Lecture Notes on Financial Market Incompleteness and Inequality c

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1 Lecture Notes on Financial Market Incompleteness and Inequality c by Dean Corbae 1 Introduction 1.1 Questions In this set of lectures, we will address questions of the following variety: 1. If financial markets are incomplete (for example, the only available asset is a noncontingent bond contracts with a borrowing limit), how much does earnings inequality account for wealth inequality? 2. How much would people be willing to pay for better (more complete) financial markets? 3. If borrowing constraints become tighter (as they have in the recent crisis), how much does wealth inequality grow? What are the welfare effects of tighter constraints? 4. How much does a doubling of unanticipated unemployment duration affect wealth inequality and welfare? 1.2 Intro to Methodology To answer these questions, we will use the simplest possible structural general equilibrium heterogeneous agent model where people receive persistent idiosyncratic shocks to their earnings and can only insure through noncontingent assets subject to borrowing constraints. Sometimes these models are known as Bewley models. 1 The basic methodology is to input an exogenous earnings shock process into a heterogeneous agent model to obtain endogenous asset decision rules and associated wealth distribution. We can then compute summary statistics of the wealth distribution like the Gini coefficient to analyze positive and normative questions about inequality. Since not all students are familiar with this methodology, let s begin with an example that is taught in virtually every first year PhD course in macroeconomics. It is a model with complete asset/insurance markets and exogenous shocks to total factor productivity. This is known as the Real Business Cycle model pioneered by Kydland and Prescott (1982, Econometrica). 1 For instance, Ljundqvist and Sargent (2004) Recursive Macroeconomic Theory use this nomenclature in Part IV. 1

2 Question: How much of the variation in real output can be accounted for by total factor productivity (technology) shocks in a complete markets stochastic growth model? Key things to note about the question: it is quantitative ( How much ). it requires us to compare moments in the data (i.e. the standard deviation of detrended real GDP) to moments from the model. Answer: the s.d. of HP filterted real gdp data =1.71% while the model sd=1.35%. Hence, exogenous variation in technology shocks in the stochastic growth model account for roughly 80% of output variation. Methodology: Underlying exogenous technology shock process z t that was parameterized off an AR1 of Solow residuals (i.e. z t+1 = ρz t +ε t+1, where ε t+1 N(o, σ 2 ε) ). Solve an RBC model via dynamic programming (or equivalently via Euler equations) for a savings decision rule k t+1 = g(k t, z t ; θ) as a function of parameters θ. Model moments. Once you have these 2 first order difference equations, can generate sequences of {k t, z t } and feed them into y t = f(k t, z t ) to obtain many different model moments to compare with the data moments. Kydland and Prescott choose parameters θ so that the model moments matched certain data moments (long run first moments like the capital-output ratio, etc.). The (overidentified) model is then tested by how well it does on other moments like the standard deviation of output. Our application: Incomplete financial markets with idiosyncratic earnings shocks. Question: How much of wealth inequality (measured by the Gini coefficient where a higher value between 0 and 1 corresponds to more inequality) can be explained by individual specific earnings shocks in an incomplete markets model? 2 Answer: the wealth gini in the data =0.8 while the model wealth gini=0.38. Hence, an incomplete financial markets model can account for roughly 50% of wealth inequality. Methodology: 2 Incompleteness (i.e. no insurance against earnings shocks) may be motivated by moral hazard problems which are not modelled specifically. 2

3 Underlying exogenous earnings process e t+1 follows a finite state Markov Process. These shocks are iid across agents. Solve the model via dynamic programming for a precautionary savings decision rule a t+1 = g(a t, e t ; θ) as a function of parameters θ. Given incomplete markets and idiosyncratic earnings shocks, even if everyone starts at the same wealth level, peoples wealth holdings will differ next period. In the limit, this fanning out generates an endogenous cross-sectional wealth distribution µ(a t, e t ; θ). Model Moments: 1.3 Lecture Outline 1. Inequality Data After choosing parameters to match certain moments in the data, can test the (overidentified) model by computing a wealth Gini coefficient (a moment that was not targetted when choosing θ) from µ(a t, e t ; θ) and compare it to the corresponding data moment. 2. A Parsimonious Quantitative Model 3. Experiments (a) Tighter Financial Constraints (b) Longer Duration of Unemployment 4. Directions for Future Research (a) Endogenize Borrowing Constraint (b) Endogenize Earnings and Mobility (c) Endogenize Redistribution 1.4 A Preview of Results The following table provides an idea of how we can use the model to understand wealth inequality. The benchmark incomplete markets model has the following parameterization (where a model period is one quarter): where β α y(e) y(u) π(e, e) π(u, u) a β is the discount rate 3

