Working, Consuming, and Dying: Quantifying the
Diversity in the American Experience
∗
Chadwick Curtis
†University of Richmond
Julio Gar´ın
‡Claremont McKenna College
Robert Lester
§Colby College
This Version: January 17, 2021
Abstract
We document how lifetime utility varies by demographic groups in the US and how these differences have evolved since the start of the 21st century. Using the equivalent variation as our measure of welfare we find that the standard deviation in cross-sectional well being between demographic groups is quite large at around 11 percent, which is comparable to the standard deviation of the logged annual income in prime earning years and more than double the standard deviation of logged consumption. Our metric includes consumption, leisure, mortality risk, and within-group inequality. The results are primarily driven by differences in consumption and life expectancy. Controlling for other demographics, welfare is increasing in educational attainment and is higher for women and those of Asian descent. This qualitative ordering is robust to classifying a broad measure of home production and child care as work and various definitions of real consumption. Finally, we show that changes in mortality rates associated with ‘deaths of despair’ disproportionately lower the welfare of less educated Whites.
JEL Classification: I31; 051. Keywords: Welfare; Life-cycle; Inequality; Demographics. ∗We are grateful to John Steenrod for research assistance on an earlier draft of this project. We also
thank Greg Casey and Kevin Donovan for useful comments and seminar participants at the Central Bank of Uruguay and the Liberal Arts Macroeconomic Workshop.
†E-mail address: ccurtis2@richmond.edu. ‡E-mail address: jgarin@gmail.com. §E-mail address: rblester@colby.edu.
1
Introduction
The facts of cross-sectional inequality across a number of dimensions are well established. Consumption, leisure, and life expectancy vary substantially between and within narrowly defined demographic groups. In this paper we aim to answer the following question: Account-ing for these well-developed metrics of well-beAccount-ing, how much does the welfare of individuals belonging to various racial, educational, and gender groups compare to the welfare of the average American?
Following Jones and Klenow(2016) (JK henceforth), we use the equivalent variation – the amount of consumption you must compensate or tax the average American to be indifferent between living life as themselves or an average member of a specific demographic group – as our measure of welfare. Whereas JK study economic welfare across countries, we focus on the distribution of welfare within the United States. A person’s utility within a period depends on consumption and leisure. Since the utility function is concave in both arguments, changes in within-group inequality will affect the welfare measure. Finally, each person receives a set of group-specific mortality rates over their life cycle which gives rise to different life expectancies across demographic groups. Thus, welfare dispersion is driven by differences in average consumption, average leisure, mortality rates, and within-group inequality.
We find that economic inequality varies widely across the population. An average American would be willing to forgo about 65 percent of their annual consumption rather than live the life path of a White or Black man without a high school degree. At the other extreme, the average American would need to increase consumption by more than 100 percent before achieving the same welfare as a college-educated Asian woman. Broadly speaking, women have higher welfare than men (within race and education categories), Asians have higher welfare than Whites and Hispanics who in turn have higher welfare than Blacks (within gender and education categories), and welfare is increasing in educational attainment. The correlation between welfare and relative lifetime income per capita is about 0.53. While lower than one might expect, some of this is because women tend to have lower incomes but higher life expectancy than men. The within-gender correlation between welfare and income is about 0.80.
Dispersion in economic welfare is comparable to the dispersion in average annual income at midlife and much higher than the dispersion in cross-sectional consumption. Groups with high consumption tend to also have longer life expectancies and these two variables together account for well over three quarters of the variance in welfare inequality. While differences in labor supply play a more modest quantitative role than consumption, those with low consumption tend to have lower labor supply. This means that the decrease in quality of life
one suffers through low consumption is partially compensated with additional leisure. We also address how within-group inequality in consumption and leisure contributes to differences in well-being. We find that, after controlling for differences in average consumption and labor supply, within-group inequality accounts for almost nothing.
Next, we study how welfare inequality has evolved since 2000. We use two metrics for this – a “relative” metric which compares the equivalent variation in 2013–2017 to 2000–2004 and an “absolute” metric which calculates the equivalent variation using each group’s 2000-2004 utility as the baseline instead of the average American. The relative metric answers how much the average member of a specific group gained or lost relative to the average American. The absolute metric tells us how much the particular changes to a group’s quality and quantity of life has evolved over this time frame. With the exception of White men and women without high school degrees, every group experienced welfare gains over the sample years. In terms of magnitudes, Black men of all education categories experienced welfare growth equal to about 50 percent over the 14 year period. Nevertheless, there was not much mobility across the population as the correlation between initial welfare levels and welfare growth is about -0.12 and the correlation between welfare at the start of the sample and welfare at the end of the sample is 0.98. The per annum growth rate averages about 1.5 percent per year which is slightly higher than the growth rate of real GDP per capita over the same time period.
Our baseline framework equates time spent outside of market work to leisure. In the data, on the contrary, people spend time on home production – producing goods and services that could otherwise be purchased on the market. Since women spend more time on home production than men on average, a concern is that our finding that women have higher welfare than men is a consequence of ignoring home production. We address this by adding home production to the utility function and use data from the American Time Use Survey to compute average time spent on home production for different groups over the life cycle. Under the most expansive definition of home production (i.e. one that includes childcare) we find that the quantitative results largely hold up. While the standard deviation of economic welfare goes down by about 13 percent with home production, welfare with home production has a correlation of 0.94 with welfare without home production. The decrease in dispersion is attributable to a narrowing of welfare between men and women in the same education and race categories. Indeed, the gender gap – the average welfare difference between men and women across demographic groups – cuts in about half from 50 percent of consumption to 23 percent. Given that we define home production in arguably the broadest plausible way, we conclude that the welfare differences between men and women are mostly due to women’s longer life expectancies rather than differences in time use.
documented by Case and Deaton (2017), we calculate the welfare gains (and the distribution of those gains) from eliminating the rise in deaths caused by suicide, drug overdose, liver failure or cirrhosis since 2000-2004. We find that less educated Whites would be willing to sacrifice the most consumption to eliminate deaths of despair while Asians would be willing to sacrifice the least. White men and women without high school diplomas would be willing to give up about eight percent of lifetime consumption to return to the early 2000s mortality rates. This finding is consistent with Case and Deaton (2017) who find that the increasing prevalence of deaths of despair is enough to drive down the life expectancies of non-Hispanic Whites without a college education, while college educated Whites and members of other groups, irrespective of education, have continued to see improvements in life expectancy.
