Update: To be fair, the paper did get published?
— Carl T. Bergstrom (@CT_Bergstrom) July 31, 2018
I got bored so I looked up some numbers…
So I have a new dream purchase, since I learned this week that the Brady Bunch house is up for sale. I’m still kinda pissed that I missed…
Personally, I like the visual that I used here, namely “index everything to 100 at the start and then see how things grow differently over time,” but I can’t tell if the approach is intuitive to everyone. Also, it’s kind of crowded, but here’s most of the numbers in one picture:
In case you haven’t seen it before, the income lines collectively give the picture for the increasing income inequality that we talk about so much. (Note, however, that inflation isn’t controlled for in these numbers, so they overstate increases in living standards but are appropriate to compare to unadjusted house prices.)
It’s causal Friday, so I’m poking around in some data trying to make a case for cause and effect. More specifically, I’m drowning in a differences-in-differences analysis trying to construct a proper control group. (In this case, identifying a control group isn’t conceptually difficult, it’s just really annoying to pull the data.)
So what is a differences-in-differences analysis? It’s…well, pretty much exactly what it sounds like- it’s kind of nice when that happens. Here’s a little thing I wrote up a while ago for my team at work (who had more of a data science than social science background), or you can consult Wikipedia. (note: you will never convince me it’s “difference-in-differences” and not “differences-in-differences”) The general principle behind differences-in-differences is that you can’t just do a before-after comparison to identify the effect of an event, since you’d also need to know what the before-afters look like for stuff that wasn’t subjected to the event. For example, consider the following hypothetical question:
Fairlife milk initiated a new marketing campaign at the beginning of 2018, and so far sales of Fairlife milk are 5 percent higher than for the same portion of 2017. Should the marketing campaign be considered a success?
Hopefully it’s at least somewhat intuitive that the answer should be “I dunno, how do the sales of non-Fairlife milk compare to last year?” If milk sales more generally are, say, also up 5 percent, it’s not particularly likely that the marketing campaign is doing much. On the other hand, if sales for the milk industry were generally down compared to last year, the marketing campaign should be viewed much more favorably.
So this is what I was trying to do, but with music sales. Remember this?
Ever wanted to quit your job? Why don’t you take a leaf out of video producer Marina Shifrin’s book and do it through the medium of “interpretive dance”?
For context, I’m using this as a motivating example for a larger analysis on music sampling. So I dutifully went through and identified two other songs from the same Kanye album that were about as popular as ‘Gone” before the video above went viral, and then I looked up the sales of all three songs (this is way more annoying than you’d think it should be) before and after the video’s posting date so I could do a very careful and nuanced analysis. Clearly I didn’t think things through, since, well…
This is only for the song used in the viral video, so I don’t technically have a comparison group (yet), but I mean COME ON…nonetheless, I persisted and added my control group:
(I changed the scale of the graph so it looked just wonky rather than useless.) You’ll be pleased to know that my confidence in the video causing a sales bump has not decreased…but let’s calculate some differences in differences anyway (it’s not really possible to run a regression here). So here are the numbers for 4 weeks before and 4 weeks after:
These numbers are pretty easy to interpret- an effect is positive if the differences-in-differences numbers are positive and vice versa. (An effect is nonexistent if the difference is close to zero.) Now I guess technically I should run a test to see whether the differences are *statistically* different from zero, but 1. that’s kind of hard with 3 data points, and 2. I mean come on.
The real punch line in all of this is the fact that the video has been taken down on copyright grounds…I’m, um, not sure you’re doing it right, record label…
Ok, story time, so go grab your blankie and a beverage…
A number of years ago, I taught an econ tutorial entitled “Sex, Drugs, and Rock & Roll”…it was a neat class- as the name would suggest, we looked at papers on birth control, drug legalization, the music industry, and so on. For reasons I’m still not sure I understand, it was a somewhat peculiar group of students- basically the football team, the kid who as far as I could tell tutored the football team, and a female transfer from Tulane (because of hurricane Katrina). (I actually confirmed with her beforehand that she was ok with the gender ratio, given the subject matter…turns out she wasn’t easily fazed and later explained to everyone how to make meth.)