4 α is the coefficient of relative risk aversion y(e) is income if employed y(u) is income if unemployed π(e, e) is probability of staying employed π(u, u) is probability of staying unemployed a is the borrowing constraint (i.e. twice income) Results from steady state of incomplete markets benchmark and comparative statics: Data Bench a = 1 π(u, u) = 0.75 Unemployment Rate (targetted) Real Interest Rate (%) (untargetted) Wealth Gini (untargetted) CE(employed) * % % CE(unemployed) * % % CE * % % where CE denotes the Consumption Equivalent welfare measure. Comparing the benchmark with data, we see that the incomplete markets model is only able to account roughly half of the wealth inequality in the model. Policy Experiment 1: Cut borrowing limits in half. Positive Effects: Households precautionary savings rise, thereby lowering interest rates and inequality roughly in half. Normative Effects: What fraction of consumption would a person of type s in a steady state of an economy where borrowing is limited to 1 times quarterly employed earnings be willing to pay in all future periods to achieve the allocation of an economy where borrowing is limited to 2 times quarterly employed earnings? 2/10 of one percent. Policy Experiment 2: Double the unemployment spell. Positive Effects: Households precautionary savings rise, thereby lowering interest rates by roughly half. Longer spells of unemployment raises wealth inequality by about a quarter. Normative Effects: What fraction of consumption would a person of type s in a steady state of an economy where the average duration of unemployment is one year be willing to pay in all future periods to achieve the allocation of an economy where the average duration is 2 quarters? Over 3%. 4

5 2 Inequality Data Main References for this section: 1. Budria Rodriguez, S., J. Diaz Gimenez, V. Quadrini, V. Rios-Rull Updated Facts on the U.S. Distributions of Earnings, Income, and Wealth, Federal Reserve Bank of Minneapolis Quarterly Review, Summer, p. 2-35, (BDQR uses 1998 SCF) 2. Diaz Gimenez, J., A. Glover, and V. Rios-Rull Facts on the Distributions of Earnings, Income, and Wealth in the United States: 2007 Update, Federal Reserve Bank of Minneapolis Quarterly Review, February, p (DGR uses 2007 SCF) 2.1 Data sources 1. Survey of Consumer Finances (SCF): A cross section of detailed balance sheet, pension, and income characteristics of US families. Conducted by NORC at Chicago every three years starting in Sample size is 4,500 and over-represents the rich. Since the SCF is not a panel, can t follow a household over time and hence cannot track mobility. 2. Panel Study of Income Dynamics (PSID): A panel of individuals (and their family) that includes income sources and amounts, employment, housing, education, age, but less detailed wealth information. Conducted by the University of Michigan. After 1997 it is conducted every three years. Sample size has grown from 4,800 in 1968 to 9,000 in Since it s a panel, it can be used to assess economic mobility. 2.2 Definitions 1. Household: A person or a couple who live together and all the other people who live in the same household who are financially dependent on them. 3 The SCF considers the male of a couple to be the head of the household in every case. In single households, the financially independent person of either sex is considered to be the head of the household. 2. Cohort: A group with a common defining observable characteristic (e.g. age). 3. Earnings: wages and salaries plus a fraction (0.86) of business income (income from professional practices, farms). 4 3 A financially independent person who lives in the same dwelling, such as a roommate or a brother-in-law, is not considered to be a member of the same economic unit. 4 The value for the fraction of business and farm income imputed to labor earnings is the ratio of labor income to labor income plus capital income. 5

