Friday, July 21, 2017

Economic Lessons: Shopping for Eyeglasses

Out of Pocket vs. Third Party Payments

I recently had to buy new glasses, because the hinge on my old pair broke. I was paying out of pocket. The initial quoted price was just above $400. I kind of balked because that was way more expensive than what I expected. Then the sales person said that the “anti-reflective coating” made up about $150 of that figure. I said “No thanks” to a feature of dubious value.

I think this is the kind of shopping people would do if they paid more out-of-pocket for routine, predictable healthcare expenses. Some people think that if patients have to pay in cash instead of paying though a third party, they will skimp on important medicine and injure their health. I think this is nonsense. A healthcare market of first-party payments doesn’t imply skimping on vaccines and routine screenings. It just means we say "No" to the anti-glare coating. Maybe it means we double up in our hospital rooms instead of getting our own suite (at least whenever someone isn’t contagious or ultra-sensitive to disturbances). Or maybe it means we shop around for the best MRI price (David Goldhill describes doing exactly this in his book Catastrophic Care).

“Affordability” is a red herring. If you can’t afford the glasses with the anti-glare coating, then you also can’t afford the insurance premiums that will pay in full for the glasses with the anti-glare coating. Likewise, if you can’t afford routine check-ups or monthly birth control, then you can’t afford an insurance policy that will pay for those things. Obviously, your insurance premiums are calculated to cover such expenses, so mandating that insurance cover more things doesn't make those things more affordable. If anything it does the opposite. You get gold-plated hospital stays instead of austere-yet-functional hospital visits. Making healthcare more affordable to people with low incomes requires explicit transfers (government programs and/or private charity), not insurance coverage mandates. 

What follows is a completely unrelated point, so don't stop here just because something about the above section put you off. The next piece could be a completely separate blog post.

Price Discrimination

"Price discrimination" simply means charging different prices for the same product because some customers are willing to pay more. Alternatively, you can think of it as meaning sellers offering discounts to capture some of the potential customers who won't pay the listed price. These are economically equivalent descriptions, but for some reason people balk at the first one. They always imagine that they are the ones paying more, and the seller is trying to squeeze them. But half they time you are the person being offered a discount because you wouldn't pay full price.

Price discrimination exists because some sellers have very high fixed costs. An optometrist's office has to operate a building. They need to maintain an inventory of glasses and frames, many of which will  never be sold because they are the display model. They need to buy equipment for performing eye exams, pay someone to man the front desk, etc. These costs will exist even on a bad day or bad week, when they have few customers. The average price of the eyeglasses must cover these costs. (Or the average price of eyeglasses + eye exam, or whatever bundle is being sold, must cover these costs.) Say I divide my total monthly expenses (including machinery, utilities, labor, rent, return on capital to the business owner) by the number of customer's serviced for a given year and it comes to $400 per customer. I'd better be collecting at least that much from each customer, or I'll be going out of business. 

But wait. Maybe it's very cheap to service one additional customer. Maybe the frames and lenses only really cost $20 or so, and perhaps nobody's busy right now so servicing an extra customer is practically free from a "cost of labor" standpoint. Maybe if you add up the costs of servicing one additional customer, it only comes to $50 or so. If you could offer a random passer-by "Eye exam plus glasses for $100?" you should do so. Your business would profit to the tune of $50 from such a deal. Unless everyone else gets wise to this special deal and starts asking for it, in which case your revenue will only be $100 per customer when you really need $400. (Perhaps you can't drum up enough additional volume to make this deal worth extending to everyone. The community serviced by an optometrist's office is limited, and people only need new prescriptions every few years or so.) 

So you have to be clever about it. You have to say things like, "Well, the price for the frames, plus lenses, is $425." (customer winces) "Of course, that includes the anti-reflective coating, which is $150 of that total." (recalculates price, customer accedes.) This is precisely the negotiation I had with the salesperson. I strongly suspected that the anti-reflective coating is a low production-cost add-on, but a useful bargaining chip if one wants to price-discriminate. They can still nab the marginal customer (like me) who might balk at the full $425 and go buy my glasses elsewhere. I have my prescription, anyway, so I can simply buy glasses online if I need to. 

My suspicion that this was some kind of price discrimination was confirmed later when I went to pick up my glasses. I had said "No" to the anti-glare coating, but they added it free of charge because it would  have taken them longer to fill my order without the coating! So for whoever manufactured my lenses, adding the coating is actually their default. They have to special-order the lenses without the coating. It's probably cheaper to produce lenses with the coating. But it is a very useful way to price discriminate. If the true cost of production were and additional $150 for the coating, they would have probably found some way to get the money out of me, or asked me if waiting was acceptable. 

