The role of credit on wealth inequality in the USA:

The role of credit on wealth inequality in the USA: 1980 2012. Rodolfo E. Oviedo Moguel Washington University in St. Louis Important: click here for the latest version Abstract In the USA, the share of total household wealth held by the richest 1% increased from 23.5 % in 1980 to 41.8% in 2012. A sharp reduction in the saving rate of the bottom 90% accounts for around 40% of the change. I construct a quantitative model that, under a reasonable calibration, is able to replicate this fact. I then use the model to decompose the total variation among some of the most likely candidates: (i) changes in credit conditions, (ii) increase in the concentration and riskiness of labor income and, (iii) reforms to the tax code. This decomposition exercise shows that, in the context of my model, the relaxation of the borrowing constraint explains around 50% of the increase in the share of wealth going to the top 1%. The credit market channel is key to match the saving patterns observed in the data and it has been ignored by the previous quantitative literature studying the changes in wealth inequality over the last 30 years. JEL lassification:d14,d31,d33,e21,e62. Keywords: Wealth Distribution, Debt, redit I am indebted to my advisor Michele Boldrin for his excellent guidance. My committee members Gaetano Antinolfi and David Wiczer provided valuable suggestions. I am also grateful to Per Krusell and Joachim Hubmer for providing me with helpful references. Part of this paper was written at the entral Bank of Mexico (Banxico) where I had very useful conversations with Raúl Ibarra, Juan Ramón Hernández, Santiago Bazdresch, Alfonso ebreros, Gustavo Leyva and Adrián de la Garza. Felipe Meza and Miguel Faria-e-astro also provided excellent suggestions. E-mail address: roviedomoguel@wustl.edu. For the latest version of this paper please go to my website.

1 Introduction. Wealth concentration in the USA has increased sharply during the last 40 years. According to Saez and Zucman (2016), the share of wealth held by the top 1% increased from 24% in 1980 to 42% in 2012. The Gini index of wealth inequality moved from.79 in 1983 to.87 in 2013, Wolff (2014). In recent years, there has been an intense debate about the causes of this increase, and several policies have been proposed to reverse this trend. In this paper, I contribute to our understanding of the possible causes of the increase in wealth concentration by evaluating the impact of changes in the credit conditions, defined as an increase in the ability to borrow, on the distribution of wealth after 1980. In the first section of the paper, I decompose changes in the wealth holdings of the top 1%, the next 9% in the top decile (hereafter [[90-99] %), and the bottom 90% into volume and capital gain effects. hanges in the stock of wealth due to savings are volume effects, while changes due to fluctuations in the market value of wealth (i.e. changes in the price of stocks or housing) are capital gains effects. I found that, between 1980 and 2012, most of the increase in the fraction of wealth held by the top 1% can be explained by volume effects: the rate of growth of wealth coming from savings for the top 1% was consistently higher relative to the other groups, and this fact explain most of the increase in concentration. The overall effect of differences in capital gains between groups was, in fact, slightly negative: it reduced wealth concentration. This is due to a well-known fact: the bottom 90% holds most of its wealth in housing which was the best performing asset class from 1980 to 2007. The increase in the price of housing during the period was a force toward equality. 1 To then understand the differences in the rate of wealth accumulation among these three groups, I compute the savings rate for each of them. Between 1950 and 1980, the savings rate of the bottom 90% and [90-99] % groups was stable, around 5 and 29%, respectively. In the next three decades, 1980-2010, the average saving rate of both groups decreased significantly to 2% and 15%, respectively. The pattern for the top 1% was different: its savings rate increased from an average of 30% between 1950 and 1980 to 37% between 1980 and 2012. The divergence in saving rates between the top 1% and the remaining groups was the most important force driving wealth concentration. To quantify the contribution of the changing saving patterns to the increase in wealth concentration, I construct hypothetical wealth holdings for the bottom 90% and the [90-99] % under the assumption that saving rates are kept at their 1950-1980 average during 1980-2012. Then, I estimate the wealth shares implied by these hypothetical series. If we assume that the bottom 90% kept saving at their historical average of 5%, then the share of the top 1% would have increased from 24% to 34% instead of 42%. This attributes around 40% of the top percentile s increase to the change in the saving behavior of the bottom 90%. Assuming 1 The subsequent crash reduced the equalizing effect of house pricing but did not eliminate it completely. 1