6 4. Income: all kinds of revenue before taxes but includes government and private transfers. Includes earnings, interest income, dividends, capital gains/losses from sale of stocks/bonds/real estate, unemployment compensation, income from social security and pensions, child support, food stamps and other welfare assistance, inheritances, disability compensation, etc. 5. Wealth: net worth includes value of financial (checking, money markets, bonds, stocks, investment accounts, cash value of life insurance, pension plans) and real assets (residences, vehicles) net of debts (mortgages, home equity loans, credit card debt, loans). 6. Lorenz Curve: The cummulative distribution function of the empirical probability distribution of wealth (or income, etc.). e.g. the bottom 20% of all households have 10% of the total wealth. A perfectly equal wealth distribution would be one in which every person has the same income. In this case, the bottom N% of society would always have N% of the income (i.e. a 45 line or the line of perfect equality ). By contrast, a perfectly unequal distribution would be one in which one person has all the income and everyone else has none. In that case, the curve would be at y = 0 for all x < 100%, and y = 100% when x = 100%. The line of perfect inequality. 7. Gini coefficient (a measure of concentration): The area between the line of perfect equality and the observed Lorenz curve (denoted A), as a percentage of the area between the line of perfect equality and the line of perfect inequality (A+B, where B is the area under the Lorenz curve). Hence, perfect equality =0, perfect inequality=1. 8. Mobility Matrix: Each element a i,j denotes the probability that an individual initially in group i will end up in group j. The sum of all the elements of each row is one. 2.3 Data Charts 1-4 (BDQR): Histograms where the levels have been normalized by the mean, so 1 on the horizontal axis represents the fraction of households at mean earnings $42,370. The median is at a level lower than 1 (we know this from Table 2). The first and last observations represent the frequencies of households with, respectively, less than -2 times and more than 10 times the corresponding averages. Note the differences in ranges (min vs. max). Chart 4 displays Earnings excluding retirees. A large share of households have zero labor earnings. 6

7 Charts 1 4 U.S. Distributions of Earnings, Income, and Wealth With Levels Normalized by the Mean* Chart 1 All Earnings % Average earnings (e) = $42,370 Minimum earnings = 20e Maximum earnings = 761e Maximum frequency = 26% Chart 2 Income % Average income (y ) = $54,837 Minimum income = 9y Maximum income = 3,124y Normalized Level Normalized Level Chart 3 Wealth % Average wealth (w ) = $287,974 Minimum wealth = 53w Maximum wealth = 1,787w Maximum frequency = 28% Chart 4 Earnings Excluding Retired Households % 28 Average earnings (e) = $50,993 Minimum earnings = 17e Maximum earnings = 632e Normalized Level Normalized Level *The first and last observations represent the frequencies of households with, respectively, less than 1 times and more than 10 times the corresponding averages. Source: 1998 Survey of Consumer Finances 7

8 Chart 5 (BDQR) and Tables 8&9 (DGR): Wealth is more unequally distributed than earnings while income, since it includes transfers, is least unequal. All measures of inequality have been rising. Mean has been growing relative median. This is potentially important for political economy models. Chart 5 The Lorenz Curves for the U.S. Distributions of Earnings, Income, and Wealth What % of All Households Have What % of All Earnings, Income, or Wealth % Earnings Income Wealth % of Households (Ranked by Amount) Source: 1998 Survey of Consumer Finances 8

9 Distributions of Earnings, Income, and Wealth Javier Díaz-Giménez, Andy Glover, José-Víctor Ríos-Rull Table 8 Changes in Concentration Gini Indexes Mean-to-Median Ratios Coefficients of Variation E I W N-H-W E I W N-H-W E I W N-H-W % Table 9 Changes with Respect to the Medians Ratios Ratios E I W N-H-W E I W N-H-W % accounts for only 31 percent of the growth in wealth which decreased by about 7 percent between 2007 and (housing equity grew by about 82 percent, but was only 1998, is an exception to this pattern. about Table 20 percent 4 of of Earnings total wealth; (DGR): thus, if only home We also find that the top tails of the distributions equity had grown, then total wealth would have grown account for most of these increases in concentration. by 17 percent), Thehousing earnings wealth poorest is much tend more evenly to have In sizable Table 9 business we report the losses ratios of but the hold earnings, income, distributed across almost people, twice as Table sample 8 shows. average The large wealth and (e.g. wealth unlucky of the 90th entrepreneurs). percentiles and the medians, and increase in asset prices implies that the average wealthto-earnings ratio which Many of the is a earnings key ratio for poor many are issues retirees increased (who in also the have top tails sizeable for all three wealth variables. of the medians and the 30th percentiles. Concentration in economics increased holdings). from 6.4 to 8.7 between 1998 When we look at the difference between the median and 2007 despite the low savings rate in the United and the poorest groups which we define to be the 30th States during Earnings those years. richest tend to be years percentile old, because college of the educated, large numbers selfemployed 1998 and 2007, andthere married. are some interesting with zero earnings or zero wealth we see a different of households Between quantitative changes in the distributions of earnings, income, and wealth. Earnings Perhaps rich the most arenoteworthy similar but of these a bit anything, younger. the poorest All part groups of advanced the hump slightly relative picture. Earnings and income witnessed little change. If changes is that shaped the concentration earnings. of Bottom all three variables line, age is to the anmedian. important However, observable the opposite characteristic. in the mean-to-median ratios, and in the when compared with is true for wealth: has increased. In Table 8 we report the changes in the in 2007 the bottom fell sharply relative to the median Gini indexes, coefficients of variation. We find that the Gini indexes Next, we ask who are the households that benefited and the mean-to-median ratios of all three variables have the most from this spurt of economic growth. To this increased. The sizes of these changes are larger for the purpose, in Table 10 we report the earnings, income, and mean-to-median ratios than for the Gini indexes, and wealth of the 30th, 50th, and 90th percentiles. The values they are largest for the coefficients of variation of earnings and income. The coefficient of variation of wealth, done so less than their respective averages. How can of all these statistics have increased, but they have all this 11 9