This reminded me of a story about a Hewlett Packard high-speed laser printer, which was more expensive than the "normal speed" model. The normal-speed model was actually identical to the high-speed printer, except that it had an extra chip that slowed it down. It was cheaper to just build the high-speed printer. The low-speed version was created simply to be able to offer a lower price to more price-sensitive customers and to keep up the facade that there was a difference in quality. This story is told in one of Tim Harford's books (The Logic of Life or The Undercover Economist, though I can't remember which one). 

A favorite write/economist of mine, David Friedman, also once used the example of selling eyeglasses as an illustration of price discrimination. It was from one of his class lecture recordings, several of which I've listened to. They are available at his website. It began: "I'm selling you a pair of eyeglasses. I say, 'That'll be $40.' You don't wince. 'For each lens.' Still no wincing. 'Plus $80 for the frame.' What have I just done?" What follows is a discussion of price discrimination. Sellers who have very high fixed costs have an incentive to figure out how price sensitive their customers are, so they can offer discounts to customers who they would otherwise lose.

Customer Service

Eight years ago, when I last bought eyeglasses, I learned an important lesson about customer service. I bought a pair of eyeglasses from the optometrist who did my eye exam, and I bought another pair from 39dollarglasses.com. Interestingly, in both cases there was a mistake in the prescription. The optometrist immediately recognized the error, and re-ordered me a pair of glasses. Of course I didn't have to pay a second time for their error. In the case of 39dollarglasses.com, the glasses I got were obviously the wrong prescription. I don't know if I had entered it incorrectly on their website or if the error was theirs, but they were completely unwilling to own any portion of the mistake. In order to correct my prescription, they asked that I send back the pair they had sent me, which I did. Then they asked for a $16 fee. Then, later, they said they wouldn't process the re-order until I sent an additional $26. I just rolled my eyes and paid it, but vowed never to buy anything from them ever again.

The pair I had purchased from the optometrist was more expensive in sheer dollar terms than the pair I had purchased from 39dollarglasses.com. But the optometrist was selling me more than just the glasses. They were selling a promise to make good on the order. 39dollarglasses.com offers a stripped-down, bare-bones product with minimal customer service and (apparently) no promise to actually make good on an order. The optometrist's office, having sunk a lot of expenses into building and maintaining a brick-and-mortar business, knows that it needs to keep its customers happy or lose a future revenue stream. All things considered, the pair of glasses I bought on line was probably slightly cheaper than the pair I bought from the optometrist, but it certainly left a bad taste in my mouth. There's no deep economic lesson here, other than "you get what you pay for." It was a pain to navigate 39dollarglasses's almost non-existent customer service, and it gave me the feeling of having been robbed. It was probably worth the extra cash to have the optometrist settle the deal and smooth out any mistakes in the order, having that built into the price of the glasses. 

Thursday, July 20, 2017

Is My Driver Tracking App Giving Me Bad Advice?

I have an app on my iPhone that tracks my driving behavior. It's called "Drive Well", but there are numerous incarnations of the same concept. It uses my phone's accelerometer and location services to figure out where I'm driving, how I'm driving, how fast I'm driving, if I'm making too many hard breaks, and so on

The concept is fundamentally sound. These kinds of devices have been tested in the market for almost a decade now, and insurance companies and data scientists have been pouring over the collected data. The data truly are predictive of future auto accidents. If you make a lot of hard breaks, you're probably a careless driver. You aren't leaving enough space between your vehicle and the one in front of you, you respond too late to risks that more observant drivers would anticipate, etc. If you speed (above and beyond normal "speeding" that everyone does), you are more likely to cause accidents, and the accidents that you cause are likely to be more severe. If you corner too sharply, if you play with your phone while driving, if you accelerate too quickly, then you are more likely to have an accident. And, of course, the more miles you drive and the more time spent on the road, the more likely you are to get into an accident through sheer exposure to the risk. Someone who had analyzed this kind of data told me that it can replace an insurance company's entire rate plan. That is to say, directly measuring driving behavior is as predictive as measuring everything knowable about the person's demographics (age, gender, marital status, credit history, state and zip code, prior accident history, etc.). The predictive power of this information can be validated against enormous, statistically credible datasets. The signal is real. These things are predictive of future auto accidents.