Anyway, I digress…the first paper I assigned was authored by a combination of friends and classmates- it wasn’t so much directly relevant to the subject matter but it has “Sex, Drugs, and Rock & Roll” in the title so I figured it would be a good place to start getting students used to reading academic research. The discussion…well, didn’t go as I expected.
Basically, the football team came in and explained that it was funny to read the paper because they participated in the experiment. So, PSA: if you use the CLER Lab at Harvard your subject pool is the Harvard football team I guess. (I don’t mean to imply this is positive or negative, just that it might affect generalizability.) Given this information, I found it far more interesting to have them talk about their experience than to jump right into talking about the results of the paper. The main thing I wanted to know was essentially “did you take the task seriously and think things through?”
The responses were “meh” at best, from what I remember. I pushed back, asking something along the lines of “but you get paid more if you performed better at the task, did that not serve as an incentive?” The response was basically this:
Again, I’m not criticizing the students- I completely believe that effort isn’t costless even when a person doesn’t have anything better to do, so it’s entirely possible that the kids were in fact maximizing their utility. But it gave me something interesting to think about regarding experimental design and how to interpret experimental results. In general, economists are wary of asking hypothetical questions about preferences and behaviors, since there’s good evidence that what people say they would do or what they think they would do doesn’t always coincide with the choices that they actually make. To mitigate this problem, experimental economists try to give subjects tasks where payoffs depend on behavior (usually in addition to giving a payment for showing up), since this supposedly gives the subjects proper incentives to treat the task as though it’s real. Economists have even been known to do their experiments in developing countries, since that enables the research budgets to create stakes that are more real than trivial.
The discussion with my students makes me think that we need to be more critical regarding whether our experiments give sufficient incentives to elicit true behaviors and preferences. In addition, economists could probably do more to assess both during and after the experiments how seriously the subjects took their assigned task. In any case, the bottom line is that the success of an experiment depends crucially on subjects taking the task seriously and behaving as expected in a logistical sense, and these characteristics can’t be taken for granted.
Or, put more succinctly, here’s a helpful warning:
don’t say nun just RT pic.twitter.com/yvANYoCSh9
— budokai (@budokai_) April 28, 2018
I’ve been watching this all day and I can’t stop laughing. (probably related: Gizmo looks a little worried at the moment) For context, there’s this thing going around Twitter where people try to see whether their dogs understand object permanence by holding up a sheet and then running away as it falls. I mean, what could possibly go wrong with this clearly rock solid experimental design?
Update: There’s a point brought up in one of the comments below that I think warrants discussion…I certainly didn’t intend for the takeaway from this post to be “experiments are bad, burn them,” but I see how it could be taken that way. If anything, I’m suggesting the opposite, so allow me to explain. If subjects aren’t fully engaged in an experiment, this probably biases the experiment towards “no effect” rather than creating effects where none exist. In the dog scenario, for example, maybe the chihuahua does in fact understand object permanence, but we can’t document the phenomenon because the dog’s behavior caused the experiment to be garbage. Therefore, I’m not advocating for questioning results so much as questioning “non results.” We talk about a “replication crisis” in economics, where a surprisingly large percentage of documented effects can’t be re-documented in subsequent experiments. These numbers are general used to call the initial findings into questions, and I guess I’m suggesting that we should go easier on this suspicion until we can confirm that such lack of replicability isn’t driven by the sorts of issues I describe above. I guess I’m also trying to help researchers make their budgets go further, since publication bias means that non results often just get shoved in the file drawer, never to see the light of day.
You guys, I love monopsonies…for starters, it’s a fun word to say, and it makes people do a double take when they initially think you said “monopoly.” Definitionally, a monopsony is a market with only one buyer- basically the economic counterpart to a monopoly, which is a market with only one seller. Not surprisingly, the buyer in a monopsony has all of the market power in much the same way that the seller in a monopoly does, and largely for a mathematically analogous reason.
Economists have been talking about monopsonies more than usual as of late, most often in the context of labor markets. In labor markets, companies are the buyers (or, perhaps more accurately given the 13th amendment, the renters) and people are the sellers of labor. When the number of employers in an area competing for workers is small, firms are generally thought to have “monopsony power.” This is a little different from literally being a monopsony, but you can think of monopsony power as the ability to act like a monopsony but to a lesser degree.
