Sure, it’s fair enough to want evidence that institutional racism actually exists. But you now agree that it’s absolutely possible for it to exist, don’t you?

Now, given my scenarios, you also have to acknowledge that because it’s being done on purpose but in secret, you will have a hard time showing absolutely for certain that it was intentional and not just an unlucky mistake. (Of course, you can know for sure if you are doing it yourself. Otherwise, not so much.) That’s why in 1991, Title VII of the Civil Rights Act was amended to include “disparate impact” as also illegal. It’s not practical to actually verify intent, so instead you hit everything that is manifestly unequal because (1) it’s unfair even if unintentional, and (2) you get rid of secretly intentional unfairness that way. Note that “oops, we messed up” followed by “but who cares” vs. “and it’s affecting white folks, wait, shh, forget we said that!, so we gotta fix this now!” is…you guessed it…institutional racism.

But these cases can still be hard to win legally, because it’s only a disparate impact unrelated to purpose that counts. An employer can have arbitrarily large disparate impact as long as “the challenged practice is job related for the position in question and consistent with business necessity” (see Civil Rights Act section 703 (k)(1)(A)(i)).

Here’s an example where Baltimore got caught rejecting otherwise qualified applicants for the police force on the basis of exams that were not related to the job: https://www.justice.gov/opa/pr/justice-department-announces-two-million-dollar-settlement-race-discrimination-lawsuit Unlucky mistake? Maaaybe. They certainly should have known better. There are many examples if you go looking.

Here’s an opposite example where New Haven failed to promote firefighters because the tests didn’t give the racially-uniform results they were expecting so they decided that it must have been an invalid test. Nope, said the Supreme Court: you made this up because of race, not because your test was unfair. (The defendants, who won, were mostly white (one Hispanic)…and yes, I consider this a case of institutional racism, where the institution tries to pick how many people of which group get what benefits via an unrelated factor (“we might get sued” — that was literally New Haven’s argument), though admittedly this is closer to classic racism because the factor is “we might get sued because the racial composition came out wrong”.) See https://en.wikipedia.org/wiki/Ricci_v._DeStefano. There aren’t as many examples like this, but you can find others. (And for the record, I’m not totally convinced that the tests weren’t themselves an example of institutional racism too. I haven’t read them myself to make sure they really were critically related to job performance. But the argument they tried to use to save themselves, in the case that their test was actually problematic, was just as bad.)

You wanted something with statistics. I’ll give you an example of both something that’s widely reported that’s apparently wrong, and something that is widely reported that’s apparently true.

It’s often stated that black people on average have to pay higher mortgage rates than whites, and this reflects institutional racism on the part of lenders. But lending is a complicated thing — for instance, you can choose to pay more in exchange for a smaller down payment. People have looked at this, and everyone is getting the same deal at least from the Federal Housing Administration, even if they pick different points on the curve: https://academic.oup.com/rfs/article/34/2/763/5827007

So this isn’t an example of institutional racism. There might be some institutional racism in which types of loans people are steered towards (indeed, there has been plenty of predatory lending of that sort in the past, which precipitated the savings and loan crisis), but in terms of the actual product itself, people aren’t getting dinged by arbitrary unrelated criteria. And maybe it’s a good thing — people are getting to do what works for them. (Maybe it’s not good that they have to be making that tradeoff, but it’s certainly not FHA’s fault once they come for a loan.) More caveats: it’s just FHA, it doesn’t address possible issues with credit scores, etc.. So it’s not a total vindication of everything. Still, it looks superficially bad, and when you dig there’s nothing there.

Here’s an example of something that is (almost surely) institutional racism: increase in sentencing. https://www.ussc.gov/research/research-reports/demographic-differences-sentencing

It’s about 20%. This is a pretty clean example because although you can think of things that may impact the outcome (most notably, and this is true, “white suspects are wealthier and can afford better lawyers”) those things are irrelevant to justice. So even if it’s true that it all comes down to income (not clear), it’s just using the underlying irrelevant difference (income) to make things worse for one group vs the other.

And then of course we have the job interview studies, where people send identical job applications and only change the name to sound characteristically black or characteristically white…and the white ones do better (how much varies by study, but it’s usually in the range of 1.5–2x more responses, if that’s how they score it). That’s institutional racism too: your name is irrelevant to pretty much every job you have. It might not be intentional, but it sure is institutional, and it sure as heck isn’t fair.

One can find lots more examples on both sides, and vastly more where nobody seems yet to have looked in enough detail to know.

Institutional racism exists. So do false reports (at least false attribution of the location of the problem, as you suggest with “it’s poverty”). You can’t make sweeping statements and stay correct. You just have to go and check every case, or find a reliable source that’s done it for you and really cares about getting it right instead of “proving” that your side is right and their side is wrong. (Whichever side it happens to be.)