Our paper relates to a long-lived literature attempting to create plausible proxies of economic welfare and then using those proxies to understand the distribution of welfare across countries and how it has changed over time within countries. An entire NBER volume in 1973 was devoted to studying how economic and social performance has evolved in the US (Moss, 1973). Anticipating future work in the subject, Nordhaus and Tobin (1971) build a measure of economic welfare that includes consumption, time use, and urban (dis)amenities.1 More recently, JK build a measure of economic welfare that includes consumption, leisure, life expectancy, and inequality. They show that cross-country welfare is strongly correlated with GDP per capita and that welfare has been growing faster than income per person on average. They note that the high correlation in the cross section hides some discrepancies between welfare and income. Falcettoni and Nygaard (2020) use the JK utility function to study how economic welfare is distributed across states in the US. Like us, they find that there is significant dispersion in welfare. While we share a common framework with Falcettoni and
Nygaard (2020), we focus on different units on observation – with ours being demographic
groups and theirs being states. Becker et al. (2005) quantify the gains to life expectancy across the globe between 1960 and 2000 and show that on average poor countries had higher welfare growth than rich countries. A related strand of literature uses subjective well being to make cross-country welfare comparisons. Frey and Stutzer (2002) and Deaton (2008) provide summaries of the approach. Murtin et al. (2017) reconcile some of the differences that emerge when using subjective well being data versus a calibrated utility function in measuring economic welfare.
Our paper is also related to a voluminous literature studying various measures of economic inequality in the US. Trends in income inequality have been extensively studied and are
1The idea here is that living in a city entails tolerating more congestion. Had Tobin been alive to
witness the proliferation of microbreweries and kombucha bars, perhaps he would have been more inclined to emphasize the upside of living in cities.
summarized in Goldin and Katz (2008) and Acemoglu and Autor (2011). The general consensus is that there exists a sizable college wage premium that has grown since the late 70s; real wages have fallen slightly over the same time period for workers without a post-secondary education, and that the increase in inequality has been concentrated in the top relative to the median rather than the median relative to the bottom. While cross-sectional consumption inequality is unequivocally lower than income inequality, the trend in consumption inequality is more controversial. Krueger and Perri(2006) document that the standard deviation of cross-sectional (log) consumption is about half of the standard deviation of (log) cross-sectional wage income. They show that the large increase in wage income inequality in the last quarter of the 20th century was not accompanied by nearly as much of an increase in consumption inequality. This conclusion has been challenged byAguiar
and Bils (2015) among others who argue that the Consumer Expenditure Survey (CE) is
subject to substantial measurement error and that once one accounts for measurement error, consumption inequality has risen about as much as income inequality. Trends in consumption inequality, including a discussion on the different ways to measure it, are summarized by
Attanasio and Pistaferri (2016). In our baseline, we use the CE interview survey and consider
some alternative definitions of consumption. These adjustments do not much change the quantitative results.
In addition to consumption and income, a number of recent papers document trends in time use. Aguiar and Hurst (2007, 2009) show that less educated individuals enjoy more leisure than highly educated individuals and this gap has expanded over time. Ramey and
Francis (2009) document a long-run decline in time spent on home production. Finally,
a number of recent papers have documented inequality in life expectancy. Chetty et al.
(2016) show that income and life expectancy are highly correlated and that differences in life expectancy by income group expanded between 2001 and 2014. Case and Deaton (2017) discuss the rising mortality rates for middle age White non-Hispanic men and women between 1999 and 2013, attributing much of the increased mortality rates to “deaths of despair.”
Novosad et al. (2020) show that these increasing mortality rates are concentrated among
the lowest ten percent of the education distribution. Our paper unifies the differences in cross-group consumption, time use, and mortality rates into a comprehensive welfare measure.
Finally, while our paper is about measurement, there is a large literature investigating the causes and consequences of rising income inequality in structural models withHeathcote,
Storesletten, and Violante (2010b) being one example. Beyond some speculation, we are
entirely silent on the economic mechanisms that give rise to the distribution of welfare. The quantified welfare differences that we present in this paper can be used in structural models that speak to specific mechanisms and evaluate welfare effects of particular policies. In that
regard, one of our goals here is to present a way of looking at the data that will be useful for structural modeling.
2
Framework
Our exercise considers the lifetime welfare of a person at age 25 who is assigned a race/ethnicity, gender, and education level. We refer to each unique combination of race/ethnicity, gender, and education level as a ‘demographic group.’ Within this group, their consumption, leisure, and mortality rates are drawn from the actual cross-section in the data at each age. Lifetime utility (or welfare) is from the perspective of the 25 year old facing this scenario: while they are aware of their demographic classification, they must factor in all the possibilities of consumption and leisure draws they may receive by being a member of this group. The measure of welfare comparisons across groups is the annual equivalent variation: At age 25, how much would the consumption of the average American need to be adjusted to equate the lifetime utility of the average American (with the adjusted consumption profile) to the lifetime utility for a member of a particular demographic group.
We choose to start at age 25 because educational investment is usually complete by this age. Consequently, we are not taking a stand on to what extent the cost of college may affect lifetime resources or how the consumption value of college affects lifetime utility. This allows us to treat education as an endowment rather than a choice and to measure lifetime utility taking education as given.
Following JK, all individuals share the common per-period utility function u= ¯u+ln c+v(l) where c is consumption and l is leisure. The function v is increasing and concave in l. ¯u is a constant which ensures flow utility is non-negative. Intuitively, if flow utility was negative, an added year of life expectancy would decrease utility. Adding the constant ensures that the value of additional life year is never negative. As described in the next section, we draw on data from the Consumer Expenditure Survey to obtain the joint distribution of consumption and leisure. We assume that someone of a given group status and age has some probability of drawing one of the flow utilities from their group and age cohort observed in the data.
We begin to track individuals at age 25 after education decisions have been completed. Each person belongs to a particular gender, race, and educational attainment category. We index each gender, race, and education level combination by i and age by a so there are Ni(a) people in an age demographic of a particular group. Letting j denote a member of
Ni(a), lifetime expected utility is ¯ Vi = 99 ∑ a=25 βa−25S(ai) Ni(a) ∑ j=1
ωi,j(a) [¯u + ln ci,j(a) + g(a − 25) + v(li,j(a))] (1)
where ωi,j(a) is the sample weight of person i in group Ni(a). We normalize the sample
weights so that∑Ni(a)
j=1 ωi,j(a) = 1 for all (i, a) pairs. g is the annual growth rate of consumption.
S(ai) are cumulative survival probabilities, i.e. the probability of surviving through age a.
