Reflections on Past and Future

Jan 19 JDN 2458868

This post goes live on my birthday. Unfortunately, I won’t be able to celebrate much, as I’ll be in the process of moving. We moved just a few months ago, and now we’re moving again, because this apartment turned out to be full of mold that keeps triggering my migraines. Our request for a new apartment was granted, but the university housing system gives very little time to deal with such things: They told us on Tuesday that we needed to commit by Wednesday, and then they set our move-in date for that Saturday.

Still, a birthday seems like a good time to reflect on how my life is going, and where I want it to go next. As for how old I am? This is the probably the penultimate power of two I’ll reach.

The biggest change in my life over the previous year was my engagement. Our wedding will be this October. (We have the venue locked in; invitations are currently in the works.) This was by no means unanticipated; really, folks had been wondering when we’d finally get around to it. Yet it still feels strange, a leap headlong into adulthood for someone of a generation that has been saddled with a perpetual adolescence. The articles on “Millennials” talking about us like we’re teenagers still continue, despite the fact that there are now Millenials with college-aged children. Thanks to immigration and mortality, we now outnumber Boomers. Based on how each group voted in 2016, this bodes well for the 2020 election. (Then again, a lot of young people stay home on Election Day.)

I don’t doubt that graduate school has contributed to this feeling of adolescence: If we count each additional year of schooling as a grade, I would now be in the 22nd grade. Yet from others my age, even those who didn’t go to grad school, I’ve heard similar experiences about getting married, buying homes, or—especially—having children of their own: Society doesn’t treat us like adults, so we feel strange acting like adults. 30 is the new 23.

Perhaps as life expectancy continues to increase and educational attainment climbs ever higher, future generations will continue to experience this feeling ever longer, until we’re like elves in a Tolkienesque fantasy setting, living to 1000 but not considered a proper adult until we hit 100. I wonder if people will still get labeled by generation when there are 40 generations living simultaneously, or if we’ll find some other category system to stereotype by.

Another major event in my life this year was the loss of our cat Vincent. He was quite old by feline standards, and had been sick for a long time; so his demise was not entirely unexpected. Still, it’s never easy to lose a loved one, even if they are covered in fur and small enough to fit under an airplane seat.

Most of the rest of my life has remained largely unchanged: Still in grad school, still living in the same city, still anxious about my uncertain career prospects. Trump is still President, and still somehow managing to outdo his own high standards of unreasonableness. I do feel some sense of progress now, some glimpses of the light at the end of the tunnel. I can vaguely envision finishing my dissertation some time this year, and I’m hoping that in a couple years I’ll have settled into a job that actually pays well enough to start paying down my student loans, and we’ll have a good President (or at least Biden).

I’ve reached the point where people ask me what I am going to do next with my life. I want to give an answer, but the problem is, this is almost entirely out of my control. I’ll go wherever I end up getting job offers. Based on the experience of past cohorts, most people seem to apply to about 200 positions, interview for about 20, and get offers from about 2. So asking me where I’ll work in five years is like asking me what number I’m going to roll on a 100-sided die. I could probably tell you what order I would prioritize offers in, more or less; but even that would depend a great deal on the details. There are difficult tradeoffs to be made: Take a private sector offer with higher pay, or stay in academia for more autonomy and security? Accept a postdoc or adjunct position at a prestigious university, or go for an assistant professorship at a lower-ranked college?

I guess I can say that I do still plan to stay in academia, though I’m less certain of that than I once was; I will definitely cast a wider net. I suppose the job market isn’t like that for most people? I imagine most people at least know what city they’ll be living in. (I’m not even positive what country—opportunities for behavioral economics actually seem to be generally better in Europe and Australia than they are in the US.)

But perhaps most people simply aren’t as cognizant of how random and contingent their own career paths truly were. The average number of job changes per career is 12. You may want to think that you chose where you ended up, but for the most part you landed where the wind blew you. This can seem tragic in a way, but it is also a call for compassion: “There but for the grace of God go I.”