10 FEDERAL RESERVE BANK OF MINNEAPOLIS QR Table 4 Earnings Partition of the 2007 SCF Sample (Gini Index = 0.636) Bottom (%) Quintiles Top (%) All st 2nd 3rd 4th 5th Averages ( x USD) Earnings , Income , Wealth 1, ,690 1,094 2,618 12, Shares of Total Sample (%) Earnings Income Wealth Income Sources (%) Labor Capital Business Transfers Other Under Over Average (years) Education (%) Dropouts High school Some college College Age (%) Employment Status (%) Workers Self-employed Retired Nonworkers Marital Status (%) Married Single w/ dependents Single w/o dependents Family size Marital Status Excluding Retired Widows Single w/ dependents Single w/o dependents Family size

11 Table 6 of Wealth (DGR): The wealth poorest have avg net worth -$79K and tend to be young earning 40K. For the young, the debt is student loans. Some of the wealth poorest are retirees who have outlived their savings. Many of the wealth poor (with avg net worth -$5K) are high school dropouts (twice the sample avg). Wealth richest hold 34 times the sample avg coming from an even split between labor, capital and business sources. Many are selfemployed (5 times sample avg). Wealth rich are similar. The share of the bottom quintile of the wealth distribution is 0.2 (i.e. we will see something like this in the model Lorenz curve). 11

12 FEDERAL RESERVE BANK OF MINNEAPOLIS QR Table 6 Wealth Partition of the 2007 SCF Sample (Gini Index = 0.816) Bottom (%) Quintiles Top (%) All st 2nd 3rd 4th 5th Averages ( x USD) Earnings Income , Wealth ,316 1,233 3,710 18, Shares of Total Sample (%) Earnings Income Wealth Income Sources (%) Labor Capital Business Transfers Other Under Over Average (years) Education (%) Dropouts High school Some college College Age (%) Employment Status (%) Workers Self-employed Retired Nonworkers Marital Status (%) Married Single w/ dependents Single w/o dependents Marital Status Excluding Retired Widows Single w/ dependents Single w/o dependents Family size

