One of the defining features of the “American Dream” is the ideal that children have a higher standard of living than their parents. …We find that rates of absolute mobility have fallen from approximately 90% for children born in 1940 to 50% for children born in the 1980s.

- Chetty et al (2016) The Fading American Dream: Trends in Absolute Income Mobility Since 1940.

Overall, the public thinks freedom of choice in how to live one’s life (77%) and a good family life (70%) are essential components of the American Dream. A somewhat smaller majority (60%) also says that the ability to retire comfortably is essential to how they think about the American Dream. About half or fewer say making valuable contributions to their community (48%), owning a home (43%) or having a successful career (43%) are essential. And just 11% think becoming wealthy is essential to their understanding of the American Dream. There are relatively modest differences between typology groups in these assessments... between 80% and 90% [of most typology groups] say either that their family has achieved, or is on their way to achieving, the American Dream. pp. 37-38

- Pew Research Center, “Political Typology Reveals Deep Fissures on the Right and Left”2/ October 2017

Unsurprisingly, the "Fading American Dream" study got lots of press from the Left (e.g., “The American Dream is dead, and voters are angry” or "Inequality Is Killing The American Dream"), while the Pew Research findings made news on the Right (e.g., American Dream is back: 82% have 'achieved' or are 'on way to achieving').

Four points.

One, the Fading Dream study ignored US Consumer Expenditure Reports, which have consistently shown Americans to be doing better than can be detected from income data alone. If one looks at what low-income Americans spend, it's always more than their reported income. You also have to factor in the quality of the goods and services bought. The average home size these days is nearly 2500 square feet, compared to less than 1000 square feet before 1950. 

Two, Americans born in the 1980s have fewer mouths to feed than those born in 1940. Fifty years ago average US household size was around 3.3; now it’s 2.5. Except for periods of recessions, median household income per household member has been steadily rising at least since 1970. 

Three, intergenerational mobility was high for earlier generations partly because the standard of living for most Americans was much, much lower than it is today. So intergenerational mobility from earlier times was relative to a lower base.  For instance, in 1901 the average US family’s income was $750 - worth about $2300 a century later. Before 1940, households spent more than a third of their income on food alone.  After WWII, there was a broad-based improvement in the economic fortunes of most American households (aka the "post-war boom").  Demographics, pent-up demand, and favorable global markets conspired to make this period especially robust. The rate and breadth of improvement lost some momentum in time, but that was expected. Economies grow more slowly after they've reached a certain income and development threshold.

Four, defining the American Dream in terms of intergenerational mobility sets up the conclusion that the American Dream is fading. But who defines the American Dream that way?  Not Americans themselves.

References:

Chetty, R., Hendren, N., Kline, P., and Saez, E. 2014b. Where is the land of opportunity? The geography of intergenerational mobility in the United States. The Quarterly Journal of Economics (2014) 129 (4): 1553-1623.

The Fading American Dream: Trends in Absolute Income Mobility Since 1940. Executive Summary December 2016. Raj Chetty, David Grusky, Maximilian Hell, Nathaniel Hendren, Robert Manduca, and Jimmy Narang

100 Years of U.S. Consumer Spending: Data for the Nation, New York City, and Boston U.S. Bureau of Labor Statistics Report 991 October 2006