Really, all I can do now is hang on and try to enjoy the ride.

Darkest Before the Dawn: Bayesian Impostor Syndrome

Jan 12 JDN 2458860

At the time of writing, I have just returned from my second Allied Social Sciences Association Annual Meeting, the AEA’s annual conference (or AEA and friends, I suppose, since there several other, much smaller economics and finance associations are represented as well). This one was in San Diego, which made it considerably cheaper for me to attend than last year’s. Alas, next year’s conference will be in Chicago. At least flights to Chicago tend to be cheap because it’s a major hub.

My biggest accomplishment of the conference was getting some face-time and career advice from Colin Camerer, the Caltech economist who literally wrote the book on behavioral game theory. Otherwise I would call the conference successful, but not spectacular. Some of the talks were much better than others; I think I liked the one by Emmanuel Saez best, and I also really liked the one on procrastination by Matthew Gibson. I was mildly disappointed by Ben Bernanke’s keynote address; maybe I would have found it more compelling if I were more focused on macroeconomics.

But while sitting through one of the less-interesting seminars I had a clever little idea, which may help explain why Impostor Syndrome seems to occur so frequently even among highly competent, intelligent people. This post is going to be more technical than most, so be warned: Here There Be Bayes. If you fear yon algebra and wish to skip it, I have marked below a good place for you to jump back in.

Suppose there are two types of people, high talent H and low talent L. (In reality there is of course a wide range of talents, so I could assign a distribution over that range, but it would complicate the model without really changing the conclusions.) You don’t know which one you are; all you know is a prior probability h that you are high-talent. It doesn’t matter too much what h is, but for concreteness let’s say h = 0.50; you’ve got to be in the top 50% to be considered “high-talent”.

You are engaged in some sort of activity that comes with a high risk of failure. Many creative endeavors fit this pattern: Perhaps you are a musician looking for a producer, an actor looking for a gig, an author trying to secure an agent, or a scientist trying to publish in a journal. Or maybe you’re a high school student applying to college, or a unemployed worker submitting job applications.

If you are high-talent, you’re more likely to succeed—but still very likely to fail. And even low-talent people don’t always fail; sometimes you just get lucky. Let’s say the probability of success if you are high-talent is p, and if you are low-talent, the probability of success is q. The precise value depends on the domain; but perhaps p = 0.10 and q = 0.02.

Finally, let’s suppose you are highly rational, a good and proper Bayesian. You update all your probabilities based on your observations, precisely as you should.

How will you feel about your talent, after a series of failures?

More precisely, what posterior probability will you assign to being a high-talent individual, after a series of n+k attempts, of which k met with success and n met with failure?

Since failure is likely even if you are high-talent, you shouldn’t update your probability too much on a failurebut each failure should, in fact, lead to revising your probability downward.

Conversely, since success is rare, it should cause you to revise your probability upward—and, as will become important, your revisions upon success should be much larger than your revisions upon failure.

We begin as any good Bayesian does, with Bayes’ Law:

P[H|(~S)^n (S)^k] = P[(~S)^n (S)^k|H] P[H] / P[(~S)^n (S)^k]

In words, this reads: The posterior probability of being high-talent, given that you have observed k successes and n failures, is equal to the probability of observing such an outcome, given that you are high-talent, times the prior probability of being high-skill, divided by the prior probability of observing such an outcome.

We can compute the probabilities on the right-hand side using the binomial distribution:

P[H] = h

P[(~S)^n (S)^k|H] = (n+k C k) p^k (1-p)^n

P[(~S)^n (S)^k] = (n+k C k) p^k (1-p)^n h + (n+k C k) q^k (1-q)^n (1-h)

Plugging all this back in and canceling like terms yields:

P[H|(~S)^n (S)^k] = 1/(1 + [1-h/h] [q/p]^k [(1-q)/(1-p)]^n)

This turns out to be particularly convenient in log-odds form:

L[X] = ln [ P(X)/P(~X) ]

L[(~S)^n) (S)^k|H] = ln [h/(1-h)] + k ln [p/q] + n ln [(1-p)/(1-q)]

Since p > q, ln[p/q] is a positive number, while ln[(1-p)/(1-q)] is a negative number. This corresponds to the fact that you will increase your posterior when you observe a success (k increases by 1) and decrease your posterior when you observe a failure (n increases by 1).