Still, I think that the app sometimes gives me bad advice. I keep getting dinged for "rapid acceleration," and my app tells me I should cool it. It's true that I rapidly accelerate to get up to speed on the interstate, even in town. It's probably true that people who accelerate rapidly statistically have more accidents, and this generalization probably applies to me whether I'd like it to or not. Please don't think I'm special pleading that "In my case it's different." But in those particular situations where I am accelerating rapidly to match the flow of traffic, I would be less safe if I were to slow it down. In other words, the app is correctly telling me that I have a higher-than-average accident frequency (on this one count, not in total, as my other driving behaviors are good), but possibly giving me bad advice on how to improve my driving.

Someone familiar with this driving behavior data once told me that driving too slow is actually predictive of accident frequency. This makes sense. If someone is driving too slow, they are probably in an unfamiliar place, possibly looking for their exit or house number. Such a distracted driver is likely to cause an accident. But it would be wrong to say, "You should drive fast because slow driving correlates with high accident frequency." No, driving fast while you're distracted and confused probably makes it even more likely that you'll get into an accident. The statistical methods used in predictive models are not capable of teasing out what is causal and what is mere correlation.

I don't want to over-encourage this kind of second-guessing. Statistical methods often surprise us. And people have funny ways of convincing themselves that their vices are actually good for them. "My speeding is fine, it's the slow drivers who drive the actual speed limit who are causing the accidents!" (Loud annoying buzzer sound!) "I've driven home drunk many times and never had a problem. I'm actually safer, because I drive extra careful to avoid police scrutiny." (Loud annoying buzzer sound!) Don't be that guy. But a touch of skepticism is warranted. No statistical method will tell you which behaviors are merely correlational, such that changing them won't affect your accident risk (or will affect it adversely). Only human ingenuity and a cleverly designed test will be able to establish what is a truly causal effect.

Monday, July 17, 2017

Illinois and Unfunded Liability

Illinois has $130 billion in unfunded liabilities and just shy of 13 million in population. So very roughly speaking the burden of those liabilities is $10,000 for every man, woman, and child in Illinois.That's the problem. Almost none of the discussions of Illinois politics really cut to the heart of the matter. Any serious discussion about Illinois' fiscal problems would recognize the magnitude of the problem and then state clearly whose ox is going to get gored: the taxpayer's ox, or the pensioner's ox.

You could make this $10,000/person figure more meaningful in various ways. One could specify the cost per household rather than per individual. (After all, what does a $10k unfunded liability mean to my non-tax-paying children?) Or by netting out the benefit to Illinois retirees, such that those people are have a positive net balance, and the remainder of the population owes more than the $10k. (After all, what does a "$10k unfunded liability" mean to you if you're the recipient of the promised payments? Those aren't a "liability" to you!) Different people are burdened with different portions of that liability. For simplicity's sake let's call it $10,000. It's a substantial stack of money that we're all being asked to cough up.

Most of the commentary I see on this problem is completely unserious.

Here would be a somewhat serious answer: "Make the taxpayers cough up the full $10,000, and pay the full value of the promised benefits." The actual problem of a $10,000 unfunded liability doesn't go away, but at least this "solution" indicates who will pay for it. It at least says, "Hey, Joe Taxpayer, your ox will get gored. Johny Pensioner's ox will not get gored at all." Note that you wouldn't have to tax the $10,000/citizen all at once, but you'd have to raise taxes such that the average citizen pays an additional $10,000 eventually.

Another somewhat serious answer: "Make the pensioners take a total haircut on that $130 billion unfunded liability. Johny Pensioner's ox will get gored completely. Joe Taxpayer's ox will not get gored at all." Again, there isn't a "solution". There's $10,000 worth of "pain" per person to spread around. That doesn't go away when you specify who takes what proportion of that hit. But at least this is an adult conversation about how to spread that pain around.

Some unserious answer are things like, "Bruce Rauner is a big meany. If only he weren't so mean, we could solve this." No. If someone waved a magic wand over Bruce Rauner, that purified his soul and changed his alignment from Lawful Evil to Lawful Good, there would still be $130 billion worth of unfunded liabilities.

Or, "Mike Madigan is a corrupt deal-broker, drunk on his own power." Sorry, but you could wave the same magic wand over Madigan and you'd still have this unfunded liability of $10,000 per person to divvy up. We can talk about Madigan's long career, how he should have solved the problem earlier, how he and his colleagues bought off a powerful voting-block by overpromising future benefits, how he manipulated the liability with unreasonable rate-of-return assumptions, how an honest way to raise state employee compensation is to vote on a tax increase specifically tied to increasing employee salaries (such that there is a democratic check and a transparent budget). But after all the blame-passing, the damage is still done. You can lay all the blame on one guy if you want. There is still a $130 billion hole, and it's too late to fill it.

