tag:blogger.com,1999:blog-4039434.post2636837110568084437..comments2023-09-12T06:30:12.415-04:00Comments on Rajiv Sethi: Threats Perceived When There Are NoneRajivhttp://www.blogger.com/profile/13667685126282705505noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-4039434.post-19168682189347723572015-10-19T21:40:59.801-04:002015-10-19T21:40:59.801-04:00You know what? I think you're right about some...You know what? I think you're right about some of your concerns (though I disagree with some of your reasons). I don't think I can honestly estimate the statistical reliability of the effect: treating each state as an individual and building a confidence interval or statistical model around that isn't really sensible.<br /><br />Of course, if I skip the step of computing things state-by-state, and I just take the overall nationwide counts, it doesn't really change the pattern in the data:<br /><br />http://i.imgur.com/KxplqRE.png<br /><br />It's still the case that there is a disproportionate risk for African-Americans, even controlling for arrest rates. It's still a really big effect. And it's still the case that the magnitude of the effect appears to be similarly big for both armed and unarmed crimes (maybe even bigger for unarmed crimes).<br /><br />Anyways, thank you for making me think harder about this. I think you're probably right that, with this limited, 2015-only dataset, it's not really possible to test the hypothesis that there's a "difference in differences." I'm still interested in seeing how this looks with a larger database.jwdinkhttps://www.blogger.com/profile/06090722041289134326noreply@blogger.comtag:blogger.com,1999:blog-4039434.post-6564716173762648462015-10-19T19:58:12.061-04:002015-10-19T19:58:12.061-04:00Here's how I see the dialectic going
I think ...<i>Here's how I see the dialectic going</i><br /><br />I think you mean "dialogue"... ;-)<br /><br /><i>There does seem to be a shooting bias, even after controlling for arrest rate. And it's not trivial, it's quite substantial in size: a 30% increase overall, and (given some assumptions), potentially a 2-fold increase for unarmed arrests.</i><br /><br />It's a very noisy proxy, and also potentially biased. If blacks are arrested at a lower rate per encounter, this will drive your estimates above Sendhil's. Plus the noise of your proxy is not included in your error bands. <br /><br />Sendhil isn't controlling for arrest rate, he's just measuring killings per encounter. Which is what we really care about, since many encounters presumably don't lead to arrests.<br /><br /><i> I tested the trend in my post, and it's statistically reliable. </i><br /><br />What test did you perform?<br /><br /><i>Why do we need to test the ratio of the probabilities? Which probabilities?</i><br /><br />P(killing|arrest,black)/P(killing|arrest,white)<br /><br />P(killing|arrest,black,unarmed)/P(killing|arrest,white,unarmed)<br /><br />P(killing|arrest,black,armed)/P(killing|arrest,white,armed)<br /><br />And, to test Rajiv's hypothesis, we'd want:<br /><br />P(killing|arrest,black,unarmed)/P(killing|arrest,white,unarmed) - P(killing|arrest,black,armed)/P(killing|arrest,white,armed)<br /><br />or<br /><br />P(killing|arrest,black,unarmed)/P(killing|arrest,white,unarmed)/P(killing|arrest,black,armed)/P(killing|arrest,white,armed)<br /><br /><i> It doesn't really matter whether it's stronger than the bias in armed cases.</i><br /><br />It doesn't if we're just discussing Sendhil's hypothesis. But if we're discussing Rajiv's hypothesis, we do need that, since Rajiv makes a different hypothesis from Sendhil's.Noah Smithhttps://www.blogger.com/profile/09093917601641588575noreply@blogger.comtag:blogger.com,1999:blog-4039434.post-9823025576386195842015-10-19T19:45:55.885-04:002015-10-19T19:45:55.885-04:00Noah, thanks for your comment but I'm a bit pu...Noah, thanks for your comment but I'm a bit puzzled by it. If you look at the argument I sketched out in the first update it predicts a racial disparity in killings per encounter if and only if you condition on the encounter being objectively safe. And Jacob's test is supportive: the disparity is small for threatening encounters, much larger for safe ones. So I have to agree with Jacob's response here. Rajivhttps://www.blogger.com/profile/13667685126282705505noreply@blogger.comtag:blogger.com,1999:blog-4039434.post-76446865178854064052015-10-19T19:29:29.346-04:002015-10-19T19:29:29.346-04:00Hey Noah,