But when p and q are small, it turns out that ln[p/q] is much larger in magnitude than ln[(1-p)/(1-q)]. For the numbers I gave above, p = 0.10 and q = 0.02, ln[p/q] = 1.609 while ln[(1-p)/(1-q)] = -0.085. You will therefore update substantially more upon a success than on a failure.

Yet successes are rare! This means that any given success will most likely be first preceded by a sequence of failures. This results in what I will call the darkest-before-dawn effect: Your opinion of your own talent will tend to be at its very worst in the moments just preceding a major success.

I’ve graphed the results of a few simulations illustrating this: On the X-axis is the number of overall attempts made thus far, and on the Y-axis is the posterior probability of being high-talent. The simulated individual undergoes randomized successes and failures with the probabilities I chose above.


There are 10 simulations on that one graph, which may make it a bit confusing. So let’s focus in on two runs in particular, which turned out to be run 6 and run 10:

[If you skipped over the math, here’s a good place to come back. Welcome!]


Run 6 is a lucky little devil. They had an immediate success, followed by another success in their fourth attempt. As a result, they quickly update their posterior to conclude that they are almost certainly a high-talent individual, and even after a string of failures beyond that they never lose faith.

Run 10, on the other hand, probably has Impostor Syndrome. Failure after failure after failure slowly eroded their self-esteem, leading them to conclude that they are probably a low-talent individual. And then, suddenly, a miracle occurs: On their 20th attempt, at last they succeed, and their whole outlook changes; perhaps they are high-talent after all.

Note that all the simulations are of high-talent individuals. Run 6 and run 10 are equally competent. Ex ante, the probability of success for run 6 and run 10 was exactly the same. Moreover, both individuals are completely rational, in the sense that they are doing perfect Bayesian updating.

And yet, if you compare their self-evaluations after the 19th attempt, they could hardly look more different: Run 6 is 85% sure that they are high-talent, even though they’ve been in a slump for the last 13 attempts. Run 10, on the other hand, is 83% sure that they are low-talent, because they’ve never succeeded at all.

It is darkest just before the dawn: Run 10’s self-evaluation is at its very lowest right before they finally have a success, at which point their self-esteem surges upward, almost to baseline. With just one more success, their opinion of themselves would in fact converge to the same as Run 6’s.

This may explain, at least in part, why Impostor Syndrome is so common. When successes are few and far between—even for the very best and brightest—then a string of failures is the most likely outcome for almost everyone, and it can be difficult to tell whether you are so bright after all. Failure after failure will slowly erode your self-esteem (and should, in some sense; you’re being a good Bayesian!). You’ll observe a few lucky individuals who get their big break right away, and it will only reinforce your fear that you’re not cut out for this (whatever this is) after all.

Of course, this model is far too simple: People don’t just come in “talented” and “untalented” varieties, but have a wide range of skills that lie on a continuum. There are degrees of success and failure as well: You could get published in some obscure field journal hardly anybody reads, or in the top journal in your discipline. You could get into the University of Northwestern Ohio, or into Harvard. And people face different barriers to success that may have nothing to do with talent—perhaps why marginalized people such as women, racial minorities, LGBT people, and people with disabilities tend to have the highest rates of Impostor Syndrome. But I think the overall pattern is right: People feel like impostors when they’ve experienced a long string of failures, even when that is likely to occur for everyone.

What can be done with this information? Well, it leads me to three pieces of advice:

1. When success is rare, find other evidence. If truly “succeeding” (whatever that means in your case) is unlikely on any given attempt, don’t try to evaluate your own competence based on that extremely noisy signal. Instead, look for other sources of data: Do you seem to have the kinds of skills that people who succeed in your endeavors have—preferably based on the most objective measures you can find? Do others who know you or your work have a high opinion of your abilities and your potential? This, perhaps is the greatest mistake we make when falling prey to Impostor Syndrome: We imagine that we have somehow “fooled” people into thinking we are competent, rather than realizing that other people’s opinions of us are actually evidence that we are in fact competent. Use this evidence. Update your posterior on that.