that both the bottom 90% and the top [10-1] % did not change their saving behavior during 1980 2012 implies that the share of the top 1% would have reached 30% in 2012 instead of the actual 42%. 2 In the second section of my paper, I built a general equilibrium model based on Bewley (1977), to quantify the importance of different plausible hypotheses in the evolution of the wealth distribution: i) changes in credit conditions, (ii) increase in the concentration and riskiness of labor income and, (iii) reforms to the tax code (reductions in corporate and personal income taxation). hanges in credit conditions are defined as increases in the ability of households to borrow and are modeled as a loosening of borrowing constraints. The initial stationary distribution of the model is calibrated to match the wealth distribution in 1980. The values for the taxation system and the labor income process after 1980 are taken from the data, and the path for the borrowing constraints is calibrated to match the evolution of the ratio of non-mortgage debt to disposable income. The model is successful at generating a transition path that matches the increase in wealth concentration observed in the data. ounter-factual simulations indicate that the credit market channel explains approximately half of the increase in wealth concentration. When all the other shocks, except the credit channel, are fed into the model, wealth concentration measured as the share of the top 1% increases only half as much compared to the baseline scenario in which the credit market channel is included. The relaxation of the borrowing constraints causes the originally constrained households to accumulate more debt and decreases the precautionary savings of those close to the constraint since the likelihood of hitting it decreases. In addition to these two forces, the increase in the real interest rate caused by the contraction in the overall supply of savings increased the saving rate of the top groups, which further increased wealth concentration. The credit channel is fundamental to match the pattern of savings observed in the data: a decreased in the overall saving rate fueled by the change of behavior of the bottom groups and a slight increase in the saving rate of the top 1%. The increase in concentration of labor income and the tax reforms, during this period also contributed to the concentration of wealth. The top wage earners tend to be the wealthiest agents in the economy and a higher share of total income going to this group mechanically increases their savings flow relative to other groups, thereby increasing concentration. The reduction in the progressivity of personal and corporate taxation increased the incentive to save for individuals from the top groups and especially from the top 1%, since they faced significantly lower tax rates on the return to capital. A higher savings rate for top groups combined with a stable saving rate for other groups generated wealth concentration. When all the shocks except for the higher concentration of labor income and the changes in taxation are included, the share of wealth owned by the top 1% increases by only 45% compared 2 Even if saving rates had remained constant, there would have been an increase of 6 points in the share of the top 1%. This is because the share of total labor income going to the richest 1% increased from 4.7% in 1980 to 8.9% in 2012. 2

with the baseline case. Finally, I should note that the last shock, increased riskiness of labor income, was a force toward equality. A riskier income process increased overall precautionary savings and this effect was particularly strong for the bottom groups, which were closer to the borrowing constraint. When only this shock is considered, the share of the top 1% in total wealth decreased. The two papers closest to mine are those of Kaymak and Poschke (2016) and Hubmer, Krusell, and Anthony A. Smith (2016). They use two variations of the Bewley model to study the effects of changes in the labor income process and in income taxation on the distribution of wealth. While there is no question about the relevance of these changes in the saving behavior of different groups, it is important to note that their overall effect in a Bewley model in which changes in the borrowing constraints are not considered- is an increase in the aggregate saving rate. This prediction is counterfactual as the aggregate saving rate decreased from 12% in 1980 to 2% in 2007. Given that the leading papers in the field abstract from the forces that decreased the overall saving rate and particularly those of the bottom groups, my main contribution is the explicit introduction of the credit market channel, which is crucial to matching the observed behavior of the saving rates and hence the causes underlying the increase in wealth concentration. 3