Apparently some people think that the budget problems would be completely solved if we just "eliminated corruption". I think this is facile. The bulk of the unfunded liabilities are for long-term retirement benefits to state employees and teachers. We could maybe have an adult conversation about how Illinois spends too much, and special interests capture some of that spending. Surely there is pork to cut out of the Illinois budget, and this would get us some of the way there. I would absolutely applaud an effort to make comprehensive cuts to Illinois' budget. But it would leave the bulk of that $130 billion untouched.

There are some hard constraints. The language of the Illinois constitution forbids reneging on a contract. See here: " Membership in any pension or retirement system of the State, any unit of local government or school district, or any agency or instrumentality thereof, shall be an enforceable contractual relationship, the benefits of which shall not be diminished or impaired." So to legally change the benefits we'd have to have a constitutional amendment. Another inescapable constraint: states can only raise taxes so high before they chase away their tax base. That's already happening in Illinois. People are seeing the writing on the wall and leaving the state. The Laffer Curve is real, but its effects are particularly acute at the state level where people can pack up and leave easily.

One might appeal to moral principles rather than practical constraints. "A pension is a promise" one might say. But there's a problem with this. "Yeah, a promise to rob me because you failed to adequately fund your pension!" one might fairly retort. There is no clear moral trump card here. While one can make the case that the pensioner's promised benefits ought to be paid, failing to acknowledge the rights and interests of whoever is paying seems to be a pretty serious omission. Anyone who just thinks "It's so obvious" that the pensioners should get 100% of their benefits, or that the taxpayer should not be liable at all for the badly managed public finances, isn't really thinking seriously about the problem. When there is a conflict of rights, the appropriate thing is to at least acknowledge both parties before you start talking about splitting the difference or resolving entirely in one party's favor. 

I'm not trying to take some lame "split-the-difference" middle-ground approach here. I have opinions, and in a different kind of post I would argue for a certain kind of resolution. I would make an argument for whose ox deserves to get gored more or less than the other party's. But this isn't that post. I'm merely trying to articulate a fair framing of the issue, which requires acknowledging that somebody's ox gets gored under any conceivable "solution." This is at its core a conflict of rights.

*The $130 billion figure appears to be under-counting. This piece from the Illinois Policy Institute suggests it's more like $200 billion when you count local government liabilities.

Biographies of the Presidents

I've been reading biographies of the presidents since some time in March. I've been going in order. I started at the beginning with one about George Washington, and I just recently started a biography of Andrew Jackson. This post won't be a deep dive into presidential history, but I've found this project interesting. Just a few comments that you might find useful.


  1. This way of reading history has a built-in redundancy. So if you're actually trying to learn what happened (the sequence of events, the significance of various events, etc.) this is a very reinforcing way to go about it.
  2. Some of these men didn't like each other, so you will get opposing points-of-view. Naturally someone who writes a book about John Quincy Adams probably thought he was a swell fellow and probably has some critical things to say about Andrew Jackson, and vice versa. John Adams (Sr.) and Thomas Jefferson were likewise political rivals. It's good to get at least two sides to a story.
  3. Why would someone write a just-the-facts book about someone who's been dead 200 years? Surely that already existed. Someone who writes this generation's definitive biography of George Washington thinks he has something special and unique to say. You certainly will read the canonical history with all the critical details and events, but you also get to hear the author's bullshit theory about what really happened, what George's true motives were, etc. Reading these books, you don't get the overwhelming sensation that the author is saying, "Psst! But this is what really happened that nobody else noticed but me..." but you do get a hint of it now and then.
  4. I picked something that was favorable to Andrew Jackson (I think, and so far it is). I already know the bad stuff. I have heard all about how he was a horrible person. I'm not worried that some folksy telling of his story is going to turn me around. But he probably deserves his due. We often remember him as a genocidal Indian killer, and he certainly was. But did you know he adopted an Indian orphan? History is a little more complicated than we sometimes like to believe. 
  5. If you come at this project with an attitude that "everyone from that time was horrible because they had horrible moral values", you won't learn very much. Yes, many of these men owned slaves (the Adams-es didn't). But it's a bit self-indulgent to think that we wouldn't have been just as morally compromised if we'd lived in that society. It takes uncommon courage to challenge a widely accepted practice in your own time. John Quincy Adams got death threats for his anti-slavery stance. And he didn't even introduce a bill to limit slavery; he merely defended the right of petitioners to raise the issue during a time when there was a gag order preventing any discussion of the topic in congress. I think it's important to give people credit for taking the baby steps toward progress that are achievable in their own time. I like to say, "Oh, so you're going to judge someone who lived 200 years ago by the moral standards of today? For your next trick, will you judge a small child's art?"
  6. Jefferson comes off as flighty and completely irresponsible with his finances. I have less respect for him as some kind of great philosopher. If he'd kept his house in order, he might have bequeathed freedom to his slaves upon his death, which George Washington actually did. His strained finances at the end of his life (and through it) ruled this out of the question. At the risk of forgetting everything I said in point (5) above, I think this compromises his character. He failed to walk the walk when it came to freeing slaves, partly because he indulged in luxuries he couldn't actually afford. I still have an overall positive view of him, but the flaws in his personal character are pretty glaring. 
  7. The Adams-es come off as likable and morally upright, also quite brilliant. 

