U.S. MEDIAN HOUSEHOLD INCOME HAS RISEN MORE THAN YOU THINK.

• Author: Cline, William R.
• Position: Report

It is a widespread perception that median incomes have stagnated in the United States for a long time. This perception seems to have increased the force of populism in the 2016 presidential elections. (1) But the story of stagnation is seriously misleading, for three reasons. Two of the reasons pertain to the specific choices Census makes in choosing its deflator and how it chooses to report household income. The third reason is the problem of choosing specific endpoints rather than calculating full-period trends, combined with the fact that in 2014, the final year with data available at the time of the election campaign, incomes were still weak from the Great Recession.

William R. Cline is President of Economics International, Inc., and Senior Fellow Emeritus at the Peterson Institute for International Economics. He thanks Olivier Blanchard for comments on an earlier draft and Fredrick Toohey and David Xu for research assistance.

The most recent Census (2018a) report does show more encouraging trends, with real median household income rising 5.2 percent in 2015,3.1 percent in 2016, and 1.8 percent in 2017 (p. 27). But this recovery was from a low level in 2014, and die Census estimate for 2017 is still only 2.2 percent above die level in 1999, implying near-stagnation (at growth of only 0.12 percent per year) over nearly two lost decades. (2) After correction for a better deflator and for household size, and considering trend rather than specific endpoints, the outcome over this period is far better.

Calculating Trend Income Growth

A classic problem in calculating long-period growth rates is the risk of arriving at misleading conclusions if the rate is calculated simply between two endpoints. If the particular endpoint years chosen show unusually low income in the initial year and unusually high income in the ending year, the result will be to exaggerate the long-term growth rate (and vice versa if the opposites are true). For this reason, it is a classic practice to estimate long-term growth rates using regressions of the logarithm of income on time, in effect giving every year in the time span an equal weight rather than being dependent on just the beginning year and the final year.

If income grows at a constant annual rate of g, income in year t is [Y.sub.t], and [Y.sub.0] what the trendline indicates would have been expected as the base income in the year prior to the beginning of the series, then:

(1) [Y.sup.t] = [Y.sub.0][e.sup.g],

where "e" is the base of the natural logarithm. (3) Taking the logarithm of both sides yields:

(2) In [Y.sub.t] = ln[Y.sub.0] + gt.

A statistical regression of the logarithm of income against time will thus yield a constant term that is the logarithm of the trendline starting point value and a linear coefficient on time that equals the growth rate "g".

Because even a casual inspection of the data does show a clear slowdown in the pace of income growth after 2000, however, it is important to incorporate a shift variable that allows the measured growth rate to decline. One can think of the level of income in the period after 2000 as being the product of the level that would have been predicted using the trend growth rate through 2000, multiplied by a factor that captures the shift in the growth rate after 2000. Thus,

(3) [Y.sub.t] = [Y.sub.0][e.sup.g]t x [e.sup.[delta]T],

where T = 0 for all years before 2000 and then takes the value of 1 for 2000, 2 for 2001, and reaches 17 for 2016. (4) The corresponding logarithmic form is then

(4) In [Y.sub.t] = ln [Y.sub.0] + gt + [delta]T.

Whereas the trendline growth rate will then be simply g in the period before 2000, thereafter the trend growth rate will be g + [delta]. In the logarithmic form, the annual growth rate equals the change in the logarithm divided by the number of years for the period in question. Both t and T rise by unity for each successive year after 2000, so the annual growth rate in the period after 2000 is g + [delta]. The expectation is that in the statistical estimate, [delta] will be found to be negative. A key question is whether the absolute value of [delta] is greater than g, in which case the trendline turns negative after 2000, or less than g, so that growth continues to be positive but at a lower rate than before.

Choosing the Right Deflator

In its annual report on incomes and poverty, Census (2018a) reports real median household income over time deflating by a "research" version of the consumer price index (CPI-U-RS, or [CPI.sub.RS]), compiled by the Bureau of Labor Statistics. In contrast, in its corresponding analysis, the Congressional Budget Office (CBO, 2016, 2018) deflates using the personal consumption expenditure (PCE) from national accounts, prepared by the Bureau of Economic Analysis. Over the past five decades, the cumulative rise in the [CPI.sub.RS] is substantially greater than that in the PCE. Thus, with the average for 1967-70 as an index base of 100, by 2017 prices rose to an index of 603.7 in the [CPI.sub.RS] but only 540.2 in the PCE. (5) Cumulative inflation over this period was thus about 12 percent higher in the [CPI.sub.RS] than in the PCE. Most analysts consider the PCE to be the better index because it takes much better account of substitutability as relative product prices change. (6)

Adjustment for Household Size

Average household size declined from 3.28 persons in 1967 to 2.62 by 2000 and 2.54 by 2017 (Census 2017b). Larger households can be expected to have greater income earning potential from the availability of more potential workers. It is thus important to adjust for household size in assessing the long-term growth of household income. Otherwise, the larger households at the beginning of the period would tend to exaggerate the income levels relative to household incomes toward the end of the period. However, the economic significance of size is likely to be less than linear. From the earning standpoint, the additional household members in the early period would tend to have included the young and the elderly, so income potential would not have been expected to be higher by the full proportion of larger household size. From the consumption standpoint, economies of scale in sharing housing costs (for example) would similarly imply that the economically meaningful size rises by less than the number of residents.

The CBO (2016, 2018) uses the square root as the metric for standardizing household size in assessing income trends. Thus, normalizing for family size...