So what’s interesting about monopsonies in labor markets? Here’s a quick summary:
This distinction is obviously important from a policy perspective, since minimum wages look way more appealing if they don’t cause people to get laid off. Now, I could try to explain to you why minimum wages work this way using some fun graphs and whatnot, but I’ve come to learn that not everyone’s brain wants to operate at an abstract conceptual level, so let’s work through a simple example instead.
Ready? I’m gonna try to do this without using any econ-specific terms (they’re not as fun to say as monopsony), and we’re going to talk about a company that makes widgets- yes, I know this is a tired econ thing, but Widget is the name of my mom’s cat so I’m asserting it’s fair game.
First, here are some numbers on how many widgets workers can produce:
You’ll note that the “incremental widgets” numbers are decreasing as more workers are added- this is generally reasonable, since most production faces a diminishing returns or “too many cooks in the kitchen” problem. Now let’s say that the company can sell as many widgets as it wants at a price of $10 each- now we can see how much each worker would add to the company’s revenue (does revenue count as an econ term?)
If we want to figure out how many workers the company wants to hire, we need to know how much the workers cost. The thing about workers is that some of them will work more cheaply than others (even if they’re of equivalent quality), and this is relevant for a monopsony, since they’re not so small that they can increase their hiring without pushing up the going market wage. (In fact, this feature is the crux of why monopsonies look different from competitive labor markets!) Let’s assume the wage required to get each worker to work looks like this: (you can think of everything in per hour terms, per day, whatever, it doesn’t really matter)
We can now calculate how much it would cost to hire 1 worker, 2 workers, etc., and we can also calculate the incremental cost of each additional worker:
I feel like this requires some explanation since it’s not really intuitive…if you want to hire the first worker, things are pretty simple, but if you want to hire the second worker, you not only have to pay the second worker the $20 to get him to work, but you also have to pay the first guy $20 rather than $10- there are a number of reasons for this, but you can just imagine that the first guy will get really pissed if he makes less money than second guy for doing the same job. This means that the incremental cost of hiring an additional worker includes not only his wage but also the additional compensation that has to be given to everyone who came before. (This is seriously the most important point so keep staring at it until it sinks in. I’ll wait.)
So take a look at the relevant numbers so far- how many workers does the company want to hire?
Does the company want to hire the first worker? Sure, since that worker brings in $120 and only costs $10. (just assume that labor is the only cost of production) Does the company want to hire the second worker? Sure, since the second worker brings in an additional $100 but only adds $30 to the company’s costs. If we keep analyzing in this way, we can conclude that the company will want to stop hiring after it hires 3 workers. (and will pay a wage of $30)
Now how do things change if a minimum wage is imposed? Let’s assume that a minimum wage of $40 is set. (Now I look real generous to those people who interpreted the numbers as being per hour.)
Workers 1, 2, 3, and 4 are happy to work for the minimum wage, so the company can hire up to 4 workers at $40 each. After 4 workers are hired, however, things change dramatically- in order to hire the 5th guy, the company not only has to pay him $50 but also has to pay each of the 4 other workers $50 rather than $40. How many workers does the company want to hire now? (This is the last set of numbers, I swear.)
Now the company would find it profitable to hire the first 4 workers but not the 5th worker. BOOM- I just showed you a case where a minimum wage would increase rather than decrease the number of workers hired.
So why did this happen? Put simply, the minimum wage took away the “well if I hire you I have to pay everyone else more too” feature of the company’s analysis, at least for the first 4 workers. That said, the minimum wage still creates somewhat of a double-edged sword in terms of employment, since it also made it incrementally more expensive to hire the 5th guy than it was before. As a result, minimum wages placed on monopsonistic markets can both encourage companies to hire more workers and discourage companies from setting wages just above the minimum wage. (This is relevant for companies that pay just above what would be the minimum wage, since it could actually cause them to decrease wages!)