S(ai) depends on age and group and we assume S(ai) = 0, for ai≥ 100, ∀i.2 We define the
equivalent variation as the amount one would have to raise or lower the average American’s consumption so that the lifetime utility of the average American with the revised consumption profile equals the lifetime utility of a member of group i. Formally, the equivalent variation, λ, solves the equation
99 ∑ a=25 βa−25S(ai) Ni(a) ∑ j=1
ωi,j(a) {¯u + ln ci,j(a) + g(a − 25) + v [li,j(a)]} = 99 ∑ a=25 βa−25S(a U S) Ni(a) ∑ j=1
ωU S,j(a) {¯u + ln [cU S,j(a)(1 + λi)] + g(a − 25) + v [lU S,j(a)]}
where the U S subscripts denote the value of each variable for the average American. Solving for ln(1 + λi) gives
ln(1 + λi) =
¯ Vi− ¯VU S
∑aβa−25S(aU S)
. (2)
λi∗ 100 is our measure of economic welfare. By definition, λU S = 0. Because the flow
utility function is additively separable, we can decompose economic welfare into five different components: ln(1 + λi) = ∑ a ∆si(a)ui(a) ´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶ Life expectancy + u(¯ci) − u(¯cus) ´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶ Consumption + v(¯li) − ¯v(¯lus) ´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶ Leisure
+ [¯u(ci) − u(¯ci)] − [¯u(cus) − u(¯cus)]
´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶ Consumption inequality + [¯v(li) − v(¯li)] − [¯v(lus) − v(¯lus)] ´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶ Leisure inequality (3)
where the terms are defined as
2Note we are assuming S(24) = 1∀i. Thus, we can infer life expectancy conditional on living to 25 from
∆si(a) = βa−1S(a i) − βa−1S(aus) ∑100 a=25βa−1S(aus) sus(a) = βa−1S(a us) ∑100 a=25βa−25S(aus) ¯ u(ci) = 100 ∑ a=1 sus Ni(a) ∑ j=1
ωi,j(a) ln ci,j(a) and ¯v(li) = 100 ∑ a=1 sus Ni(a) ∑ j=1
ωi,j(a)v(li,j(a))
u(¯ci) = 100 ∑ a=1 sus(a) ln ⎡⎢ ⎢⎢ ⎢⎣ Ni(a) ∑ j=1
ωi,j(a)ci,j(a)
⎤⎥ ⎥⎥ ⎥⎦ and v(¯li) = 100 ∑ a=1 sus(a)v⎛ ⎝ Ni(a) ∑ j=1
ωi,j(a)li,j(a)⎞
⎠ ui(a) = ¯u + g(a − 25) + ωi,j(a) [¯u + ln ci,j(a) + v(li,j(a))] .
The derivation is contained in Appendix A. In a robustness exercise, we report results using a compensating variation, i.e. how much one would have to change consumption of group X to be indifferent between living the life path of a member of group X with the revised level of consumption or the life path of the average American. The main difference comes in the life expectancy component. Under the equivalent variation, the life expectancy component is weighted by group i’s flow utility. If the group has low flow utility, adding additional life years will not add much to welfare. Conversely, if the group has high flow utility, the life expectancy term will matter more. The compensating variation replaces ui,a with uU S,a.
The life expectancy term will then matter more for groups with relatively low flow utilities compared to those groups with relatively high flow utilities.
3
Data and Calibration
3.1
Data
Our primary sample is from 2013-2017. Our demographic groups are combinations of gender, racial/ethnic, and education groups. We use two genders (male and female) and three education groups by highest degree: less than high school, high school degree but less than a bachelor’s degree, and bachelor’s degree or more. We also define four race/ethnicity categories: Black non-Hispanic, White non-Hispanic, Asian non-Hispanic, and Hispanic. This results in 24 unique gender-race-education groups. Because of sample size issues, we group everyone into non-overlapping five-year age bins beginning at age 25. Hence, every individual in a given age bin receives the same flow utility.
(CE). The CE consists of an interview component in which households are interviewed over five consecutive quarters. In the first quarter surveyors collect demographic and economic characteristics of the household and then track detailed consumption patterns in the subsequent four quarters. The CE also consists of a diary survey in which respondents are asked to record their purchases. Bee, Meyer, and Sullivan (2013) show that the diary survey fails to track the Personal Consumption Expenditure data in the National Accounts for most product categories. On the other hand, they show that the interview survey tracks most of the largest consumption categories in the PCE quite well.3 With this in mind, we use the interview survey as for consumption data.
Some groups have a rather low sample size for individual years, so we merge subjects into five-year age bins from ages 25 to 99. The unweighted sample size for each group for 2013-2017 are shown in Table 6of Appendix A.
Consumption is measured at the household level. To transform into an individual level, we divide household consumption by OECD equivalent scales. We calculate real consumption by dividing nominal consumption by the good-specific consumer price index.4 As is well known, the CE under counts consumption relative to the NIPA.5 To account for this, we adjust consumption by a scaling factor such that average real per capita consumption on nondurables and services in our sample equals the corresponding figure in the NIPA.6 Because we want to track consumption rather than expenditure, our definition of consumption excludes purchases of durable goods. We do, however, include the imputed rent of owner occupied housing in our consumption measure. In a robustness exercise, we report the results assuming durable good expenditure counts as consumption.
The CE interview survey also asks about average time spent working per week and number of weeks worked in a year. We define hours worked as the product of these two variables and leisure as 1−hours worked365×16 . Due to age censoring in the CE, consumption expenditures for older ages are grouped into one age category and we cannot separate by five-year age groups past 80. Therefore, for those age 85 and older, we forecast consumption by regressing group specific consumption on a quadratic in age and then using the group-specific coefficients to predict consumption. Further, we assume that leisure equals 1 past age 85. Appendix B
contains a detailed description on this technique. The life-cycle consumption and leisure profiles from the years 2013-2017 are shown in Figure 1.
3Some of the exceptions include food purchased away from home and furniture. 4See appendix for a complete list of the categories.
5SeeHeathcote et al.(2010a) for a discussion of this.
20 40 60 80 100 2 4 6 8 10 4 20 40 60 80 100 2 4 6 8 10 4 20 40 60 80 100 0.6 0.7 0.8 0.9 1 20 40 60 80 100 0.7 0.8 0.9 1 Less HS HS College
Figure 1: Life-cycle consumption profiles.
Notes: Top panels show average consumption by age and highest degree completed for men and women. Bottom panels show leisure as a share of time by age and highest degree for men and women. Data is from the CE, 2013-2017.
Consumption is always higher for those with more education. For most groups, consump-tion increases at the beginning of the life cycle and then drops off during retirement. This is broadly consistent with Fernndez-Villaverde and Krueger (2007) and Gourinchas and Parker
(2002). The life-cycle trends in leisure are shown in the bottom two panels of Figure 1. These trends are also broadly consistent with the evidence. Leisure is higher for groups with less education as observed in Aguiar and Hurst(2007) and leisure increases towards retirement age, consistent withFrench (2005). Men enjoy less leisure than women throughout the life cycle although a large portion of the differences is attributable to gender differences in time spent on home production and child care. We revisit the topic later in the paper.
We also obtain income data from the CE. In particular, we calculate per capita income by summing each individual’s pre-tax wage and self-employment income with the household’s other sources of income divided by the number of adults in the household. As an example, if a household consists of two members, A and B, who earn $40,000 and $50,000 in wage income respectively and collectively the household earns $10,000 in dividend income, we would assign $45,000 in income for A and $55,000 for B. The panel on the left of Figure 2
shows how lifetime income varies with lifetime consumption across groups7 where income
7By ‘lifetime’ we mean the present discounted value of each flow measure. We use a discount rate of two
and consumption are normalized by their respective US averages. As one would expect, consumption and income are positively correlated with a correlation coefficient of about 0.91. Meanwhile, the right panel of Figure 2shows that income and leisure are negatively correlated with a correlation coefficient around -0.83.
0 0.5 1 1.5 2 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 0 0.5 1 1.5 2 0.78 0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94
Figure 2: The relationship between consumption, leisure, and income.
Notes: Left panel plots per person consumption by group against income and right panel plots per person leisure against income. Data is from CE, 2013-2017.
