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Whether and How to Adjust Income Trends For Declining Household Size

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Scott Winship

I recently wrote a scintillating essay on the best way to adjust household income growth to take inflation into account. If you loved that one—and you both know who you are—the next 3,000 words are going to be pure bliss. The conclusion of the cost-of-living essay was that researchers looking at income growth should use a specific price index—the “Personal Consumption Expenditures” (PCE) deflator—to put incomes into constant dollars. The conventional approach understates the extent to which living standards have improved over the long run.

This time I will make the case that incomes also should be adjusted for household size when looking at trends, and I will argue that the conventional way of doing so is not only reasonable, but conservative compared with other approaches that have been used. It is important to adjust incomes for household size when analyzing trends in living standards because households are smaller today than in the past. Once incomes have been adjusted to constant dollars to take inflation into account, $50,000 today goes further than it did in the 1960s because it must be shared by fewer household members. This improvement in living standards is neglected if we ignore the fact that three people living together need less than four people. But I’m getting ahead of myself.

Should We Adjust for Declining Household Size?

Many analysts and commentators believe that adjusting for declining household size is wrong-headed if we are interested in assessing changes in living standards over time. They view shrinking households as a reflection of growing hardship. As times have become tougher, fewer people feel comfortable having children or having as many as they would like. Others delay marriage or forego it entirely, either because they cannot afford to support a family or cannot find a partner who is able to do so. Divorce reduces household size, and economic stress has made divorce more common over time. Given these trends, “adjusting” incomes to account for the drop in household size is perverse—it makes trends in living standards look better than they are when in actuality we should be making an adjustment in the other direction.

In contrast, the argument for size-adjustment is that the drop in household size either has nothing to do with economic trends or reflects the rising affluence of Americans. With increasing wealth, families have substituted more “stuff” for the children they would have had in the past. Greater wealth has also enabled more people to move out of their parents’ home, delay or forego having to live with a spouse or partner, walk away from unfulfilling relationships, and live without roommates.

Which side has the better case? It’s not even close.

The table below shows trends in household composition for thirtysomethings in the Current Population Survey (CPS), the primary source of income estimates. Focusing on adults in their thirties prevents changes in the age distribution from influencing the trends. The table reveals the 1970s as a period of dramatic change. The number of thirtysomethings with children fell from 85 percent in 1970 to 76 percent in 1980, and the number of children among parents fell from 2.9 to 2.2. These changes reduced average household size from 4.5 to 3.7.


hhsizetab1Source: Annual Social and Economic Supplement, Current Population Survey microdata.

These trends continued in the 1980s and to a limited extent in the 1990s, but at a diminished pace. In contrast, the number of adults per household among thirtysomethings did not fall at all through 1990. Marriage declined, but cohabitation appears to have increased. The conclusion is that from 1970 to 1990, household size shrank considerably, largely because fewer adults had children and those that did had fewer of them.

Did the falling number of children reflect rising prosperity or rising hardship? One clue is provided by the fact that the number fell between 1970 and 1990 among both lower- and higher-educated Americans. In the CPS we can track, roughly, the lowest-educated 12 percent of thirtysomethings, the highest-educated 30 percent, and the majority between them. (Since educational attainment is lumpy—with many more people having, for instance, 12 years of schooling than 11 or 13 years—it isn’t possible to look at, say, the bottom and top fifth of educational attainment.) The chart below shows that among the least-educated thirtysomethings, average children per household fell from 2.82 to 1.82 between 1970 and 1990. In the group of moderately-educated thirtysomethings, the fall was from 2.56 to 1.46. Meanwhile, among the thirtysomethings with the most education, the drop was from 2.21 to 1.15 children. The average, in other words, dropped by a full child among all three groups. If worsening economic conditions were leading families to have fewer children, we would expect that the decline in the number of children would be larger among less-educated adults. But the opposite is true: the more educated the person, the scarcer children became.


hhsizechart1Source: Annual Social and Economic Supplement, Current Population Survey microdata.

After 1990, the evidence also goes against the claim that diminished living standards have driven changes in household size. Household size actually rose a bit between 1990 and 2010, from an average of 3.5 people to 3.6. That means that during this period, adjusting for household size will tend to make income growth look smaller than it does without any adjustment, not larger. The increase in household size after 1990, however, is dwarfed by the decline in the preceding twenty years.