2 Facts about wealth inequality in the USA. Saez and Zucman (2016) estimated the top wealth shares for USA using the capitalization method for the period 1913-2012. Wealth is defined as the current market value of all assets owned by households net of all debts. 3 Figure 1 presents the share of total net household wealth held by the wealthiest 1% of the families in USA: 0.55 Share of total household wealth. 0.5 0.45 0.4 0.35 0.3 0.25 0.2 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 Figure 1: Wealth Share of the Top 1%, 1913-2012. The share of wealth owned by the top 1% reached a peak of 51.4% in 1928 followed by a dramatic decrease during the Great Depression and World War II. It stabilized around 29% between 1950 and 1968 and then suffered another significant decrease that started in 1968 reaching its lowest level at 22.9% during 1978. Starting in the early 80s, and accelerating around 1986, the wealth share of the top 1% experienced a dramatic recovery reaching 41.8% in 2012. In this paper, I focus on studying the causes of the increase in wealth inequality between 1980 and 2012. What happened to the wealth share of the families outside of the top 1%? For simplicity, we divide the population according to their wealth holdings in three categories: families in the bottom 90%, the [90-99]% (the top decile excluding the top 1%) and the top 1%. The key events of the period 1950-2012 were the following: the share of the group [90-99]% was stable around 43% between 1950-1978, it then monotonically decreased during 1978-1988 stabilizing at around 38%. The Great Recession did not affect the share of this group significantly. The share of the bottom 90% went from 26% in 1962 to 36% in 1986. In 1987, 3 Assets include all the non-financial and financial assets over which ownership rights can be enforced and that provide economic benefits to their owners. 4

it started a decreasing trend that was intensified by the Great Recession reaching 23% in 2012. So far, we have talked about the share of wealth going to each group in the distribution. In Figure 2, we can see the evolution of the stock of wealth of the three groups in real terms. The wealth of the three groups increased almost monotonically between 1980-2000. It then decreased around the bust of the dot-com bubble -specially for the top 1%- and increased between 2002 and 2007. The Great Recession affected the three groups significantly but the top 1% had already surpassed its 2007 level by 2012 while the Bottom 90% and the [90-99]% were still considerably bellow its pre-crisis level. 6 5 4 3 2 1 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 Bottom 90 % [90-99] % Top 1 % Figure 2: Wealth by group in 2010 USD [1980 =1] 2.1 A framework to understand changes in wealth inequality. In this subsection, I introduce a framework in which it is possible to decompose the changes in the level of wealth holdings of the top 1%, the [90-99] %, and the bottom 90% into volume and capital gain effects. hanges in the stock of wealth due to savings are volume effects, while changes due to fluctuation in the market value of wealth (i.e. changes in the price of stocks or housing) are capital gains effects. Let denote a group of individuals with wealth in period t equal to W t, which is equal to the sum of the market value of all asset classes held by this group (housing + equities + sole proprietorship and partnerships + fixed income + pension funds - debt): W t = iɛi W t (i) 5

The wealth of group in t + 1 is a function of changes in price of wealth of group, q t, and the flow of savings, S t : [ ] Wt+1 = [1 + qt ][Wt + St ] = Wt [1 + qt ] 1 + S t Wt (1) In the previous expression, it is assumed that savings are made before the realization of price changes. Also, qt is defined to be the price change of wealth between period t and period t+1 and is a weighted average of the price change of every asset class, q t (i): q t = iɛi [ W t (i) + St ] (i) q Wt + St t (i) (2) In equation 2, the implicit assumption is that the return of group, within each asset class, i, is equal to the aggregate return of that asset (i.e the average change in the prices of houses or equities). This assumption reflects the lack of individual level data on the composition of the portfolio for different wealth groups. I will discuss the potential effects of this assumption on the decomposition exercise at the end of the section. Using equation 1, we can obtain an expression for the share of wealth going to group as follows: [ ] 1 + s t Y t W t+1 = W t [1 + qt ] W t+1 W t [1 + q t ] W t [ 1 + styt W t ] (3) Notice that, in equation 3, the flow of savings, St, is expressed as s t Yt, where s t and Yt denote the net saving rate and disposable income of group respectively. hanges in the share of wealth owned by group are a function of the ratios s c t/s t, qt c /q t and Yt c /Y t. Intuitively, if the saving rate, the capital gains or the income of group are above the average then the share of wealth going to this group will increase. If, instead of considering the change between t and t+1, we are interested in the change between t and t+j, it is possible to iterate on equation 3 and obtain: W t+j = W t W t+j W t t+j 1 i=t [ 1 + q i 1 + q i ][1 + s i Y i Wi 1 + s iy i W i ] Let a t+j t and b t+j t be defined as: a t+j t = t+j 1 i=t [ 1 + q i 1 + q i ] b t+j t = t+j 1 i=t [ 1 + s t Y t Wt 1 + sty it W t ] 6