Our final piece of data concerns mortality rates. We get the number of deaths by age for each demographic group from the US National Vital Statistics System of the National Center for Health Statistics. We divide the number of deaths for each demographic group by the population of that group in the American Community Survey (ACS).8 As in the CE, we pool all the years 2013–2017 and average over five-year age bins. Once we have mortality rates we can convert them into life expectancies at age 25. The relationship with income and life expectancy is shown in Figure 3. Income and life expectancy are modestly correlated with a correlation coefficient of about 0.28. This correlation of income and life expectancy within genders is 0.52 and 0.43 for men and women respectively. There is wide variation in life expectancies with Asian women (of all education levels) expecting to live into their mid 80s whereas the White and Black men without a high school diploma only expect to live until about age 68. To put this in perspective, the difference in life expectancy at birth between the United States and Cambodia is about 15 years.9
8Both the ACS data and the time use data we use later in the paper were obtained in the IPUMS (Ruggles
et al.,2020).
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 68 70 72 74 76 78 80 82 84 86
Figure 3: The relationship between life expectancy and income.
Notes: This plots per person (normalized) lifetime income by demographic group against life expectancy at age 25. Data is from 2013-2017.
To summarize, income is strongly positively correlated with consumption, strongly nega-tively correlated with leisure, and modestly posinega-tively correlated with life expectancy. Because lifetime utility is increasing in consumption, leisure, and life expectancy, these empirical relationships point to ambiguous effects on overall welfare. To understand how income varies with welfare, we must put more structure on how we measure the latter, which is what we turn to next.
3.2
Model parameter values
While we pool our results into five-year age bins, the model period is one year. For example, we pool the data for white college-educated men from 25-29 to calculate consumption, leisure, and flow utility. So in the model, white college educated men from 25-29 will have the same values for these variables. FollowingJones and Klenow (2016), we set the discount rate, β, to 0.99. We set the growth rate in annual consumption to 1.25 percent which was the rate of growth in real expenditures on nondurables and services between 2013 and 2017 in the NIPA.
Recall, the within period utility function is ¯u+ln c+v(l). We assume v(l) = −1+θ1 (1−l)
1+1
where is the Frisch elasticity which we assume is 1. The intratemporal first order condition for leisure choice can be written as
θ= (1 − τ) w c(1 − l).
We let τ = 0.21 so as to match the average labor income tax from 2013-2015 according to the series assembled by McDaniel (2007). Assuming a Cobb Douglas production function with an elasticity of output with respect to labor equal to two thirds, we calibrate θ to be consistent with a consumption to output ratio of two thirds and average time worked in the CE. This implies a value for θ of 10.08.
We choose ¯u so that the value of a statistical life for the average person at age 40 is equal to $7,000,000 in 2012 dollars. This is conceptually identical to Jones and Klenow (2016) and
Falcettoni and Nygaard (2020). To put the value of statistical life in utility units, multiply
by the marginal utility of consumption at age 40. That is V40= $7, 000, 000
c(40) . So the value of life at age 40 is
$7, 000, 000 c(40) =
99
∑
a=40
βa−40S(a)[¯u + ln c(a) + g(a − 40) + v(l(a))].
Solving for ¯u gives
¯ u= $7,000,000 ¯ c(40) − ∑ 99
a=40βa−40S(a)[ln c(a) + g(a − 40)v(l(a))]
∑99
a=40βa−40S(a)
This implies a value of ¯u= −5.81.10 Of course, changing either the value of a statistical life or the utility function will imply a different ¯u. We consider both changes in the robustness section. Table 1shows the parameter values.
Table 1: Parameter Values
Parameter Interpretation Value Target
¯
u Constant in utility function -5.81 VSL of$7,000,000 (2012 dollars)
θ Disutility of labor 10.08 Average hours of 0.28
g Annual Growth rate of consumption 0.0125 Growth of real consumption in NIPA
β Annual Discount rate 0.99 Jones and Klenow(2016)
10Falcettoni and Nygaard(2020) calibrated value of ¯u is 7.2. While their utility function is slightly different
than ours, the main difference is that they normalize per capita consumption to be 1. Aggregate real per capita consumption for 2013–2017 is about$35,200. Adding ln(35, 200) to our value of ¯u gives about 4.66 which is much closer to their value.
4
Results
Figure 4 shows the cross-sectional distribution of economic welfare. A positive (negative) number means that the group is better (worse) off than the average American. Quite intuitively, welfare is generally increasing in educational attainment within gender and race-ethnicity categories.11 This means that the additional consumption and life expectancy for highly educated groups dominates the disutility from more work. Within education and race-ethnicity categories, women have higher welfare than men. While woman and men have fairly equal consumption streams, women tend to live longer and devote less time to market work. Finally, within gender and education categories, Asians tend to have the highest welfare, Blacks the lowest, and Whites and Hispanics somewhere in the middle. In fact, Asian and Hispanic women have higher welfare than the average American whereas Black men and women with less than a college degree have lower levels of welfare than the average American.
While the qualitative results provide a sense of the welfare orderings, we are ultimately after quantitative results. How big are the welfare differences quantitatively? Quite large. The economic welfare of the average college-educated Asian woman is 152 percent higher than the welfare of the average American while the average Black or White man without a high school degree is about 65 percent lower. Translated into equivalent variations, a person would be indifferent between living the life path of the average Black or White man without a high school degree and the life path of the average American with 65 percent lower consumption. Put another way, the average American would be willing to forgo up to 65 percent of annual consumption to avoid living the life path of a White or Black man who did not complete high school.
11The only exception is Asian males without high school degrees have higher welfare than Asian males
who completed high school. This is coming from the fact that the former group expects to live about a year longer.
Less HS HS College -100 -50 0 50 100 150 Less HS HS College -80 -60 -40 -20 0 20 40 Less HS HS College -50 0 50 100 150 200 Less HS HS College -40 -20 0 20 40 60 80
Figure 4: Baseline Equivalent Variation.
Notes: Equivalent variation is amount one would change the average Americans consumption so that lifetime utility equals that of each demographic group. It is expressed as λ× 100 where λ comes from Eq. (2). Time period is 2013-2017.
On the other end of the distribution, the average American would need to raise their consumption by 152 percent to be indifferent between living that life path and the life path of the average college-educated Asian woman. These figures are also large for college-educated White women (118 percent) and college-educated Hispanic women (74 percent). The college education premium, defined in this context as the difference in welfare between high school graduates and those with at least a bachelor’s degree, ranges from 50 percent (Hispanic women) to 105 percent of consumption (White women) and is 71 percent on average. The high school education premium, defined analogously, is 20 percent on average and ranges from from -4 percent (Asian men) to 55 percent (White women). The numbers are probably an upper bound for the welfare premiums of additional school because we start the analysis after education decisions have been made and their resource and time costs have been incurred.12 How do cross-sectional differences in welfare compare to cross-sectional differences in income? Within each group we calculate average pre-tax wage income and total income weighting by the CE sample weights. Lifetime income is defined as the present discounted value of income over all ages for a given group with a discount rate of two percent. All of
12We say “probably” because there might be a consumption value to school that dominates the sum of the
time cost and resource cost paid at the time. If college graduates in the data are paying back loans, that will be reflected in lower consumption.
our measures of income are in relative terms, i.e. group i’s income relative to the average American. In calculating the cross-sectional standard deviations, we weight each group by their share in the population according to the 2013-2017 ACS. Table 2 shows the results. The standard deviation of economic welfare is 35 percent higher than in lifetime income, but comparable to income inequality at midlife. The standard deviation of consumption is less than half of the standard deviation of welfare. These results point to potential shortcomings of inferring welfare inequality from consumption inequality.