Saturday, July 15, 2017

Repurposing an Old Joke to Express How Much I Despise Corporate Management Seminars

Here is the original version of the joke, which most people have probably heard. (It's the original inspiration for the "Death By Snu-Snu" episode of Futurama, actually titled "Amazon Women In the Mood.") Here goes.
Two explorers are captured by a tribe of natives. The tribal leaders says to them, “You have trespassed on our sacred lands. There are but two penalties in our society, and you may choose which to suffer. One is a multi-day corporate management seminar. The other is death by unga-bunga.” 
Explorers 1 and 2 look at each other. 
Explorer 1: Uh, yeah, we’ll take the death by unga-bunga.
Explorer 2: Yeah. It’s, like, not even close.
Explorer 1: I don’t even actually know what unga-bunga is, but I already know I’d rather have that then the other thing. (Explorer 2 whispers something into Explorer 1’s ear.) Oh, yeah, that’s way better than the other thing.
Explorer 2: Yeah, the other thing is like being unga-bungad for eight straight hours a day, but without the sweet release of death.
Explorer 1: Look, there will probably be other explorers stumbling though here. If you see more guys who look like us, just go ahead and unga-bunga them on sight.
Explorer 2: Yeah, really. If they *do* pick the other thing, it’s because they don’t know what they’re getting into. 
Perhaps silly posts like this one will ruin my credibility when I attempt a more serious post in the future. It's worth it. 

Monday, July 10, 2017

Environmental Regulation In Practice

Excerpt from The Economists View of the World by Steven E. Rhoads:

It would be incorrect to suggest that all the federal air pollution laws and regulations have accomplished nothing. Lawrence White find, for example, that the motor vehicle standards have led to substantial reductions in emissions. White also finds, however, that alternative approaches could have done as well at much less cost. And all in all the clean air gains over the last decade are less than one might expect could be achieved from polices costing over $25 billion a year. 
Economists are not surprised by this unimpressive performance. Crandall notes that “no organization could possibly cope with the continuing flow of legislation and the detailed regulatory responses required of EPA.” For example, there are more than 200,0000 existing stationary sources subject to air-emission limitations. Approximately 23,000 of these are major sources, each capable of emitting more than 100 tons of pollutant per year. Though 94 percent of these major sources are in “compliance” this does not necessarily mean that they have done anything. Typically it means that they are continuing to use the required “best engineering practices.” In most cases the firms are certified on the basis of their own reports that they are complying with the state plan and all relevant standards. The General Accounting Office has found many errors in reports of compliance. As one would expect, the over 1,400 major sources not even “certified” as being in compliance are the most serious sources of pollution. 
These uncertified major sources use the courts to fight the EPA regulations with great vigor. As one authority notes, each sources argues that “(1) he is in compliance with the regulations; (2) if not, it is because the regulation is unreasonable as a general rule; (3) if not, then the regulation is unreasonable in this specific case; (4) if not, then it is up to the regulatory agency to tell him how to comply; (5) if forced to take steps recommended by the agency, he cannot be held responsible for the results; and (6) he needs more time.” The EPA, unable to fight every battle, negotiates as best as it can, and , for the worst violators, it often welcomes agreements promising future action. If not carried out, these agreements are then subject to renegotiations.
This back-and-forth between regulators and private industry will sound familiar to any actuary who has had to defend a rate filing against a hostile department of insurance. Some background. In every state (except Wyoming, bless them), insurance companies have to file their rate plans with the state department of insurance (DOI). The department then reviews the filing and sometimes comes up with a litany of objections, the best of which are only borderline relevant. The insurer must often argue with the state DOI: our methodology is sound and you misunderstood it, the statute you cite does not apply in this case, your instructions contradict other instructions you gave us on a previous round of objections, etc. My job is in part to respond to these questions. It is interesting to see that this process takes place in other regulated industries. I'm curious if the process is just as dysfunctional in emissions regulation, an area where unlike insurance regulation there is an actual externality/market failure problem.

