Empirical means of discerning "economy" and "bubble" In the news lately and in previous administrations, one of the most popular sound bytes I've heard was: "so and so is not growing the economy, he's growing the bubble." As with much sensationalism in the news, this is a rather normative statement. What I want to investigate is:

Question: what is a positive statement that can be said for the same argument?

Seeing as the federal reserve themselves have openly said they have no formal definition of a "bubble" and we can take it all the way back to the tulip mania days, but I think it's still interesting to see what is the most persuasive quantifiable metric that would suggest if the bubble is growing or if the economy itself is growing.

My best attempt One metric I noticed was in America home ownership is down and yet the real estate prices are increasing, suggesting that the valuation of homes is from the speculation of a wealthy few. Now, I concede this is only representative of one part of the economy, to see the bigger picture we would have to include more industries. Perhaps the same technique, but using a composite basket of such metrics?
You are probably not far off the mark. While there may be no consensus what a bubble is, one proposed definition is

Unusual changes in single measures, or relationships among measures (e.g., ratios) relative to their historical levels. For example, in the housing bubble of the 2000s, the housing prices were unusually high relative to income.
For stocks, the price to earnings ratio provides a measure of stock prices relative to corporate earnings; higher readings indicate investors are paying more for each dollar of earnings.

I'm not aware of [more] composite measures... but I'm not sure it would be very useful either. Generally one wants to know where exactly the problem is (whic sector) when there's a bubble.
Although Wikipedia doesn't seem to mention this, there's obvious caveat to such a method. Quoting from a fairly cited review of Camerer:

Any apparent bubble could be evidence of a variable which affects intrinsic value but is not observed by the econometrician.

Basically a problem of confounding variables, as far as I understand it.
As a putative example (of the latter), Camerer gives:

An example might be the Hong Kong stock market, which rose l0 times in value
between 1970 and 1973, then dropped 75% in a year. These enormous price swings
might indicate a bubble or fad, or they could be rational swings based on changing beliefs about what will happen when Hong Kong reverted to China after the British lease expires in 1997.

More examples like that are supposed to be given in a paper by Flood et. al (cited by Camerer), but I haven't read it.