Table 2: Standard Deviations of Relative Income and Welfare St. Dev. λ 11.31 Lifetime income 8.73 Average income 8.38 Average consumption 4.92 Age 40-54 income 10.07 Age 40-54 wage income 11.49
Figure 5 shows the correlation between lifetime income (expressed in relative terms) and economic welfare. There is an obvious positive, albeit imperfect, correlation between welfare and income. The correlation is about 0.55. This is much lower than the correlations between welfare and GDP across countries as in Jones and Klenow (2016) and across states as in
Falcettoni and Nygaard (2020). Part of this is coming from the fact that, on average, women
earn lower income over their lifetimes but enjoy longer life expectancies and less time spent on market work. The correlation between welfare and income within genders is 0.83 for women and 0.88 for men. Falcettoni and Nygaard (2020) report a correlation of about 0.80 across American states.
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -100 -50 0 50 100 150 200
Figure 5: Relationship between lifetime income (normalized by US average) and welfare.
Notes: Equivalent variation is amount one would change the average Americans consumption so that lifetime utility equals that of each demographic group. It is expressed as λ× 100 where λ comes from Eq. (2). Income by demographic group is normalized to 1. Time period is 2013-2017.
4.1
Decomposing the components of welfare
As we discussed in the previous section, economic welfare can be decomposed into its five constituent parts: life expectancy, average consumption, average leisure, within-group consumption inequality, and within-group leisure inequality. The variance of total economic welfare can be decomposed into the associated covariances using Equation 3. Stacking the results for life expectancy, consumption, leisure, consumption inequality, and leisure inequality into a 24 by 5 matrix, X, then,
Var[ln(1 + λ)] = 5 ∑ i=1 5 ∑ j=1 cov(Xi, Xj)
where i and j index columns. Transforming this into shares gives
1= ∑ 5 i=1∑ 5 j=1si,j s2 λ .
Table 3 shows the results. The variance of economic welfare is overwhelmingly driven consumption and life expectancy inequality. Life expectancy alone accounts for about half of the total variance. Inequality in leisure plays a non-negligible role especially once one includes the negative covariance between leisure and consumption. Within-group inequality accounts for almost none of the variance. Consequently, the differences in economic welfare
across groups are almost entirely driven by differences in group-specific average values of consumption, leisure, and life expectancy rather than differences within groups. In other words, White men without high school diplomas have lower welfare because of lower average consumption and life expectancy and not because there is a lot of within-group inequality.
Table 3: Variance Decomposition of Welfare Components Life exp Cons Leis Cons ineq Leis ineq
Life exp 50.93 18.60 -2.35 -0.15 1.01
Cons 26.35 -7.81 -0.72 0.34
Leis 4.90 0.13 -0.23
Cons ineq 0.07 0.01
Leis Ineq 0.08
Along the same lines as Table 3, we can decompose each group’s welfare into its five constituent parts. Figures 6 and 7 show the results from men and women, respectively. It is clear visually how big of a role consumption and life expectancy play. For instance, Black women with a high school diploma have 27 percent lower welfare than the average American. Leaving the average American’s consumption and leisure the same, going from the life expectancy of the average American to the average high school educated Black woman (a difference of about 1.3 years) lowers welfare by about 10 log points or 9.66 percent (100∗ exp(−0.1016) − 1). Likewise, the lower average consumptions for high school educated Black women lower welfare by 33 log points and higher average leisure raises welfare by 7.5 log points.
Less HS HS College -80 -60 -40 -20 0 20 40 Less HS HS College -80 -60 -40 -20 0 20 Less HS HS College -50 0 50 Less HS HS College -60 -40 -20 0 20 40
Figure 6: Decomposition of Economic Welfare for Men.
Notes: Equivalent variation is decomposed into its five components shown in Eq. (3). E(T ): life expectancy; c: consumption; l: leisure; ˜c: within group consumption inequality; ˜l: within group leisure inequality. Time period is 2013-2017.
With the exception of Asian men and women, the educational gradient of life expectancy is enormous. Hispanic men who graduate college expect to live more than four years longer than those with only high school degrees. This raises welfare by about 36 percent. Similarly, White women who graduate college expect to live close to five years longer than high school graduates. This raises economic welfare by 65 percent.
Less HS HS College -40 -20 0 20 40 60 Less HS HS College -60 -40 -20 0 20 40 Less HS HS College -40 -20 0 20 40 60 80 Less HS HS College -50 0 50
Figure 7: Decomposition of Economic Welfare for Women.
Notes: Equivalent variation is decomposed into its five components shown in Eq. (3). E(T ): life expectancy; c: consumption; l: leisure; ˜c: within group consumption inequality; ˜l: within group leisure inequality. Time period is 2013-2017.
If one considers the “quality of life” to be the consumption and leisure one enjoys in each period as well as the disutility one suffers from within-group inequality, then the quantity is more important than the quality for most groups. Specifically, ‘quantity’ is defined as the life expectancy portion of the welfare decomposition and ‘quality’ is defined as the sum of the other four variables that make up welfare. Figure 8 gives an idea of the quantitative magnitudes of quality versus quantity and how they are related. There is a strong correlation between quality and quantity of life with a correlation coefficient of 0.62. At the same time, one observes that the variation in quantity of life is much bigger than the variation in quality of life. The relatively lower variation in quality of life is coming from the fact that those who enjoy less consumption on average tend to take more leisure. Taken together, inequality in quality of life is much lower than inequality in quantity of life although both are quantitatively significant.
-50 -40 -30 -20 -10 0 10 20 30 40 -80 -60 -40 -20 0 20 40 60 80
Figure 8: Quality and Quantity of Life
Notes: Equivalent variation is decomposed into its 5 components shown in Eq. (3). ‘Quantity of life is life expectancy (E(T )). ‘Quality of life is the sum of the remaining components. c: consumption; l: leisure; ˜c: within group consumption inequality; ˜l: within group leisure inequality. Time period is 2013-2017.
4.2
The Evolution of Welfare over Time
We now turn our attention to how welfare has changed over time. In particular, we compare the distribution of economic welfare in 2013-2017 to economic welfare from 2000-2004. We choose the starting date of 2000 because that is the first year of the American Community Survey. In principle, we could also calculate mortality rates using the 1980 or 1990 censuses, but the race and ethnicity classifications have changed over time which complicates comparisons with the more current data.