Then, W t+j = W t W t+j W t a t+j t b t+j t (4) Thus, a t+j t and b t+j t summarize the change in the wealth share of group between t and t+j due to capital gains and savings respectively. To bring this framework to the data, I need series for {W t, q t } and {Wt, qt }. Given that my interest is in the increase in wealth concentration and that the groups inside of the top 1% played an important role in it, I use the data provided by Saez and Zucman (2016) for computing equation 4. Their estimations of the top wealth shares are based on administrative tax data and have the advantage of capturing the movements at the very top of the wealth distribution. Alternative estimates based on the Survey of onsumer Finance (Wolff (2014)) sub estimate families at the very top and hence are not ideal for my purposes. W t, the value of total net household wealth, is taken from the US Financial Accounts. For each type of asset, i, q t (i) is estimated as a residual using W t (i) from the Financial Accounts and the Investment flows for each period which are obtained from additional sources. The movements that are not explained by investment flows are attributed to price changes. The aggregate capital gains, q t, are then defined as the weighted average of each asset capital gains, q t (i): q t = iɛi [ Wt (i) + S t (i) W t + S t ] q t (i) The value of Wt for the bottom 90% and different groups inside the top 10% of the wealth distribution come from the estimations of Saez and Zucman (2016). Wt is obtained using the capitalization method: for each asset class, i, we observe both its aggregate stock, W t (i), (from the US financial Accounts) and its total capital income reported by taxpayers to the IRS, I t (i). 4 The capitalization factor for this asset is then defined as F t (i) = [W t (i)/i t (i)] which is used to estimate Wt (i) as It (i)f t (i).furthermore, the series of q t (i) allow makes it possible to construct qt using equation 2. Figure 3 presents the values of a t+j t and b t+j t for the top 1% with t = 1980 and j = 1,..., 32. The bulk of the increase in the wealth share of the top 1% was due to volume effects (changes in relative savings and disposable income). The role of changes in relative capital gains was marginal and negative in the years after the bust of the dot com bubble. The reason behind this finding is the following: the bottom groups held most of its wealth in housing and this was the best performing asset in terms of capital gains. The increase in the price of Housing between 1980 and 2007 was a force toward equality. The subsequent crash partially reverted this situation. 4 There are some assets, like own-occupied housing, and pension funds, that do not generate taxable income and, for those cases, Saez and Zucman use additional sources. 7

1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1 0.9 0.8 1980 1984 1988 1992 1996 2000 2004 2008 2012 ab a b Figure 3: a t+j t, b t+j t and a t+j t b t+j t for the Top 1% Figure 4 presents the compounded capital gains by each asset class, (i), for t = 1980 and j = 1, 2,..., 32. t+j t (i) = t+j 1 k=t [ ] 1 + qk (i) = [1 + qt (i)][1 + qt+1(i)] [1 + qt+j 1(i)] Figure 4: ompounded capital gains by asset class 8

From Figure 3, it is possible to conclude that most of the increase in wealth concentration was due to volume effects. In other words, the growth rate of wealth of the top 1% coming from savings was consistently higher than the one of the average between 1980 and 2012: s T op1% t Y T op1% t W T op1% t s ty t W t for t = 1980,..., 2011 To understand the mechanics behind this fact, it is necessary to observe the behavior of s c t/s t and Y c t /Y t for different groups. From equation 1, it is possible to obtain s c t as a residual: s t = [ W t+1 q t ] 1 Wt Yt (5) The saving rate of the bottom 90%, the [90-99]% and the top 1% are presented in Figure 5: 0.5 0.4 0.3 0.2 0.1 0-0.1 1950-1954 1955-1959 1960-1964 1965-1969 1970-1974 1975-1979 1980-1984 1985-1990 - 1989 1994 1995-2000 - 2005-2008 - 1999 2004 2007 2010 2011 Bottom 90% [90-99] % Top 1% Figure 5: Saving rate by wealth class The saving rate of the Bottom 90% decreased continuously from an stable average of 5% between 1950 and 1980 to -8% in 2006. It then bounced back to 0% after the Great Recession. The saving rate of the group [90-99]% followed a similar pattern. It was stable around 29% between 1950 and 1980 and then started falling until reaching 0% in 2000. It then partially recovered and reached 14% in 2011. The saving rate of the top 1% showed much more variability than the one of the other groups but, overall, it went from an average of 30% between 1950 and 1980 to 37% between 1980 and 2012. It is important to mention that these saving rates are synthetic in the sense that they abstract from mobility between groups. This limitation comes from the fact that it is not possible to follow a particular group of individuals over time using administrative tax data. The same situation emerges while using the Survey of onsumer Finances. 5 5 Bosworth and Anders (2008) estimates the saving rates by wealth groups using supplementary questions of the PSDI and conclude that measurement errors are a particularly serious problem using this panel. 9