Thanks for the feedback. I think I'...Hey Noah,<br /><br />Thanks for the feedback. I think I'm a little confused by your overall view of what would constitute getting at the 'real' question. Here's how I see the dialectic going:<br /><br />Sendhil: There is not really a shooting bias, once you control for arrest-rate, or if there is, it's trivial when compared to other racial biases.<br />Me: There does seem to be a shooting bias, even after controlling for arrest rate. And it's not trivial, it's quite substantial in size: a 30% increase overall, and (given some assumptions), potentially a 2-fold increase for unarmed arrests.<br /><br />Hopefully this makes sense? I'm also confused by many of your points:<br /><br />"The error bars are quite wide, first of all - wide enough that this new approach doesn't really contradict Sendhil's story."<br /><br />This point doesn't make sense to me. I tested the trend in my post, and it's statistically reliable. This suggests the estimates I described in the previous paragraph are not just due to chance. Given the variability, it of course could be the case that the effect size is smaller than what I've estimated. Or it could be bigger. There's no reason to suspect either direction: all we know is that the effect size probably isn't zero (that's what the statistical test suggests). On balance, our best guess is the 30% measure I cited before— a substantial effect.<br /><br />"But more importantly, what we need is an estimate of the ratio of the probabilities, which is not equal to a ratio of the two estimates (and will also have wider error bars)."<br /><br />Why do we need to test the ratio of the probabilities? Which probabilities?<br /><br />"Also, to test Rajiv's hypothesis, what we need is an estimate of the ratio of ratios (or if you want, the difference in differences) that shows that the rate of deaths/arrest is more skewed toward blacks when no gun is present. That would show that nonthreatening encounters are more likely to result in killings when the subject is black."<br /><br />I disagree that this is what's needed. There is an overall bias, and it is robust when considering *only* the unarmed cases (I didn't show this test but I can post it if you'd like). It doesn't really matter whether it's stronger than the bias in armed cases.<br /><br />"Also, I'm not clear on how you proxied for the number of arrests by race in each state, without having arrest data to begin with. How did you do that?"<br /><br />I have arrest data for the whole US, split by race. I just partitioned this to each state, according to its population. This is a horrible and noisy method, but it shouldn't be a biased one, and therefore shouldn't effect any of the conclusions.<br />jwdinkhttps://www.blogger.com/profile/06090722041289134326noreply@blogger.comtag:blogger.com,1999:blog-4039434.post-10782466887342134532015-10-19T19:14:29.082-04:002015-10-19T19:14:29.082-04:00Jacob, with all due respect (and "good job&qu...Jacob, with all due respect (and "good job", etc.), I don't think your analysis tells us much new. " basically a noisy proxy for Sendhil's "shooting bias". The error bars are quite wide, first of all - wide enough that this new approach doesn't really contradict Sendhil's story. But more importantly, what we need is an estimate of the ratio of the probabilities, which is not equal to a ratio of the two estimates (and will also have wider error bars).<br /><br />Also, to test Rajiv's hypothesis, what we need is an estimate of the ratio of ratios (or if you want, the difference in differences) that shows that the rate of deaths/arrest is more skewed toward blacks when no gun is present. That would show that nonthreatening encounters are more likely to result in killings when the subject is black.