We are interested in two related questions. First, what has happened to each group’s relative welfare ranking over time? And second, how has welfare, in an absolute sense, evolved over time for each group? To answer the first question, we again use the equivalent variation as our measure of welfare and compute them for the 2000-2004 period using the average American in 2000-2004 as the base group. If the equivalent variation in the later period is higher than in the earlier period, then the group has improved relative to the average American.
Figures 9 and 10 show how the relative welfare rankings have changed over time. The most striking observation is that college-educated individuals of all genders and races have improved their relative standing in the later period. This is consistent with the polarizing
of mortality rates as emphasized by Case and Deaton (2017). The second observation is that Black and Hispanic men experienced increases in their welfare relative to the American average across all education levels.
Less HS HS College -100 -50 0 50 Less HS HS College -80 -60 -40 -20 0 20 Less HS HS College -20 0 20 40 60 80 Less HS HS College -60 -40 -20 0 20 40
Figure 9: 2013-2017 vs 2000-2004 Welfare: Men
Notes: Equivalent variation is amount one would change the average Americans consumption so that lifetime utility equals that of each demographic group for each time period: Early=2000-2004 and Late=2013-2017. It is expressed as λ× 100 where λ comes from Eq. (2).
To answer how welfare has changed in absolute terms, we calculate the percent one would have to change consumption of the average member of group i in 2000-2004 to be indifferent between living as a member of that group in 2013-2017 and living as a member in that group in 2000-2004 with the revised consumption profile. We infer the group experienced an increase in welfare if the equivalent variation is positive.
Less HS HS College -50 0 50 100 150 Less HS HS College -60 -40 -20 0 20 40 Less HS HS College 0 50 100 150 200 Less HS HS College 0 20 40 60 80
Figure 10: 2013-2017 vs 2000-2004 Welfare: Women
Notes: Equivalent variation is amount one would change the average Americans consumption so that lifetime utility equals that of each demographic group for each time period: Early=2000-2004 and Late=2013-2017. It is expressed as λ× 100 where λ comes from Eq. (2).
Figure 11 shows the results. Black men of all education categories experienced welfare gains of about 50 percent over the 14 year interval. Hispanic men also increased welfare gains of about 30 percent across education categories. On the other end of the spectrum, White men and women without high school degrees experienced welfare decreases and there was approximately no change in welfare among Whites with high school degrees. The correlation between welfare growth and initial welfare levels is -0.12, implying a limited degree of convergence.
It is likely that the low equivalent variations for the group with the least education could be coming from, in part, a change in group composition. In particular, the fraction of the adult population with at least a high school degree has increased over the last 20 years.13 If the low education group is increasingly negatively selected for, this will lower the equivalent variations for the dropout group. At the same time, the gains experienced by the college educated are likely understated as that group has expanded as a fraction of the adult population since 2000. Consequently, we cannot say how much of these changes are coming from a change in composition.
Even if some of the changes over time are driven by composition, the fact remains that
13In the ACS, adults without a high school degree make up about 17 percent of the sample in the early
there is increasing dispersion along the dimension of education. The disparity of welfare gains over the last two decades could be connected to the political polarization that Autor
et al.(2020), among others, speak to. On the other hand, the small degree of convergence
between groups that we observe is similar in spirit to the converging occupation shares across demographic groups thatHsieh et al. (2019) highlight. Their analysis starts in 1960 when there was much more misallocation, so it’s natural to expect less convergence in our sample years. Later we show that the rise of deaths of despair have played a particularly important role in affecting the changes in welfare for lower educated Whites.
Less HS HS College -20 0 20 40 Less HS HS College 0 20 40 60 Less HS HS College 0 10 20 30 40 Less HS HS College 0 10 20 30 40
Figure 11: Welfare Growth 2000-2004 to 2013-2017
Notes: Welfare growth is the equivalent variation is amount one would change the average member of each demo-graphic groups consumption in 2000-2004 so that lifetime utility equals that of the same demodemo-graphic group in 2013-2017.
4.3
The Geography of Economic Welfare
In a similar framework to ours, Falcettoni and Nygaard (2020) examine the distribution of economic welfare across states in the US. While we do not directly address the question of geography, we do have the demographic composition of each state from the ACS data. We estimate the welfare for a state by taking a weighted average of each demographic group’s economic welfare with the weights being equal to the proportion of a demographic group in a state. We then compare our estimates for each state’s economic welfare with the calculations
inFalcettoni and Nygaard.
The results are shown in Figure 12. The correlation between the two series is 0.78. The models are very closely aligned on the states with low economic welfare which is shown in the top right of the plot. Eight of the ten states with the lowest welfare in our model are also in the bottom 10 of Falcettoni and Nygaard’s model, with Indiana and Georgia being the exceptions (38th and 40th respectively in Falcettoni and Nygaard). Our predictions are different at the top of the distribution where only five of the ten states with the highest welfare in our model are in Falcettoni and Nygaard’s top ten.
0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50
Figure 12: Comparison of Two Welfare Measures
Notes: Each states equivalent variation is λ× 100 for each demographic group from Eq. (2) and weighted by each states demographic composition. The CGL rank is the states ranking in equivalent variation by highest to lowest and is plotted against the corresponding state rank inFalcettoni and Nygaard(2020).
This high correlation is somewhat surprising given that Falcettoni and Nygaard (2020) include the consumption of housing and also incorporate different prices for consumer goods across states while our measure is solely driven by demographic composition. Nevertheless, it is reassuring that we come up with a similar ranking.
4.4
Summary
In summary, the results show that differences in economic welfare are primarily driven by differences in consumption and life expectancy. Cross-sectional differences in leisure play a more modest role quantitatively and within-group inequality accounts for almost nothing. Groups that consume less on average also tend to work less which dampens quality of life differences. There are large educational gradients in economic welfare and women have higher welfare than men (within education and race-ethnicity categories). Black individuals have the lowest welfare on average, Asians the highest, and Whites and Hispanics in the middle. We have thus far equated time spent not working to leisure. For anyone who has toiled in a garden or folded laundry, this is an obvious mischaracterization.14 One may wonder to what extent the welfare differences in gender are driven by equating time not at work to leisure. In the next section we use the American Time Use Survey to further delineate leisure time from other near work activities.
5
Extending the Model
5.1
Home Production
Equating “leisure” with the residual of time spent on market work may not be a completely accurate way of capturing the work/life dichotomy. From surveys, we know that some portion of time spent outside of market work is devoted to home production – producing goods and services at home that could alternatively be purchased in the market – and to care for children. Figure 13 shows that, within education and race-ethnicity groups, men spend more time in market work than women while women spend more time on home production and child care than men.15 Consequently, including time spent on home production and caring for children shrinks the difference in leisure between men and women.
14Some people derive utility from working in a garden; the authors do not.
15Data is from the American Time Use Survey and compiled bySandra L. Hofferth and Backman(2020).
M W M W M W 0 0.1 0.2 0.3 0.4 0.5 M W M W M W 0 0.1 0.2 0.3 0.4 0.5 M W M W M W 0 0.1 0.2 0.3 0.4 0.5 M W M W M W 0 0.1 0.2 0.3 0.4 0.5 College Less HS HS HS Less HS College College HS Less HS HS College Less HS
Figure 13: Market Work and Home Work.