The fact that the bottom 90% and the [90-99]% decreased their saving rates while the one of the top 1% increased slightly explains an important fraction of the increase in wealth concentration. In addition to this fact, there were also movements in the share of total income income going to each wealth group, Yt /Y t. Figure 6 summarize this changes. The income share of the Bottom 90% was very stable around 69% between 1950 and 1985, it then decreased continuously until reaching 60% in 2012. The income share of the group [90-99]% has been stable around 22% during 1950-2012. There was not a major trend over the period. The share going to the richest 1% went from 9% in 1980 to 17.9% in 2012. It almost doubled in a period of 32 years. Figure 6: Share of Disposable Income by wealth class 2.2 ounter-factual exercise: the effect of the change in the saving patterns on wealth inequality. To quantify the contribution of the changing saving patterns to the increase in wealth concentration, I construct hypothetical wealth holdings for the bottom 90% and the [90-99] % under the assumption that their saving rates are kept at their 1950-1980 average between 1980 and 2012. Then, I estimate the wealth shares implied by these hypothetical series. The original accumulation equation is given by: Wt+1 = [1 + qt ][Wt + s t Yt ] To construct the hypothetical wealth holdings for the bottom 90% and the [9 0-99]% groups between 1980 and 2012, I substitute s t by s t which is defined as the average saving rate of group between 1950 and 1980. The hypothetical wealth holdings are given by: 10

Wt+1 = [1 + qt ][Wt + s t Yt ] I then use the series of Wt to compute hypothetical wealth shares under three different assumptions: i) the bottom 90% is assumed to save its historical average of 5% between 1980 and 2012, ii) the group [90-99]% is assumed to save its historical average of 29% between 1980 and 2012, iii) Both the bottom 90% and the [90-99]% are assumed to save their 1950-1980 average between 1980 and 2012. The results of these simulations are presented in Figure 6. 0.41 0.39 0.37 0.35 0.33 0.31 0.29 0.27 0.25 0.23 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 Hypothetical Bottom 90% Hypothetical [90-99]% Hypothetical Bottom 90% and [90-99]% Data Figure 7: Share of the top 1%: observed and hypothetical. If we assume that the bottom 90% kept saving at their historical average of 5%, then the share of the top 1% would have increased from 24% to 34% instead of 42%. This attributes around 40% of the top percentile s increase to the change in the saving behavior of the bottom 90%. Assuming that both the bottom 90% and the [90-99] % did not change their saving behavior during 1980 2012 implies that the share of the top 1% would have reached 30% in 2012 instead of the actual 42%. Notice that even if the saving rates of the bottom 90% and the [90-99] % had remained constant, there would have been an increase of 6 points in the share of the top 1%. This is mainly because the share of total labor income going to the richest 1% increased from 4.7% in 1980 to 8.9% in 2012 and also because of the slight increase in the saving rate of this group. Its important to mention that these estimations ignore general equilibrium effects and they are an accounting exercise that provide us with a first -imperfect- estimation of the importance of the change in the pattern of savings. 11