13 FEDERAL RESERVE BANK OF MINNEAPOLIS QR Table 7 and 10 (DGR): Inflation adjusted avg earnings, income, wealth, and nonhousing wealth all rose. But these averages hide who gained; the poorest lost and the richest gained. Table 7 Average Earnings, Income, Wealth, Nonhousing Wealth, and Household Size Nonhousing Earnings Income Wealth Wealth HH Size ,820 83, , ,235 FEDERAL RESERVE 2.56 BANK OF MINNEAPOLIS ,542 71, , , QR % f the household heads in this group completed college. Many of them (48 percent, which is more than four average), and almost all of them are nt). ich. The earnings-rich are still rich ensions, but appreciably less so than st. Their average earnings, income, out three times the sample averages. rces are similar to the sample averared with the earnings-richest, more mes from labor and less from busiources. The household heads are still s, but on average they are about five n the earnings-richest. A very large ehold heads have completed college he share of married households is still percent). ichest. The income-richest are very dimensions. Their average earnings, h are 17, 21, and 26 times the sample ompared with the earnings-richest, t are clearly wealthier. Large shares me from capital and business sources t). The household heads are old. Their and 20 percent of them are over 65. completed college (85 percent), many mployed (51 percent), and almost all d (95 percent). ich. The income-rich are rich along ns, but their earnings, income, and out three times the sample averages. ith the income-richest, most of their om labor and less from capital and Their average age is 50 years old, m on average 6 years younger than t. Most of the household heads have (68 percent), they are mostly workers (69 and 20 percent), and a very large married (87 percent). ichest. The wealth-richest own exalth holdings (34 times the sample tively smaller earnings (12 times the Their income is almost evenly split ital and business sources (30, 34, and are quite old (the average age of the s 59, and 31 percent of them are over highly educated, with 86 percent having completed college. A very large share of them are self-employed (49 percent, which is almost five times the sample average), and almost all of them are married (91 percent). Table 10 The Wealth-Rich. The wealth-rich are still rich along all Changes three dimensions, in Earnings, Income, but there andis Wealth: a gap 30th, between 50th, their and 90th Percentiles wealth holdings and their labor earnings (4.2 and 2.4 times the sample averages). BottomBusiness 30 and capital income Median Top 10 are still important, E but I a larger W share N-H-W of their Eincome I W N-H-W E I W N-H-W comes from labor, as compared with the wealth-richest ,369 28,301 26,500 8,500 37,021 47, ,430 40, , , , ,500 (51 and 30 percent). The household heads are old ( ,910 25,819 22,764 8,237 36,147 44,022 91,287 37, , , , ,204 years on average), they have completed college (64 percent), % and 3.6 many of 9.6 them have 16.4 retired 3.2 (27 percent) Although most of them are married (75 percent), the share of singles without dependents is also sizable (18 percent). be? Because the lion s share of the gains of growth went variables have become more concentrated in their very to the households in the top tails of the distributions. The top tails, and the bottom tails have changed little. Therefore, a Hump fair conclusion shaped is that earnings, the lion s share butof productiv- Changes gains Table for households in the 11 Last andaround 10 Figure Years the 30th 2A,B percentile (DGR) were on Age: Although meager in this terms paper of earnings 3.6 looks at inequality, percent whereas many economists average care even gain about conditioning was how 12.9 U.S. percent. households onin age, terms fared there of wealth, over is atime. the lot of inequality within a cohort. Table the ity growth and asset price increases experienced between 1998 and 2007 went to the rich and the very rich. In gains Table of 197, this shows we group report there were average even have smaller 16.4 values not been of earnings, percent big changes income, whereas wealth, the average and wealth gain net was of home 54 percent. equity (nonhous- Similar over the last 10 years. ing changes wealth) occurred per household for the median in 1998 household. and 2007, Its measured earnings increased 2007 dollars by a paltry using 2.4 the percent barely consumer price 0.25 index percent (CPI) as per the year but price deflator. its wealth 3 We went find up that by household 31.9 percent. earnings Even increased households by in 13 the percent, 90th percentile that income fared increased worse than by the 18 percent, average: and their that earnings wealth went increased up by 9.7 by percent an impressive and their 54 wealth percent. by Even percent. though If we the look growth further in in home the top equity tail of the wealth distribution, we find that the wealth of the 95th and 99th percentiles increased by 65 and 72 3 As is well known, there is much debate about the extent to which using the CPI percent. does a good job of allowing for a comparison between dollars of different years. For example, To summarize, the Boskin Commission there (Boskin has been et al. 1996) an states increase that using in the CPI main yields numbers measures about 1.1 of percent inequality below those in that the would last obtain 10 using years. more The sophisticated three methods. Still, we use the CPI as the price deflator here because it is the one most commonly used. 4 The 2007 SCF was conducted at the peak of assets markets. After 2007, the value Table of 11total wealth in the United States dropped by about 30 percent, according to data from the Flow of Funds. Age Partition of the 2007 SCF Sample Other Dimensions of Inequality Some characteristics of households that are closely related to earnings, income, and wealth are age, education, employment status, marital status, and financial trouble. In this section, we discuss how these characteristics contribute to earnings, income, and wealth inequality. We do so by sorting the population according to those five criteria and reporting for each of the groups their average earnings, income, and wealth; their Gini indexes; the average shares of their income source; the relative group size; and the average number of people per primary economic unit. 10 Averages Income Sources (%) Gini Indexes Coefficients of Variation Age E Y W L d K e B f Z g O h E a Y b W c E a Y b W c H (%) i Size j Total a Earnings; b income; c wealth; d labor; e capital; f business; g transfers; h other; i percentage number of households per group; j average number of persons per primary economic unit.