Notes: Decomposition of share of time spent in market work, home production, and child care. Components of market work and child care are detailed in AppendixB.4. Data is from the American Time Use Survey, 2013-2017.
To account for time spent on home production we change the within-period utility function to
¯
ui= ¯u + ln(¯c) + v(¯l) (4)
where ¯l= 1 − ¯hhome− ¯hwork. That is, we now evaluate the utility at the means for consumption
and leisure rather than taking mean utility. We do this because time spent on home production comes from a different data set than consumption so we cannot obtain the joint distribution. An implication of this is that we cannot talk about within-group inequality. Fortunately, the variance decomposition results from the last section showed that within-group inequality accounted for very little of the variance in economic welfare. There are two, perhaps larger, concerns. The first is the assumption that home production has the same disutility as market work. Ramey and Francis (2009) provide evidence that people find some home production activities more pleasurable than market work. Additionally, there is an argument as to whether care for children and other family members should be included in home production since those services might be difficult to purchase on the market. The second concern is
that home production only accrues a cost with no offsetting benefit. That is, the utility function does not include “home consumption.” The reason for this is we would need to take a stand on the home production technology. While both these concerns are valid, we think our approach is useful because it provides an upper bound on the effects of home production. By defining home production in the broadest way possible (i.e. including care of children) and making it as displeasurable as market work, our measure of leisure, and women’s leisure in particular, will be most affected. Not including consumption of home produced goods will also disproportionately lower women’s welfare. This is because (within education and racial groups) women have longer life expectancies than men and will therefore get more out of the increases in flow utility coming from consumption of home produced goods.16 Adding home consumption or making home production activities more valuable will shrink the differences between the model with home production and the model without it. For comparisons sake, we present results when we count child care as home production versus not counting it as home production. In each case, we recalibrate the disutility of labor parameter, θ, to match average time use (market work plus home work).17
Less HS HS College -100 -50 0 50 100 Less HS HS College -60 -40 -20 0 20 40 Less HS HS College -50 0 50 100 150 Less HS HS College -40 -20 0 20 40 60 Men Women
Figure 14: Economic Welfare Including Child Care
Notes: Equivalent variation is amount one would change the average Americans consumption so that lifetime utility equals that of each demographic group. It is expressed as λ× 100 where λ comes from Eq. (2). Leisure is defined as time not working, in home production, or childcare. Time period is 2013-2017.
16Technically, this argument assumes that the home produced output is equally split among household
members, which is the same assumption we make in the CE data, and that there is not complementarity between leisure and consumption.
17More specifically, θ =(1−τ )w
Less HS HS College -100 -50 0 50 100 150 Less HS HS College -60 -40 -20 0 20 40 Less HS HS College -50 0 50 100 150 Less HS HS College -40 -20 0 20 40 60 Men Women
Figure 15: Economic Welfare Excluding Child Care
Notes: Equivalent variation is amount one would change the average Americans consumption so that lifetime utility equals that of each demographic group. It is expressed as λ× 100 where λ comes from Eq. (2). Leisure is defined as time not working or in home production. Time period is 2013-2017.
Figures 14 and 15 show the results with including and excluding child care in home production. The qualitative patterns share some similarities with the results in the previous section. Welfare is higher for the better educated and for women. The quantitative results, on the other hand, are somewhat different. First, there is a reduction in the range of welfare across groups but the ranking is about the same. Black and White men without a high school degree continue to have the lowest welfare and Asian women with college degrees have the highest. The gaps in welfare between men and women are smaller than in the baseline.
Table 4reports summary statistics of the economic welfare with home production and welfare without home production. As in the previous section, the means and standard deviations are weighted by population shares in the ACS. Several observations stand out. First, economic welfare without home production is highly correlated with economic welfare with home production regardless of whether child care is included in home production. Second, including home production shrinks the cross-sectional variance of welfare. This is expected since women have higher welfare than men in the baseline calculations but also work more at home. We can think of the gender gap in this context as the differences in economic welfare across gender for given education and race-ethnicity categories. This leads to the final observation that, under the broadest definition of home production, the gender gap is cut in half from the model without home production but remains quantitatively large.
Indeed, this says that the difference between what the average American would need to be compensated to live life as the average man versus the average woman is about 23 percent of annual consumption.
Table 4: Comparing Welfare with and without Home Production Statistic Corr(λhp+cc, λbase) 0.94 Corr(λhp), λbase) 0.97 std(λbase) 11.31 std(λhp) 10.25 std(λhp+cc) 9.86
Gender gap (without hp) 49.94 Gender gap (with hp) 30.63 Gender gap (with hp + cc) 22.75
Due to the simplifying assumptions we made with home production, we conclude that 49.94 is an upper bound for the gender gap in welfare and 22.75 is the lower bound. Evidently, the benefits of longer life expectancy dominate the costs of more time spent working.
How do these results compare to the gender gap under more conventional definitions such as wages? The unconditional gender wage gap (i.e. the ratio between average annual earnings for women and annual earnings for men) in 2014 was about 79 percent (Blau and Kahn, 2017). This number changes once one controls for relevant economic variables. In our framework, the average gender difference in welfare already controls for race-ethnicity and education. Consequently, our lower-bound estimate of the gender gap in welfare (with home production) is quantitatively similar to the unconditional gender gap in wages, which is generally thought to be an upper bound.
5.2
Deaths of Despair
Case and Deaton (2017) document a rise in midlife mortality for less educated White
Non-Hispanics beginning around 1998. They trace these increasing mortality rates to the proliferation “deaths of despair” which include suicide, drug and alcohol poisoning, chronic liver disease, and cirrhosis. Indeed, the increase in deaths of despair were large enough to increase mortality rates despite mortality rates of other causes of death declining. They conclude that had mortality rates stayed at their 1998 level, 96,000 deaths would have been avoided between 1999–2013. In this section we ask what would happen to economic welfare had the probability of a death of despair in 2013-2017 stayed the same as 2000-2004.
Our quantitative exercise is slightly different from the earlier sections. In particular, we ask how much consumption a person in a given demographic group facing 2013-2017 mortality rates (and 2013-2017 levels of consumption and leisure) would be willing to sacrifice to live an alternative life where the probability of a death of despair equals its value from 2000-2004. Our data includes the cause of death, which allows us to measure the contribution of deaths of despair to overall mortality. In this exercise, we compute counterfactual mortality rates for 2013-2017 by replacing the mortality rates from deaths of despair with their 2000-2004 levels and leave the death rate from all other causes equal to their 2013-2017 levels.
Figure 16 shows the results. Consistent with the findings of Case and Deaton (2017), the welfare losses are largest for Whites. A White man or woman without a high school degree would give up about eight percent of annual consumption to return to the 2000-2004 mortality rates for deaths of despair. At the other end of the distribution, college educated Black men experienced a decrease in deaths of despair between 2000-2004 and 2013-2017.