2. Don’t over-update your posterior on failures—and don’t under-update on successes. Very few living humans (if any) are true and proper Bayesians. We use a variety of heuristics when judging probability, most notably the representative and availability heuristics. These will cause you to over-respond to failures, because this string of failures makes you “look like” the kind of person who would continue to fail (representative), and you can’t conjure to mind any clear examples of success (availability). Keeping this in mind, your update upon experiencing failure should be small, probably as small as you can make it. Conversely, when you do actually succeed, even in a small way, don’t dismiss it. Don’t look for reasons why it was just luck—it’s always luck, at least in part, for everyone. Try to update your self-evaluation more when you succeed, precisely because success is rare for everyone.

3. Don’t lose hope. The next one really could be your big break. While astronomically baffling (no, it’s darkest at midnight, in between dusk and dawn!), “it is always darkest before the dawn” really does apply here. You are likely to feel the worst about yourself at the very point where you are about to finally succeed. The lowest self-esteem you ever feel will be just before you finally achieve a major success. Of course, you can’t know if the next one will be it—or if it will take five, or ten, or twenty more tries. And yes, each new failure will hurt a little bit more, make you doubt yourself a little bit more. But if you are properly grounded by what others think of your talents, you can stand firm, until that one glorious day comes and you finally make it.

Now, if I could only manage to take my own advice….

Will robots take our jobs? Not “if” but “when”.

Jan 5 JDN 2458853

The prospect of technological unemploymentin short, robots taking our jobs—is a very controversial one among economists.

For most of human history, technological advances have destroyed some jobs and created others, causing change, instability, conflict—but ultimately, not unemployment. Many economists believe that this trend will continue well into the 21st century.

Yet I am not so sure, ever since I read this chilling paragraph by Gregory Clark, which I first encountered in The Atlantic:


There was a type of employee at the beginning of the Industrial Revolution whose job and livelihood largely vanished in the early twentieth century. This was the horse. The population of working horses actually peaked in England long after the Industrial Revolution, in 1901, when 3.25 million were at work. Though they had been replaced by rail for long-distance haulage and by steam engines for driving machinery, they still plowed fields, hauled wagons and carriages short distances, pulled boats on the canals, toiled in the pits, and carried armies into battle. But the arrival of the internal combustion engine in the late nineteenth century rapidly displaced these workers, so that by 1924 there were fewer than two million. There was always a wage at which all these horses could have remained employed. But that wage was so low that it did not pay for their feed.


Based on the statistics, what actually seems to be happening right now is that automation is bifurcating the workforce: It’s allowing some people with advanced high-tech skills to make mind-boggling amounts of money in engineering and software development, while those who lack such skills get pushed ever further into the margins, forced to take whatever jobs they can get. This skill-biased technical change is far from a complete explanation for our rising inequality, but it’s clearly a contributing factor, and I expect it will become more important over time.

Indeed, in some sense I think the replacement of most human labor with robots is inevitable. It’s not a question of “if”, but only a question of “when”. In a thousand years—if we survive at all, and if we remain recognizable as human—we’re not going to have employment in the same sense we do today. In the best-case scenario, we’ll live in the Culture, all playing games, making art, singing songs, and writing stories while the robots do all the hard labor.

But a thousand years is a very long time; we’ll be dead, and so will our children and our grandchildren. Most of us are thus understandably a lot more concerned about what happens in say 20 or 50 years.

I’m quite certain that not all human work will be replaced within the next 20 years. In fact, I am skeptical even of the estimates that half of all work will be automated within the next 40 years, though some very qualified experts are making such estimates. A lot of jobs are safe for now.