14 average gain was 12.9 percent. In terms of wealth, the gains of this group were even smaller 16.4 percent whereas the average gain was 54 percent. Similar changes occurred for the median household. Its earnings increased by a paltry 2.4 percent barely 0.25 percent per year but its wealth went up by 31.9 percent. Even households in the 90th percentile fared worse than the average: their earnings went up by 9.7 percent and their wealth by 44.6 percent. If we look further in the top tail of the wealth distribution, we find that the wealth of the 95th and 99th percentiles increased by 65 and 72 percent. To summarize, there has been an increase in the main measures of inequality in the last 10 years. The three 1998 and 2007 went to the rich and the very rich. Other Dimensions of Inequality Some characteristics of households that are closely related to earnings, income, and wealth are age, education, employment status, marital status, and financial trouble. In this section, we discuss how these characteristics contribute to earnings, income, and wealth inequality. We do so by sorting the population according to those five criteria and reporting for each of the groups their average earnings, income, and wealth; their Gini indexes; the average shares of their income source; the relative group size; and the average number of people per primary economic unit. Distributions of Earnings, Income, and Wealth Javier Díaz-Giménez, Andy Glover, José-Víctor Ríos-Rull Table 11 Age Partition of the 2007 SCF Sample Averages Income Sources (%) Gini Indexes Coefficients of Variation Age E Y W L d K e B f Z g O h E a Y b W c E a Y b W c H (%) i Size j Age and Inequality Earnings 52.3 and 54.6 income inequality 91.8 tend 0.9 to increase with age, whereas wealth inequality 85.9 decreases until 2.0age We 0.47 report 0.46 these 0.76 statistics 2.50in Table and becomes almost constant thereafter Some of the differences in earnings, income, and wealth across households can be safely 66.1 attributed to the 6.9dif- ferences in 67.4people s ages so much 15.5so that 18.3 there 17.4is a large literature in economics that organizes its models around the households life cycle. The SCF is not a panel, and therefore we cannot follow the same group of households as their members age. Instead, to describe the relationship between age and inequality, we organize the SCF sample into 10 cohorts according to the age of Total a Earnings; b income; c wealth; d labor; e capital; f business; g transfers; h other; i percentage number of households per group; j average number of persons per primary economic unit. Figure 2 12 the household head. We compute the relevant statistics for each cohort, and then we compare them with the statistics for the other cohorts and for the entire sample. In Panel A of Figure 2, we represent the average earnings, income, and wealth of each cohort, once they have been normalized by dividing by their corresponding sample averages. Earnings and income display the typical hump shape conventionally attributed to the life cycle. But, perhaps more interestingly, the life-cycle pattern of average wealth increases until retirement and only decreases thereafter. Average cohort earnings are monotonically increasing in the age of household heads until age 55, and they start to decline thereafter. Not Average Earnings, Income, and Wealth (Panel A); Gini Indexes (Panel B); Income Sources (Panel C); and Coefficients of Variation (Panel D) for 10 Age Cohorts Ratio Income Panel A Earnings Wealth >65 Age Gini Index Panel B Wealth Earnings Income >65 Age Share Panel C Ratio Panel D Labor Table 12 (DGR) on Education: Higher Capital education means higher earnings Business (college premium is 5 times more Transfers than dropouts and 2 times more than some college) and there is more earnings inequality among dropouts than Wealth higher educated. Table 20 shows there has been a large increase in proportions who are becoming more educated. Income Earnings Table 13 (DGR) on Employment Type: Partition into workers (60% of >65 sample), self-employed Age (10% of sample), retirees (19% of sample), and nonworker (11% of sample defined as someone who does not work but doesn t consider themselves to be retired (e.g. disabled)). Self-employed entrepreneurs are the big winners. Table shows there are not large changes in fractions of each type >65 Age 14

