I would be interested to see more statistics and trends of people over time. Many of the statistics I see divide people into classes by income, but ignore the fact that the people within those classes change. For instance, let's say that people in the next generation decide to go to college for 10 more years, leaving at 32 rather than 22. Then, when they get out, they make 50% more income than the previous generation…
But when you look at trends, income is stagnant, wages are stagnant AND measures of social mobility are low as well as studies that show a lack of evidence for second and third generation immigrants being significantly better off.
That plus the (admittedly anecdotal) evidence that single earner lower middle class families who own their homes and cars are much rarer seems to indicate that the shrinking middle class is a reality (measured mostly by some vague "quality of life" metric.)
So it's complicated. The most compelling argument I've heard is that necessities are getting more expensive relative to general inflation (gas, food, housing) On the other hand, what you get for your money is much more advanced now technologically. So it's not like we're strictly speaking worse off even if our relative purchasing power has decreased.