Once again, it was the number of children per household (which increased) that mattered, not the number of adults (which declined). The number of children in the average thirtysomething’s household rose among the least- and most-educated thirtysomethings and among the people between them. From 1990 to 2010, the increase was from 1.82 to 2.28 for the least-educated and from 1.15 to 1.62 among the most-educated. Changes in the number of children follow the same pattern regardless of educational attainment.

The decline in the number of children born to families did not begin in the 1970s. The following chart shows “total fertility rates” in the United States for white and black women. The total fertility rate is the number of children that would be expected to be born to the average woman if the age-specific birth rates in a given calendar year prevailed throughout a woman’s lifetime as she aged. Total fertility declined steadily from around seven births per white woman in 1800 to just over two in the early 1930s. For black women, the decline was from nearly eight births in 1850 to just under three by 1940. This was a period of unambiguously rising prosperity (at least until 1929), as shown by the increase in logged GDP per capita (the dashed black line in the chart).


hhsizechart2Sources: Historical Statistics of the United States, Millenial Edition, Tables Ab52-117 (1800-1989); National Center for Health Statistics, National Vital Statistics Report 64(1), 2015 http://www.cdc.gov/nchs/data/nvsr/nvsr64/nvsr64_01.pdf (1990-2013); Louis Johnston and Samuel H. Williamson, “What Was the U.S. GDP Then?” MeasuringWorth, 2010 (www.measuringworth.org/usgdp).

The chart then shows a temporary rise in fertility rates—the baby boom depicted as an anomalous bump in the long-term trend. The 1960s and 1970s represent the downward part of this bump, and by 1972 fertility was at a new low for white and black women. After bottoming out at 1.7 births per woman in 1975, the total fertility rate among white women then rose slightly. Hispanics have comprised an increasing share of “whites” in recent decades, so a proper comparison over time should look only at non-Hispanic whites. That data goes back only to 1990 (see the red line). It is clear that the total fertility rate for white women remains near historic lows, and well below the 1960 or 1970 levels. Among black women, the secular decline in the fertility rate continues to this day and the rate has more or less converged with that of whites (after a temporary rise in the second half of the 1980s).

In short, the decline in household size since the 1960s was driven by declining fertility in the 1960s and the first half of the 1970s, which reduced children per family through the 1980s. The drop in fertility began in the late 1950s during the thick of the “Golden Age” of the mid-twentieth century, a time when middle-class incomes were growing rapidly, poverty was dropping, and inequality was flat or declining. The decline in fertility extends back at least to the start of the 19th century. Not only was this a period of rising prosperity for Americans, but fertility declined dramatically among both whites and blacks. Both the highest educated and lowest educated thirtysomethings had fewer children over time between 1970 and 1990, suggesting that economic conditions were unrelated to the decline. The average number of children for both groups was constant during the economically strong 1990s and rose during the “Lost Decade” of the 2000s. None of this is consistent with the claim that falling household size reflects rising hardship.

What else is wrong with the claim? Well, hardship did not actually rise. That is, it is not necessary to adjust for household size to see that living standards have risen over time. The Census Bureau indicates that “money income”—income from private sources, plus cash from federal transfer programs—rose by 10 percent between 1969 and 2013 and by 20 percent from 1969 to the more-comparable year of 2007. Using the PCE deflator to adjust for the rise in the cost of living, the increase was 23 percent from 1969 to 2013 and 31 percent from 1969 to 2007. In fact, these are very conservative estimates, because they do not take into account the value of health insurance or deduct taxes. Health insurance has become a bigger share of employee compensation, and Medicare and Medicaid for older Americans have become more generous. Taxes have fallen significantly since 1969. The point here, however, is just that no matter how you measure income or inflation, the middle class has become more prosperous over time, not less.

Similarly, poverty has declined. That’s not true of the official Census Bureau estimates (though they show poverty among female-headed families with children declining), but all of the various attempts to correct the flaws of the official poverty measure show poverty lower today than in 1969.

Nor have the earnings of middle-class or low-skilled men declined over this period, though they have not risen appreciably. While many observers insist that the drop in the number of children over time reflects lower marriage rates that were, in turn, caused by a decline in the number of “marriageable men,” this claim falls apart if men’s earnings today are no worse than they ever were.

There is simply no evidence to support the idea that smaller households today reflect a deterioration in living standards rather than improved living standards. Therefore, the question is not whether we should adjust incomes for household size when looking at income trends, but how to do so.

How Should We Adjust For Declining Household Size?