15 Distributions of Earnings, Income, and Wealth Javier Díaz-Giménez, Andy Glover, José-Víctor Ríos-Rull Table 12 Education Partition of the 2007 SCF Sample Averages Income Sources (%) Gini Indexes Coefficients of Variation Education E Y W L d K e B f Z g O h E a Y b W c E a Y b W c H (%) i Size j Dropouts High school FEDERAL 4.3 RESERVE BANK 1.5 OF MINNEAPOLIS Some college College QR Total a Earnings; b income; c wealth; d labor; e capital; f business; g transfers; h other; i percentage number of households per group; j average number of persons per primary economic unit. ences in either earnings or wealth. This is partly due to the equalizing effect of transfers, which are much larger for Table high 13 school dropouts. In the second block of Table 12, we report the income sources Employment of the Status education Partition groups. of the 2007 Labor SCF is Sample the main source of income for all four of our education groups. Capital income is increasing in education. College graduates are the most enterprising of the four groups, as measured by their share of business income. But, interestingly, high school graduates obtain more income from business sources than households with only some college. And transfers are clearly decreasing in education. In the third block of Table 12, we report the Gini indexes of the education groups. We find that the maximum differences are 12 percentage points for income, 10 j average number of persons per primary economic unit. for earnings, and 8 for wealth. But their maximum and minimum The self-employed values correspond make up to 10.5 different percent groups. of the Earningple and are are most the unequally third most distributed numerous group. among It high is remark- school sam- dropouts able that as and much least as among 10 percent the households of the household with heads some college. in the United Income States inequality declare is that monotonically they spend increasing a majority in of education. their And wealth is most unequally distributed there time in areentrepreneurial not large changes. activities. Among the among employment households status groups, with some the college self-employed and least are among kings high of the school hill: their graduates. earnings, income, and wealth are 2.1, 2.2, The and picture a whopping of inequality 3.6 times within the sample education averages. groups provided Finally, by households the coefficients headed of by variation a nonworker is different make up from 10.9 Table 14 percent that of the of the Gini population. indexes for Of earnings those, 6.3 and percent income. are The disabled Marital high Status school who Partition do dropouts not plan of the have to 2007 work very SCF small again. Sample coefficients The average of variation earnings, relative income, to and all wealth the other of nonworker groups, and households the group with are 26 some percent, college 35 percent, has the highest. and 24 percent Again, of this the points sample to more average. inequality at the bottom of the distribution rather than Two at the aspects top. of the Gini indexes of earnings, income, and In wealth the 2007 differ SCF sizably sample, across there the are employment many more households groups more who have so than completed across any their other education either partition of the status high 2007 school SCF sample. or college than Earnings is households most equally who distributed failed to complete among workers either and high most school unequally or college. distributed Interestingly, among retirees. This is not surprising; although most households with a retired head have zero earnings, other households headed by retirees have other members fully engaged in working in the market and therefore have sizable labor household size is decreasing in education until we reach the group of households who have completed college. The size of households in this group is larger than that for households with only some college. Employment Status and Inequality If you want to be income-rich and wealthy, make sure that you are self-employed, and avoid being a nonworker. Averages Income Sources (%) Gini Indexes Coefficients of Variation Occupation E Y W L d K e B f Z g O h E a Y b W c E a Y b W c H (%) i Size j Worker Self-employed Retired Nonworker To document the relationship between employment status and inequality, we partition the 2007 SCF sample into workers, self-employed, retirees, and nonworkers according to the employment status declared by the household heads. In Table 13 we report the averages for earnings, income, and wealth; the shares of income Distributions of Earnings, obtained of Income, variation from and give Wealth various the same sources; picture the of Gini inequality indexes for and the Javier Díaz-Giménez, Andy Glover, coefficients employment José-Víctor of status Ríos-Rull variation; groups, the with relative only one group exception: sizes; and the Table 14 (DGR) on Marital Status: Married the coefficient average (60% of number of variation sample) of people of wealth have in these for higher the four workers employment (5.4) avg earnings and lower earnings inequality status is larger than groups. than singles. that for the Table self-employed 22 shows (4.2). It The turns differences out that the in differences income sources across are these very employment across status the employment groups are substantial. status groups Workers by are construc- by far large the tion. largest Interestingly, group (accounting the shares of for labor 59.9 income percent of the sample); self-employed, their earnings the retirees, and and income the are nonworkers close to are the sample sizable: average a third, (117.1 a fifth, and 99.7 a surprising percent), 51 but percent they are of significantly their incomes. wealth-poorer We conjecture than that the majority sample average of these (their labor incomes wealth is were 63 percent earned by of the household average). members other than Retirees the household are the second head. Finally, most numerous the retirees group, and accounting nonworkers for are a startling the largest 18.7 recipients percent of of the transfers: 2007 SCF 47 the Averages Income Sources (%) sample. Naturally, Gini Indexes they are Coefficients and 33 percent. both earnings- of Variation and incomepoor (their earnings and income are 25 and 70 percent of Marital the sample Status average), and Inequality but their wealth is greater than the If sample you want average to be (122 earnings percent). and This income-rich suggests that, and on average, wealthy, retirees it pays supplement to be married, their according income by to the running 2007 down SCF. their wealth holdings. Total a Earnings; b income; c wealth; d labor; e capital; f business; g transfers; h other; i percentage number of households per group; Marital Status E Y W L d K e B f Z g O h E a Y b W c E a Y b W c H (%) i Size j Married Single Single w/dependents Male Female Single w/o Single males w/o Single females w/o To 2.0 document the relationship between marital 14.5 status 1.00 Retired widows (females) and 2.7inequality, we partition the SCF 2.63 sample into Total married households and single households with 2.56 and earnings. a Earnings; Income is also most equally distributed among without dependents according to the marital status of b income; c wealth; d labor; e capital; f business; g transfers; h other; i percentage number of households per group; workers, j average number of persons per primary economic unit. but it is most unequally distributed among the household heads. We also subdivide these last two the self-employed. This is because some of them run groups according to the sex of the household heads. We successful businesses and others run businesses that refer to these groups as the marital status partition. 5 Finally, with dependents, because of their with nontrivial a Gini index size, of we only look 0.44, at retired is the fail. coefficients Wealth of is variation; most unequally the relative distributed group sizes; among and nonworkers, number of and people its Gini per indexes primary are economic similar unit for the for these other the widows smallest. separately. In Table 14 we report the averages employment marital Tables status status groups 23 groups. and for 25 We the (DGR) conjecture entire sample. on that Financial some of Status: for Finally, earnings, SCF wealth income, asks inequality and respondents wealth; is largest the shares among if of income singles the The nonworkers majority are of very the sample wealthy, (59 and percent) they choose lives not in obtained with dependents, from various followed sources; by married the Gini households indexes and to households work because where they the can head live is married. off their Notice wealth. that Others, this by singles without dependents. Their Gini indexes are however, number refers are incapable to the share of holding of households. a job, a condition Since the 15that average them household among size the in wealth-poorest. the sample is 2.56, The the coefficients share of 0.83, 0.80, and When we consider the sex partition, 5 Note singles without children do not necessarily live alone; they may also puts live we with find either that adult with dependents a Gini or index other financially of 0.84, independent wealth adults. inequality married people in the sample is somewhat smaller (46 is largest among single females with dependents. percent). Married households have substantially higher Financial Trouble and Inequality earnings and income, and their wealth is substantially 16 In this subsection, we use the SCF to describe the demographic and economic features of U.S. households higher than that of their single counterparts. Specifically, the average earnings, income, and wealth of married in financial trouble and to examine the relationship households are higher than the sample averages, and between financial trouble and inequality. The SCF asks those of all other groups are lower. its respondents whether they have filed for bankruptcy. The shares of income accounted for by labor, capital, Unfortunately, it does not ask them which chapter of