I’m not trying to convince you that minimum wages are good, I’m just walking you through some numbers so that you don’t do the “I took one econ class once and models of competitive markets are always applicable” thing that causes economists to call you an ass clown behind your back. One last thing- in case you (understandably) have the follow-up question of “how prevalent is monopsony power in labor markets?”, here’s some reading material for you to peruse. Spoiler alert: the answer is “too prevalent to ignore.”
Update: You can see a version of this story on Medium if you prefer.
Every Friday at about 5pm or so, Justin Wolfers declares it beer o’clock on Twitter:
By the power vested in me by Scott Pruitt, I suggest you enjoy an EPA by ordering from a secret email address, getting a lobbyist to pay, deleting it from your calendar, firing staff who won’t play along, and thanking the President for the opportunity to serve this beer o’clock. pic.twitter.com/t1dPzenpUk
— Justin Wolfers (@JustinWolfers) July 6, 2018
This is nice and all (and, honestly, a helpful reminder to maybe stop working even though I generally ignore it), but I’ve always felt like we could do better with the econ-associated beverages. And it turns out we can…
Maybe, as a behavioral economist, I’m biased, but this is just so good. Also, here’s the reference in case you’re not familiar, so you even get some weekend reading material with your weekend booze suggestions.
Okay I know we just talked about fireworks, at least indirectly, but I think we need to have another conversation since i’m not convinced that we’re doing them right:
PRIVATE FIREWORKS FOR EVERY FAMILY IS A BAD IDEA pic.twitter.com/jJvFD7ZXNd
— Andrew Heiss (@andrewheiss) July 5, 2018
I guess the good news is that my concerns regarding free riding leading to underprovision of fireworks are pretty much abated. The bad news is that I’m not sure people have caught on to the whole nonrival consumption thing. Here’s the basic idea: a good is nonrival in consumption (or has low rivalry in consumption, or is simply nonrival) if one person consuming the good doesn’t prevent others from consuming the same unit of the good. In this instance, this is a fancy way way of saying “you can all watch the same fireworks my eyes don’t somehow absorb them and prevent your ocular enjoyment.”
When goods are rival in consumption (the opposite of nonrival, as you would expect), we determine how many of the good the market wants via a process of “horizontal addition.” (This makes physical sense if you take a quick look at a demand curve.) Let’s say that there’s a market that consists of me and Mr. Econgirl, and at a price of $5 we each want to consumer 1 ice-cream cone. This means that market demand is 2 at a price of $5 since we can’t both fully consume the same ice cone. (Even if we physically could…well, ew. I guess my dad shared a Dairy Queen cone with our rottweiler once and didn’t die but I’m still not recommending it.) But, as I said, this isn’t how nonrival goods work.
Let’s say instead that Mr. Econgirl and I are each willing to pay $5 to watch a fireworks display. (He’s not, but let’s pretend.) This is sort of a hypothetical payment since obviously we would both try to free ride, so it’s more accurate to say that we would each get $5 of benefits from watching a fireworks display. This implies that the market values a fireworks display at $10 (arrived at via “vertical addition,” in case you’re curious), in which case it’s efficient to provide a fireworks display if it costs $10 or less.
This last point gets at why I”m so annoyed at the individual fireworks people- if you believe that a fireworks display that costs $10 is cooler than 2 fireworks displays that each cost $5 (I’m not an expert but am pretty confident that this is true), then having each house do their own fireworks is an incredibly inefficient use of resources. I mean, wouldn’t you rather all coordinate and have this?
I guess there are a couple of explanations for the outcome that we see. One is simply that the households don’t want to coordinate- either they just don’t feel like it or are worried about the free-rider problem creeping up. Another, more interesting, potential explanation is that the households get utility from producing the fireworks, whereas I’ve been assuming that only consumption is enjoyable. (probably related: I have no desire to set off fireworks myself) In general, economic models don’t take this possibility into account, but they probably should, at least in some cases. For example, if we take into account the fact that musicians specifically like producing music, a lot of what we see in the music industry coincides far more nicely with our economic models. Unfortunately, one of the things that becomes explainable is the fact that prices pretty quickly get driven to zero. But yay, free* fireworks at least?
* do not start with the “there’s no such thing as free fireworks here” since the thing about nonrival goods is they do in fact have zero marginal cost