3 Model In Section 2, we established that around 40% and 60% of the increase in the wealth share of the top 1% can be attributed to the change in the saving patterns of the bottom 90% and the [90-99]%. Given this fact, it logically follows that studying the causes behind the decrease in the saving rate of these groups is fundamental to understand the increase in wealth concentration. The empirical literature has found that changes in credit conditions, defined as shocks that increased the household s ability to borrow, contributed significantly to the decrease in the saving rate of the bottom groups. Mian and Sufi (2011) show that the increase in the price of housing, which is typically used as collateral for borrowing, explains a good portion of the increase in non mortgage debt and the decline in the saving rates between 2002 and 2006. This evidence suggest that an important proportion of households were credit constrained. arroll (1997) argues that various financial innovations allowed households to transform future income into current purchasing power, thereby reducing saving rate of previously credit constrained households. Along the same lines, Parker (2000) concludes that the increase in debt can explain one third of the observed decline in the overall saving rate. The quantitatively macroeconomic literature uses the Bewley (1977) model as the standard framework to study the wealth distribution. In a Bewley model, each agent faces uncertainty regarding labor income and, since markets are incomplete, it is optimal to self-insure against labor income shocks. Different realizations of income shocks generate different saving rates and this determines a non degenerated distribution of wealth. Aiyagari (1994), Hansen and Imrohoroglu (1992) and Huggett (1996) solved general equilibrium versions of the Bewley model. Several modifications have been proposed to the basic model in order to better match the observed distribution of wealth. De Nardi and Fella (2017) surveyed the different versions built on top of the basic Bewley model proposed in the literature in the recent years. In the next section, I construct a general equilibrium model based on Bewley (1977), to quantify the importance of different plausible hypotheses on the evolution of the wealth distribution: i) changes in credit conditions, (ii) increase in the concentration and riskiness of labor income and, (iii) reforms to the tax code (reduction in corporate and personal income taxation). hanges in credit conditions are defined as increases in the ability of households to borrow and are parsimoniously modeled as a loosening of borrowing constraints. The initial stationary distribution of the model is calibrated to match the wealth distribution in 1980. The values for the taxation scheme and the labor income process after 1980 are taken from the data, and the path for the borrowing constraints is calibrated to match the evolution of the ratio of non-mortgage debt to disposable income. The two papers closest to mine are Kaymak and Poschke (2016) and Hubmer, Krusell, and Anthony A. Smith (2016). Both papers use different variations of the Bewley model to study the effects of i) changes in the labor income process (higher concentration and riskiness) 12

and ii) reforms in the tax code (reductions in progressivity and corporate taxation) on the distribution of wealth in the previous 50 years. While there is no doubt that these shocks are important for the saving decisions of individuals, the overall effect of them in a Bewley model is an increase in the total saving rate of the economy. Given that the leading papers in the field abstract from the forces that decreased the saving rate of the bottom groups, my paper contributes to the literature by explicitly modeling one of the key forces behind this decrease: changes in credit conditions. I find that this channel is crucial to match the observed patterns of the saving rates and hence the causes responsible for the increase in wealth concentration. 3.1 Description of the model The economy is populated with a continuum of infinitely lived, ex-ante identical agents that choose streams of consumption to maximize the their expected lifetime utility: {[ [ t E 0 t=0 s=0 ]} β s ]u(c s ) The instantaneous utility function takes the RRA form with parameter σ: (6) u(c t ) = c1 σ t 1 σ Each period, the agent faces the following budget constraint: c t + [a t+1 a t ] = [w t l t (p t, v t ) + r t a t ][1 τ t (I t )] + T t (7) I t = w t l t (p t, v t ) + r t a t (8) In equation 7, c t denotes the level of the consumption good and a t+1 is an asset that provides (1 + r t+1 )a t+1 units of the consumption good the next period. w t and r t are the market wage and real interest rate respectively. The agent does not value leisure and always supplies the full amount of effective units of labor, l t (p t, v t ). I t denotes the total pretax income from labor and capital which is taxed at a rate τ t (I t ). The tax rate τ t (I t ) is an increasing function of total income I t. Lastly, T t is a lump-sum transfer financed with the proceeds from taxation. In addition to the budget constraint, the agent also face a borrowing constraint: a t a t (9) There are two sources of uncertainty for the agent: the discount factor, β t and the effective units of labor, l t (p t, v t ). At every period t, the factor at which the agent discounts the next 13