I was going to write a much longer post about the pointlessness of regulation in theory and the dysfunction of regulation in practice. I'll save that for another post that I can dedicate specifically to insurance regulation. But it seems like my experience with the regulatory state generalizes pretty well.

The above post is leading up to an argument for pollution taxes, rather than having "emissions standards." You can see the problem from the excerpt: What standard ought to apply to my factory? This kind of unclear law leads to endless argumentation, legal battles, and delays. A tax gets around this by essentially saying, "Pollute all you want, but you will pay the social cost of that pollution."

Thursday, June 22, 2017

Study on Auto Accident Frequency in Legal Cannabis States

This story has been making the rounds. It was actually e-mailed to me by my boss. A study by the Highway Loss Data Institute (HLDI, pronounced "Hildy") supposedly finds that states that recently legalized recreational cannabis have seen an increase in auto accidents. They reach this result using a naive sort of time-series trend analysis. This is highly dubious.  I wanted to get down a few quick reactions.

- Why are they looking just at auto collision? Why not also look at the liability coverages? Presumably liability property damage should show a similar trend. If there are more stoners and these stoners are hitting things with their cars, it should show up here. Liability bodily injury should ideally show the same trend, although admittedly this is a lower frequency coverage, so noise can swamp even a real trend. Still, it's another data source to validate their results on collision.

-In Colorado the overall collision frequency is about 5%. (As in, 5% of motorists will file a claim in a given year.) A 3% increase to this (the effect overall effect size found in the HLDI study) changes this to a whopping 5.15%. We're talking about small potatoes here.

-And yet...the effect is actually too large to be plausible. According to this document (second table, past month cannabis use rates), the population of users in Colorado rose from 7.3% in 2008/09 to 14.7% in 2014/15. So let's say 7% of the population were previously non-users but have become somewhat-regular users of cannabis (this figure would be 4% for Oregon and also 4% for Washington). For 7% of the population to drive a 3% increase in accidents, the accident frequency for those drivers would have to increase by an implausibly large 43%, which I think is higher than what anyone actually believes. Maybe if all of these new "past month users" were high all the time, but even then this is near the high end of what anyone believes is a plausible effect size.

-The calculated increase in collision frequency was 14% in Colorado, 6% in Washington, and 4.5% in Oregon. But when calculated on a "states combined" basis, the effect size was only 3%, which is smaller than any individual state. There's no mystery here; see Simpson's Paradox. The aggregate effect size can be smaller than any group's effect size (generally, whatever you're measuring) for a number of reasons. I just want to note the very wide range of estimates. It would be a mistake to pick any single one of them as the effect size. Considering my argument in the preceding bullet point, the by-state effect sizes are even more implausible than the overall effect size.

-If you look at a time series of collision frequency (industry-wide data) for Colorado and its comparison states (Utah, Nebraska, and Wyoming), nothing really jumps out at you. Colorado and Utah are sort of trending up, Nebraska is sort of flat, and Wyoming is sort of trending down. But you could easily look at the pattern and say that collision frequency is basically flat, but oscillating randomly around the 4-5% range. Any trends picked out by your eye or by regression analysis are likely to be spurious. The study is looking for very small trends (in the -5% to +5% annual change range), and saying: "We should predict that Colorado would be X based on how its neighbors are trending, but instead it's 14% above X." And it's attributing this difference entirely to cannabis legalization. Similar for the other states. This is not even close to identifying cannabis as a causal factor.

Perhaps I'll have more later.

One more thing. From the link up top: "Moore of the Highway Loss Data Institute said they hope the study's findings will be considered by lawmakers and regulators in states where marijuana legalization is under consideration or recently enacted." Matt Moore is a fine gentlemen. I've met him once and I've had several e-mail contacts with him. But I sincerely hope that lawmakers will not use his study. The study is a fine piece of time-series analysis, perhaps a good exercise for a first course in econometrics. But it's pretty lousy social science.