Economic Studies, Vol. 23: 83-100. [34] Kaldor, N. (1961). Capital Accumulation and Economic Growth. In Friedrich A. Lutz and Douglas C. Hague (eds.), The Theory of Capital. Proceedings of a Conference Held by the International Economics Association, pp. 177-222. St. Martin’s Press, New York. [35] Kalecki, M. (1951). The Distribution of the National Income. In: Irwin, Richard D. (ed.) American Economics Association, Readings in the Theory of Income Distribution, pp. 197-220. [36] Keynes, J.M. (1936). The General Theory of Employment, Interest, and Money. Harcourt, Brace: New York, NY. [37] Klass, O. S., Biham, O., Levy, M., Malcai, O., & Solomon, S. (2007). The Forbes 400, the Pareto Power-Law and Efficient Markets. The European Physical Journal B - Condensed Matter and Complex Systems, 55, 143-147. [38] Krugman, P. (1994). Past and Prospective Causes of High Unemployment, Federal Reserve Bank of Kansas City Economic Review, Fourth Quarter 1994: 23-43. [39] Krusell, P., & Smith Jr, A. A. (1998). Income and Wealth Heterogeneity in the Macroeconomy. Journal of political economy, 106(5), 867. [40] Kuznets, S. (1955). Economic Growth and Income Inequality. American Economic Review, Vol. 45: 1-28. [41] Mersch, Y. (2014). Keynote speech, Corporate Credit Conference, Zurich (17 October 2014). [42] Modigliani, F. and A. Ando (1960). “The Permanent Income and Life Cycle Hypothesis Of Saving Behavior: Comparison and Tests, in Consumption and Saving.” edited by Irwin Friend and Robert Jones. Philadelphia: University of Pennsylvania II: 49-174. [43] Munk, C., C. Sørensen and T. Nygaard Vinther (2004). Dynamic Asset Allocation under Mean-reverting Returns, Stochastic Interest Rates and Inflation Uncertainty: Are Popular Recommendations Consistent with Rational Behavior? International Review of Economics & Finance, 13(2): 141-166.

26

[44] Murphy, K.M., Riddell, W.C., and Romer, P.M. (1998). Wages, Skills, and Technology in the United States and Canada, In Elhanan Helpman (ed.), General Purpose Technologies and Economic Growth, pp. 283-309. MIT Press, Cambridge, MA. [45] Nirei, M., & Souma, W. (2007). Two Factor Model of Income Distribution Dynamics. Review of income and wealth, 53(3), 440-459. [46] Platen, E. and W. Semmler (2009). Asset Markets and Monetary Policy. Research Paper Series 247, Quantitative Finance Research Centre, University of Technology, Sydney. [47] Pigou, A. C. (1951). Professor Duesenberry On Income And Savings. Economic Journal, 61(244): 883-885. [48] Piketty, T. (2013). Le capital au XXIe siècle. Paris: Seuil. [49] Piketty, T., & Saez, E. (2003). Income Inequality in the United States, 1913-1998. The Quarterly journal of economics, 118(1), 1-39. [50] Quadrini, V. (1999). The importance of entrepreneurship for wealth concentration and mobility. Review of Income & Wealth, 45(1), 1-19. [51] Quadrini, V. (2000). Entrepreneurship, Saving, and Social Mobility. Review of Economic Dynamics, 3(1), 1-40. doi: 10.1006/redy.1999.0077 [52] Reich, R. (2014). The Year of the Great Redistribution. Retrieved January 6, 2014 from http://robertreich.org/post/72265646495 [53] Reich, R. (2012). A Diabolical Mix of US Wages and European Austerity. Financial Times. Retrieved from http://www.ft.com/cms/s/0/7b84f1c8a977-11e1-9772-00144feabdc0.html - axzz2pTSSy2a8 [54] Richardson, D.J. (1995). Income Inequality and Trade: How to Think, What to Conclude, Journal of Economic Perspectives, Vol. 9: 33-55. [55] Riley, J.G. (1976). Information, Screening and Human Capital, American Economic Papers, Papers and Proceedings, Vol. 66: 254-260. [56] Romer, P.M. (1990). Endogenous Technological Change, Journal of Political Economy, Vol. 98: S71-102. [57] Rubart, J., A. Greiner and W. Semmler (2004). Economic growth, skillbased technical change and wage inequality : a model and estimations for the U.S. and Europe, Publications of Darmstadt Technical University, Institute of Economics (VWL) 22656, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute of Economics (VWL).

27

[58] Saltz, I. (1999). An Examination of the Causal Relationship Between Savings and Growth in the Third World. Journal of Economics & Finance, 23(1): 90. [59] Spilerman, S. (2000). Wealth and Stratification Processes, American Review of Sociology 26(a): 497–524. [60] Stiglitz, J.E. (1975). The Theory of Screening, Education, and the Distribution of Income., American Economic Review, Vol. 65: 283-300. [61] Vickrey, W. (1947). Resource Distribution Patterns and the Classification of Families. Studies in Income and Wealth, NBER, Volume 10. [62] Wachter, J. (2002). Portfolio and Consumption Decisions under MeanReverting Returns: An Exact Solution for Complete Markets. Journal of Financial and Quantitative Analysis, 37(1): 63-91. [63] Wolff, E. N. (1996). Top Heavy. New York: The New Press. [64] Wolff, E. N. (2004). Changes in household wealth in the 1980s and 1990s in the U.S. Working Paper No. 407. Annandale-on-Hudson, NY: The Levy Economics Institute of Bard College. [65] Wolff, E. N. (2006). Changes in household wealth in the 1980s and 1990s in the U.S. In E. P. Ltd. (Ed.), International Perspectives on Household Wealth (pp. 107-150). Northampton, MA. [66] Wolff, E. N. (2010). Recent trends in household wealth in the United States: Rising debt and the middle-class squeeze - an update to 2007. Working Paper No. 589. Annandale-on-Hudson, NY: The Levy Economics Institute of Bard College. [67] Wolff, E., & Zacharias, A. (2007). The Impact of Wealth Inequality on Economic Well-Being. Challenge, 50(4), 65-87. [68] Yellen, J. (2014). Perspectives on Inequality and Opportunity from the Survey of Consumer Finances. Speech given at the Conference on Economic Opportunity and Inequality, Federal Reserve Bank of Boston, Massachusetts (October 17, 2014) available at http://www.federalreserve.gov/newsevents/speech/yellen20141017a.htm#f15

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