period consumption, β t+1, is known. However, the discount factor β t+2 is stochastic and assumed to follow a Markov process: 6 β t = ρ β β t 1 + (1 ρ β )µ β + ɛ β t ɛ β t N(0, σ β ) (10) The effective units of labor, l t (p t, v t ), are a function of p t and v t, the persistent and transitory components of labor income. They are assumed to behave according to: v t N(0, σ v t ) (11) p t = ρ p p t 1 + ɛ t ɛ p t N(0, σ p t ) (12) Piketty and Saez (2003) estimated top wage shares for the USA and found that the share of the total wage bill going to the top wage earners has increased sharply in the previous 35 years. To be able to match this fact, I follow Hubmer, Krusell, and Anthony A. Smith (2016) and use the following functional form for l t (p t, v t ): l t (p t, v t ) = ψ t (p t )exp(v t ) (13) Let F pt denote the unconditional cumulative distributive function of p t. The function ψ t (p t ) is defined as follows: if the value of p t is less than or equal to the 90 percentile of F pt then ψ t (p t ) = exp (p t ) (the standard case); if the realization of p t is in the top 10% then ψ t (p t ) takes the following form: ( ) Fκ 1 Fpt (p t ) 0.9 t (14) 1 0.9 F κt is the cumulative distributive function of a Pareto distribution with coefficient κ t and lower bound exp (F pt (.9)). Since the right tail of the labor income distribution is very well approximated by a Pareto distribution, changes in the tail parameter κ t can be used to match the fraction of labor income going to the top 10%, top 1% and the top.1%. So far, we described the problem that each agent faces taking the sequence of w t, r t and the taxation scheme as given. The production function is obb-douglas, firms are perfectly competitive and the overall supply of effective units of labor is equal to 1. The market wage and real interest rate are then: r t = F K (K t, L t ) δ (15) w t = F L (K t, L t ) (16) 6 This kind of heterogeneity was introduced by Krusell, Smith, and Jr. (1998) and is a parsimonious way of obtaining a realistic level of wealth concentration. 14

The government budget constraint is always balanced: the homogeneous transfer, T t, is financed with resources coming from taxation. An stationary equilibrium in this economy is a level of capital K and the prices associated to it r and w such that: given r, w and a taxes and transfer system (τ, T ), the policy function of the agents induce an invariant distribution over the unique asset in the economy a t. In equilibrium, the assets held by the agents are equal to the aggregate capital K. 3.2 Description of the exercise and calibration The objective of the model is to quantify the relative importance of i) changes in credit conditions, (ii) increase in the concentration and riskiness of labor income and, (iii) reforms to the tax code (reduction in corporate and personal income taxation) on the evolution of wealth concentration after 1980. To achieve this goal, I use the following strategy: 1. alibrate the parameters ρ β, µ β, σ β, and δ to match the share of the top 10%, top 1% and top.1% as well as the ratio K/Y observed in the data in 1980. 2. I then fed the observed paths for the taxation scheme (τ t ), the concentration of labor income (κ t ) and the riskiness of labor income (σ p t and σ v t ) between 1980 and 2012 into the model. 3. The path of a t between 1980 and 2012 is set to match the change in the ratio non mortgage debt to disposable income for the bottom 90% (Figure 8). The values for τ t, κ t, σ p t, σ v t and a t are assumed to remain fixed at their last observed value. The model eventually converge to a new stationary distribution associated to these values. During the transition from the original stationary distribution to the new one, it is assumed that the agents have full knowledge of the path of the shocks. This is an assumption that will be relaxed as a robustness check of my results. Once the transition is solved, then it is possible to compare the prediction of the model with the data and perform counterfactual exercises to estimate the relative importance of each one of the shocks in the evolution of the wealth distribution. The path of (σ p t, σ v t ) is taken from Heathcote et al. (2010) who estimated the values for the standard deviations of the permanent and transitory shocks to labor income from 1967-2000 using data from the PSID (Figure 8). The path for κ t is chosen to match the share of total wage income going to the top wage earners estimated by Piketty and Saez (2003). Since the right tail of the distribution of labor income is approximately Pareto, changing the parameter κ t in equation 16 allows me to closely match the top wage shares every period. Figure 10 present the top wage shares in the last 50 years. 15

0.38 0.33 0.28 0.23 0.18 0.13 0.08 0.03 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 Bottom 90% [90-99] % Top 1% Figure 8: Non-mortgage debt to Disposable Income Figure 9: ross-sectional Standard Deviations Lastly, Piketty and Saez (2007) estimated the effective tax rate for eleven income brackets for the years 1967-2000. The function τ(i t ) is a step function that is calibrated to match the changes in corporate and progressive taxation after 1980. After 2000, it is assumed that taxes are fixed at this level. 16