16 FEDERAL RESERVE BANK OF MINNEAPOLIS they filed for bankruptcy (1% of sample) and if they are delinquent by 2 months or more (5% of sample). Not surprisingly QR they are poor. Fraction of bankrupts was higher in 1998, due to changes in bankruptcy law in Table 23 Late and Timely Payers in 1998 and 2007 Late Payers Timely Payers Earnings, Income, and Wealth Earnings 32,738 39, ,630 57, Income 38,471 43, ,212 72, Wealth 117,848 75, , , Sources of Income Labor Capital Business Transfers Other Education Dropouts High school College Employment Status Workers Self-employed Retired Nonworkers Marital Status Married Single Single w/ dependents Single w/o dependents Other Features Debt-to-income ratio % % Debt-to-wealth ratio % % Debt 80,033 51, % 98,063 60, % Age Household size Late Payer Households There was a slight decline in the fraction of households that declared themselves to be late payers from 6.0 percent in 1998 to 5.5 percent in Earnings, Income, and Wealth. Between 1998 and 2007, the changes in the average wealth of late and timely payers have been similar and sizable: average wealth has increased by 57 and 53 percent (see Table 23). In contrast, the changes in their average earnings and income have been smaller and very different: the earnings and income of late payers have decreased by 18 and 12 percent, and those of timely payers have increased by 14 and 18 percent. Consequently, the gaps in earnings and income between late and timely payers have increased sizably, whereas the gap in wealth has remained about the same. Sources of Income. Between 1998 and 2007, the business and capital income of late and timely payers have changed in different directions. Both types of income have risen for timely payers (1.5 percent and 1.1 percent) and have fallen for late payers ( 0.6 percent and 2.4 percent). Late payers have experienced a larger rise in transfers than timely payers (5.7 percent versus 1.4 percent)