<br /><br />Also, I'm not clear on how you proxied for the number of arrests by race in each state, without having arrest data to begin with. How did you do that?Noah Smithhttps://www.blogger.com/profile/09093917601641588575noreply@blogger.comtag:blogger.com,1999:blog-4039434.post-32072331519200079422015-10-19T16:44:36.753-04:002015-10-19T16:44:36.753-04:00I think it comes down to what we mean by likelihoo...I think it comes down to what we mean by likelihood of killing conditional on arrest being "about" the same for the two races. <br /><br />It is about the same, but not *exactly* the same in the dataset I'm using: 0.000132 for black, 0.000115 for white. That's a difference of .0000169. If we split by armed vs. unarmed, we get differences of .0000159 and .0000280, respectively. And there are far more armed crimes overall, so the overall mean is closer to the armed mean. <br /><br />What we're seeing is a small difference that matters a lot, especially (for unarmed crimes) if we look at the proportion increase, rather than the absolute increase.jwdinkhttps://www.blogger.com/profile/06090722041289134326noreply@blogger.comtag:blogger.com,1999:blog-4039434.post-84946269903235933532015-10-19T16:09:09.781-04:002015-10-19T16:09:09.781-04:00Thanks for the clarification Jacob, but if likelih...Thanks for the clarification Jacob, but if likelihood of killing conditional on both events (armed/unarmed) is higher for black versus white, while unconditionally they are about the same (Sendhil's point) doesn't there have to be a composition effect (blacks more likely to be unarmed)? What am I missing? Rajivhttps://www.blogger.com/profile/13667685126282705505noreply@blogger.comtag:blogger.com,1999:blog-4039434.post-66277914751297736132015-10-19T16:01:34.038-04:002015-10-19T16:01:34.038-04:00"This, together with the fact that rates of a..."This, together with the fact that rates of arrest and killing are roughly equal across groups, implies that blacks are less likely to be armed than whites, conditional on an encounter. In the absence of bias, therefore, the rate of killing per encounter should be lower for blacks, not equal across groups. So we can't conclude that "removing police racial bias will have little effect on the killing rate." That was the point I was trying to make in this post. "<br /><br />I'd actually be very cautious about making claims like this, given that my analysis uses a "per-arrest" metric that doesn't capture differences in armed/unarmed arrests. I should maybe try to remedy that…<br /><br />Just a clarification!jwdinkhttps://www.blogger.com/profile/06090722041289134326noreply@blogger.comtag:blogger.com,1999:blog-4039434.post-65930294650931376252015-10-17T06:51:43.800-04:002015-10-17T06:51:43.800-04:00Nick, a simple first test would be to compare the ...Nick, a simple first test would be to compare the rates of killing per encounter by white versus black officers. All the examples mentioned by Sendhil (Tamir Rice. Eric Garner. Walter Scott. Michael Brown) involved white officers. I believe that if a suspect looks a bit like your brother or cousin or the guy with whom you watched a football game last Sunday you are less likely to perceive a threat when there is none.<br /><br />Look at the quote from Leon Lashley in my post on the Gates arrest. Lashley defended his white colleague, but added: “Would it have been different if I had shown up first? I think it probably would have been different... black man to black man, it probably would have been different."<br /><br />http://rajivsethi.blogspot.com/2009/11/leon-lashley-and-gates-arrest.html<br /><br />APAA, yes, the numbers could be biased the other way... my point was that the numbers don't tell us what he claims they do, and to give reasons why I think they are biased in a particular way. Obviously we need better tests (see my response to Nick above).<br /><br />I'm aware of the statistics in violent crime, and linked in the post to a paper of mine with Dan O'Flaherty that tries to explain the disparity. Fear and preemption are central to the argument:<br /><br />http://www.sciencedirect.com/science/article/pii/S0094119010000343<br /><br />Part of the problem is the extremely low clearance rate for homicides with black victims, as discussed by Danielle Allen here:<br /><br />http://t.co/icCif0UXrN<br /><br />Thanks to both of you for the comments. Rajivhttps://www.blogger.com/profile/13667685126282705505noreply@blogger.comtag:blogger.com,1999:blog-4039434.post-76270936617747130402015-10-17T05:31:10.509-04:002015-10-17T05:31:10.509-04:00Rajiv: I think I get your point. How could we test...Rajiv: I think I get your point. How could we test it?<br /><br />Suppose we were talking about men and women. Assume 50% of each in the population. If (say) 60% of police encounters were with men, and (say) 70% of those shot by police were men, I don't think we would infer that police were biased against men. We would probably be looking at data on percentage of homicides done by men?Nick Rowehttps://www.blogger.com/profile/04982579343160429422noreply@blogger.com