Less HS HS College -8 -6 -4 -2 0 Less HS HS College -2 -1 0 1 Less HS HS College -2 -1 0 1 Less HS HS College -1.5 -1 -0.5 0 Men Women
Figure 16: Welfare Gains from Counterfactual Deaths of Despair
Notes: Deaths of despair are defined as in Case and Deaton(2017). Counterfactual deaths of despair replaces mortality rates from deaths of despair for each demographic group in 2013-2017 with each groups deaths of despair observed in 2000-2004. Equivalent variation is amount one would change the average demographic groups con-sumption in 2013-2017 so that lifetime utility equals that of each demographic group facing counterfactual deaths of despair, holding all consumption and leisure components constant.
By and large, people with less education would be willing to sacrifice more consumption to avoid deaths of despair. This is particularly true among Whites. Our findings are consistent
with Novosad, Rafkin, and Asher (2020) who show that increasing mortality rates among
Whites is attributed to rising mortality in the bottom part of the education distribution. Referring back to Section 4.2, we found that less educated Whites were the only group in which our welfare measure decreased from 2000-2004 to 2013-2017, and this rise of deaths of
despair for these groups in particular may be a significant factor behind this finding.
5.3
Robustness
In this section we show that our quantitative findings are robust to changing preferences and different ways of defining and measuring consumption.
First, consider a more general within-period utility function
u(c, l) = (c exp ( θ 1+1(1 − l) 1+1 )) 1−σ − 1 1− σ .
Of course, our utility function in the previous sections was just the special case of σ = 1. We perform comparative statics by changing σ, , and the value of a statistical life. For a given σ, , and VSL, we recalibrate ¯u and θ to match the VSL and average hours worked respectively. We ignore home production and within-group inequality. That is, we evaluate the utility function at the group average rather than calculating average utility. Our definition of economic welfare continues to be the equivalent variation, which can be solved for in closed form. The derivations are in Appendix A.
Figure 17 shows the box plots of the equivalent variations. The left most plot shows the equivalent variation as we change holding all other parameters constant. The distribution is not much affected by . The VSL and σ, however, play a much larger role. As the VSL increases, the equivalent variations become more dispersed. This is not very surprising in light of our findings that life expectancy accounts for much of the welfare differences across groups. As the VSL increases, those with low mortality rates benefit disproportionately. Since those with low mortality rates had high welfare to begin with, larger VSLs increase cross-group inequality. As σ increases, an individual with these preferences becomes less willing to intertemporally substitute. This also increases inequality across groups.18
18As σ increases our results become quite sensitive to how we define consumption. That is, defining
consumption as relative to the average in the US (asJones and Klenow(2016) andFalcettoni and Nygaard
-50 0 50 100 150 0 100 200 300 VSL = 6 VSL=7 VSL=8 -50 0 50 100 150 (baseline) (baseline) (baseline)
Figure 17: Changing Parameters
Notes: Boxplots show the distribution of equivalent variation across all 24 demographic groups for various param-eterizations. The baseline distribution is given as middle series in each plot. Equivalent variation is amount one would change the average Americans consumption so that lifetime utility equals that of each demographic group. It is expressed as λ× 100 where λ comes from Eq. (2). Time period is 2013-2017.
Next, we go back to our baseline utility function, but consider several variants of the consumption measure. In all of our previous results, we have used consumption of non-durables and services where each consumption category is deflated using a good-specific price deflator from the CPI. The first alternative consumption measure is to include durables, while continuing to deflate by the good-specific CPI. Additionally, we consider case where nominal consumption (excluding durables) is deflated by the total CPI and the PCE.
The results are displayed in Figure 18. The results are very similar across specifications. The correlations between economic welfare in the baseline and any of the three alternatives are all greater than 0.99.
Durables CPI PCE Baseline -50 0 50 100 150
Figure 18: Changing the Definition of Consumption and Price Indices
Notes: Boxplots show the distribution of equivalent variation across all 24 demographic groups for various defini-tions of consumption and price indices for deflating consumption. Equivalent variation is amount one would change the average Americans consumption so that lifetime utility equals that of each demographic group. It is expressed as λ× 100 where λ comes from Eq. (2). Time period is 2013-2017.
Finally, we compare the equivalent variations to compensating variations, i.e. the fraction of consumption the average member of group i needs to be compensated in order to be indifferent between living as a member of group i and the average person in the US. These two numbers will be different because groups do not share the same mortality rates. Nevertheless, as Figures 19 and20 show, the compensating and equivalent variations are very close to each other.
Less HS HS College -100 -50 0 50 Less HS HS College -80 -60 -40 -20 0 20 Less HS HS College -20 0 20 40 60 80 Less HS HS College -40 -20 0 20 40
Figure 19: Compensating and Equivalent Variation - Men
Notes: Equivalent variation is amount one would change the average Americans consumption so that lifetime utility equals that of each demographic group. Compensating variation is amount one would change the average member of demographic group i so that lifetime utility equals that of the average American. Time period is 2013-2017.
Less HS HS College -50 0 50 100 150 Less HS HS College -60 -40 -20 0 20 40 Less HS HS College 0 50 100 150 200 Less HS HS College 0 20 40 60 80
Figure 20: Compensating and Equivalent Variation - Women
Notes: Equivalent variation is amount one would change the average Americans consumption so that lifetime utility equals that of each demographic group. Compensating variation is amount one would change the average member of demographic group i so that lifetime utility equals that of the average American. Time period is 2013-2017.
6
Conclusion
A wide range of economic research is devoted to understanding economic inequality in the US. We contribute to this body of research by documenting how economic welfare is distributed across the population and how that distribution has changed over the last 20 years. We find that, conditional on other demographic information, women have higher welfare than men, Asians have the highest welfare and Blacks the lowest, and welfare is rising with educational attainment. The qualitative rankings are robust to a variety of ways in defining consumption and leisure and parameter choices in the utility function.
We also make some progress towards understanding how income correlates with economic well-being. The correlation between our baseline measure of economic welfare and pre-tax lifetime income is about 0.5, but rises significantly when we compute the correlation within genders. In terms of dispersion, the standard deviation of welfare is 35 percent higher than the standard deviation of lifetime income, but comparable to the standard deviation of income during prime earning years. While quality of life (which is a function of consumption and leisure) is distributed more equally than income, the vast differences in quantity of life, and the fact that quality and quantity of life are positively correlated, imply that the welfare distribution is more unequal than the lifetime income distribution.
While we included several important components of welfare, we omitted innumerable others. A non-exhaustive list includes: utility from public goods, exposure to pollutants, morbidity, and occupational differences in the disutility of work. In terms of differential morbidity, Hosseini et al. (2019) develop a frailty index to study how health evolves over the life cycle. Kaplan and Schulhofer-Wohl(2018) document how feelings at work vary by race, education, and gender. We conjecture that our framework could be adapted to take into account both of these features. Thus, we see them as attractive areas for future research. Finally, using our framework, it could be worthwhile to investigate inequality in childhood. This is something we intentionally excluded, because including cohorts in which education decisions have not yet materialized may obscure inequities driven by education. In other words, we focus on welfare differences across education groups rather than welfare differences stemming from different probabilities of educational attainment by demographic groups. Future work could quantify the role of variable childhood environments on lifetime welfare differences.