Figure 10: Share of the labor income by wage class The average of the ratio capital-output during 1960-1980 -using Piketty and Zucman (2014) data- was 3.9 which implies that µ β =.917 and δ =.05. The parameters ρ β and σ β are calibrated to match as closely as possible the shares held by the top 10% and top 1% of the wealth distribution in 1980 (ρ β =.986, σ β =.0041). The value of a t in the initial stationary distribution is the one that match the average ratio debt to income for the bottom 90% between 1960-1980. (a ss =.41). The shares of the top groups come from Saez and Zucman (2016) and the share of the Bottom 50% comes from the Survey of onsumer Finances. Given that the top of the wealth distribution is very well approximated by a Pareto distribution and that the type of uncertainty in the model yields a stationary distribution that is Pareto at the top it is possible to match very closely the distribution in 1980: Top 10% Top 1% Bottom 50% Data 65.1 % 23.5 % 1.1 % Model 64.8 % 25.79 % 1.5 % Table 1: Distribution of Wealth in 1980: data and stationary distribution 17

4 Results Figure 11 presents the share of the top 1% estimated by Saez and Zucman (2016) against the share of the top 1% implied by the model. The fit of the model is good, except for the Dot-om bubble and the Great Recession in which the predictions of the model and the data diverge. The change in the distribution of wealth in a Bewley model depends on the saving behavior of different groups and it abstracts from changes in the relative prices of assets. For this reason, any change in the shares that comes from large movements on the price of assets (like the Dot-om bubble and the aftermath of the Great Recession) is not captured in this class of models. For example, the increase in the share of the top 1% between 2007 and 2012 was mostly due to the fact that the price of housing -the main asset held by the bottom 90%- decreased significantly relative to other assets. Figure 11: Wealth Share of the Top 1%: Model (Red) and Data (Blue) In Figure 12, I evaluate the importance of the credit market channel (loosening of borrowing constraints). When all the other shocks, except for the changes in borrowing constraints, are fed into the model the share of the top 1% increases only half as much compared to the baseline scenario in which the credit market channel is included. The relaxation of the borrowing constraints causes the originally constrained households to accumulate more debt and decreases the precautionary savings of those close to the constraint since the likelihood of hitting it decreases. In addition to these two forces, the increase in the real interest rate caused by the contraction in the overall supply of savings increased the saving rate of the top groups, which further increased wealth concentration. The credit channel is fundamental to 18

match the pattern of savings observed in the data: a decreased in the overall saving rate fueled by the change of behavior of the bottom groups and a slight increase in the saving rate of the top 1%. Figure 12: Wealth Share of the Top 1%: All shocks except for redit (Blue), Data (Red) The increase in concentration of labor income and the tax reforms, during this period also contributed to the concentration of wealth. The top wage earners tend to be the wealthiest agents in the economy and a higher share of total income going to this group mechanically increases their savings flow relative to other groups, thereby increasing concentration. The reduction in the progressivity of personal and corporate taxation increased the incentive to save for individuals from the top groups and especially from the top 1%, since they faced significantly lower tax rates on the return to capital. A higher savings rate for top groups combined with a stable saving rate for other groups generated wealth concentration. When all the shocks except for the higher concentration of labor income and the changes in taxation are included, the share of wealth owned by the top 1% increases by only 45% compared with the baseline case. The last one of the shocks, the increase in the riskiness of labor income, was a force toward equality: a riskier income process increases overall precautionary savings and particularly for the bottom groups which are motivated to avoid the borrowing constraint. If we only consider this shock, the share of the top 1% would decrease from 24% to 21%. 19

In Figure 13, I consider the effect of three types of shocks in isolation: i) Only changes in the credit conditions or increase in the borrowing constraints (red line), ii) Increase in concentration of labor income (κ t ) and changes in taxation (yellow line) and iii) Increase in the riskiness of labor income (purple line). Figure 13: Yellow (τ and κ), Purple (σ p t, σ v t ), Red (a t ) 5 onclusions In this paper, I first go to the data and conclude that between 40% and 60% of the increase in wealth concentration, between 1980 and 2012, can be attributed to the dramatic decrease in the savings rate of the households at the bottom 99% of the wealth distribution. I then construct a general equilibrium model to evaluate the importance of three forces on the evolution of the wealth distribution: i) changes in credit conditions (increase in the ability to borrow), ii) reforms to the tax code, iii) changes in the labor income process. The model captures the increase in concentration. According to the counterfactual exercises, the loosening of borrowing constraints explains close to half of the increase in the share of wealth going to the top 1%. hanges in credit conditions are crucial to match the decrease in the savings rate of the bottom groups and, to the best of my knowledge, this is the first attempt to explicitly model this channel in the quantitative literature studying the causes behind the increase in wealth concentration after 1980. 20

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