Indeed, my job is probably pretty safe: While there has been a disturbing trend in universities toward adjunct faculty, people are definitely still going to need economists for the foreseeable future. (Indeed, if Asimov is right, behavioral economists will one day rule the galaxy.)

Creative jobs are also quite safe; it’s going to be at least a century, maybe more, before robots can seriously compete with artists, authors, or musicians. (Robot Beethoven is a publicity stunt, not a serious business plan.) Indeed, by the time robots reach that level, I think we’ll have to start treating them as people—so in that sense, people will still be doing those jobs.

Even construction work is also relatively safe—actually projected to grow faster than employment in general for the next decade. This is probably because increased construction productivity tends to lead to more construction, rather than less employment. We can pretty much always use more or bigger houses, as long as we can afford them. Really, we should be hoping for technological advances in construction, which might finally bring down our astronomical housing prices, especially here in California.

But a lot of jobs are clearly going to disappear, sooner than most people seem to grasp.

The one that worries me the most is truck drivers. Truck drivers are a huge number of people. Trucking employs over 1.5 million Americans, accounting for about 1% of all US workers. It’s one of the few remaining jobs that pays a middle-class salary with entry-level skills and doesn’t require an advanced education. It’s also culturally coded as highly masculine, which is advantageous in a world where a large number of men suffer so deeply from fragile masculinity (a major correlate of support for Donald Trump, by the way, as well as a source of a never-ending array of cringeworthy marketing) that they can’t bear to take even the most promising “pink collar” jobs.

And yet, long-haul trucking is probably not going to exist in 20 years. Short-haul and delivery trucking will probably last a bit longer, since it’s helpful to have a human being to drive around complicated city streets and carry deliveries. Automated trucks are already here, and they are just… better. While human drivers need rest, sleep, food, and bathroom breaks, rarely exceeding 11 hours of actual driving per day (which still sounds exhausting!), an automated long-haul truck can stay on the road for over 22 hours per day, even including fuel and maintenance. The capital cost of an automated truck is currently much higher than an ordinary truck, but when that changes, trucking companies aren’t going to keep around a human driver when their robots can deliver twice as fast and don’t expect to be paid wages. Automated vehicles are also safer than human drivers, which will save several thousand lives per year. For this to happen, we don’t even need truly full automation; we just need to get past our current level 3 automation and reach level 4. Prototypes of this level of automation are already under development; in about 10 years they’ll start hitting the road. The shift won’t be instantaneous; once a company has already invested in a truck and a driver, they’ll keep them around for several years. But in 20 years from now, I don’t expect to see a lot of human-driven trucks left.

I’m pleased to see that the government is taking this matter seriously, already trying to develop plans for what to do when long-haul trucks become fully robotic. I hope they can come up with a good plan in time.

Some jobs that will be automated away deserve to be automated away. I can’t shed very many tears for the loss of fast-food workers and grocery cashiers (which we can already see happening around us—been to a Taco Bell lately?); those are terrible jobs that no human being should have to do. And my only concern about automated telemarketing is that it makes telemarketing cheaper and therefore more common; I certainly am not worried about the fact that people won’t be working as telemarketers anymore.

But a lot of good jobs, even white-collar jobs, are at risk of automation. Algorithms are already performing at about the same level as human radiologists, contract reviewers, and insurance underwriters, and once they get substantially better, companies are going to have trouble justifying why they would hire a human who costs more and performs worse. Indeed, the very first job to be automated by information technology was a white-collar job: computer used to be a profession, not a machine.

Technological advancement is inherently difficult to predict: If we knew how future technology will work, we’d make it now. So any such prediction should contain large error bars: “20 years away” could mean we make a breakthrough next year, or it could stay “20 years away” for the next 50 years.

If we had a robust social safety net—a basic income, perhaps?—this would be fine. But our culture decided somewhere along the way that people only deserve to live well if they are currently performing paid services for a corporation, and as robots get better, corporations will find they don’t need so many people performing services. We could face up to this fact and use it as an opportunity for deeper reforms; but I fear that instead we’ll wait to act until the crisis is already upon us.