Adjusting incomes to make households of varying sizes comparable requires an “equivalence scale”—a mapping of different household configurations to new household “sizes” that reflect their varying needs. One could, for instance, simply assume that a household of two people needs twice as much income as a single person living alone to have the same level of wellbeing. That’s clearly not right though. Two people living together do not have to pay rent to two different landlords or pay off two mortgages. The most common way of adjusting for the needs of different households is to simply take the square root of household size and then divide household income by this amount. This approach assumes that a household of four people needs twice as much income as a single person living alone (since the square root of four is two and the square root of one is one).

Any number of alternative adjustments are possible. For instance, one might count children as fractional adults to reflect the presumption that an additional child requires less income than an additional adult to maintain living standards. In the past, the Organisation for Economic Co-operation and Development (OECD) has counted additional adults beyond the first as 50 percent of a person and children as 30 percent of a person, then incomes are adjusted by this modified household size.

Alternatively, rather than taking the square root of household size—where the exponent of household size is 0.5—one might use an exponent of 0.3 or 0.7. An influential National Academy of Sciences (NAS) panel in 1995 proposed using an exponent between 0.65 and 0.75, but after multiplying the number of children by 0.7. In the context of declining household size and rising income over the past 45 years, choosing an exponent that is higher than 0.5 will produce larger increases in size-adjusted incomes over time. For instance, using an exponent of 0.5 would mean dividing the incomes of four-person households by 2 in 1969 and dividing the incomes of one-person households by 1 today. But using an exponent of 0.99 would approximate simply dividing the incomes of the earlier four-person households by 4 while continuing to divide the incomes of the later one-person households by 1. Since dividing by 4 will produce smaller initial size-adjusted incomes than dividing by 2, using an exponent of 0.5 will produce smaller gains over time than using an exponent of 0.99.

In the context of falling household size and rising income, dividing income by the square root of household size generally will produce conservative estimates of income gains relative to the gains dividing by the NAS or OECD alternatives. To illustrate, imagine that there was no change in aggregate household income over time. Imagine further that initially all households were comprised of three adults, while today they are all comprised of two adults. Let’s say we simply divide incomes by household size to adjust them. In the initial year, incomes would be divided by three, and in the ending year they would be divided by two, and size-adjusted income would increase by 50 percent (line 8 in the table below).


Now, moving from left to right across lines 1-7 shows the amount by which we would divide incomes to adjust them using different equivalence scales. As we move rightward across lines 2 and 3, the amount by which incomes are adjusted decreases. That means that the size-adjusted incomes will be larger moving from left to right. Line 8 shows that in our hypothetical example where households shrink from three adults to two, adjusting household income for size differences by taking the square root of household size will indicate less of an income gain than if the OECD or NAS approaches were used.

Lines 9 through 14 show the same calculations as line 8 but for different types of household-size decline. In general, adjusting for household size declines by taking the square root of income is the most conservative option. The exception is when households get smaller because there are fewer with any children (lines 11 and 12), where the OECD approach is more conservative. The differences between taking the square root of household size and using the OECD or NAS approaches, however, are modest compared with the extremes of not adjusting incomes at all or simply dividing by household size.

Dividing by the square root of household size (and using the PCE deflator to adjust for inflation), median household income rose not by 23 percent between 1969 and 2013, but by 45 percent. Using the OECD equivalence scale, the increase was 48 percent, and using the NAS scale it was 50 percent.
Taken together, my previous essay on inflation adjustment and this one on household-size adjustment make a crystal-clear case for measuring inflation using the PCE deflator and adjusting incomes by dividing them by the square root of household size. While the Census Bureau estimates suggest that median household income rose by just 10 percent from 1969 to 2013, the methods I have justified using indicate the increase was 45 percent.

Indeed, this estimate also understates the improvement in living standards, for a variety of reasons, including the failure to take health insurance benefits, noncash government transfers, and taxes into account and the comparison of 1969 (a business cycle peak) to 2013 (only a few years into the recovery). My preferred estimates that address these issues indicate that median disposable size-adjusted household income rose by roughly 60 percent from 1969 to 2007 (estimating the effect of health insurance, noncash benefits, and taxes on income from 1969 to 1979 using the impact for 1979 to 2007).

But I’ll put that aside if we can agree that the lower bound on the improvement in living standards for the median household since 1969 is 45 percent, or $22,000 in today’s purchasing power for a family of four. Disagree? Make your case.


[“source – forbes.com”]
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