# A Bellman Equation About Nothing

#### Cold Open [Introduction]

A few years ago I came across a short paper that I desperately wanted to understand. The magnificent title was “An Option Value Problem from Seinfeld” and the author, Professor Avinash Dixit (of Dixit-Stiglitz model fame), therein discussed methods of solving for “sponge-worthiness.” I don’t think I need to explain why I was immediately drawn to an academic article that focuses on Elaine Benes, but for those of you who didn’t learn about the realities of birth control from this episode of 1990’s television, allow me to briefly explain the relevant Seinfeld-ism. The character Elaine Benes[1] loyally uses the Today sponge as her preferred form of contraception. However, one day it is taken off the market and, after trekking all over Manhattan, our heroine manages to find only one case of 60 sponges to purchase. The finite supply of sponges poses a daunting question to Elaine… namely, when should she choose to use a sponge? Ie, when is a given potential partner sponge-worthy?

JERRY: I thought you said it was imminent.

ELAINE: Yeah, it was, but then I just couldn’t decide if he was really sponge-worthy.

JERRY: “Sponge-worthy”?

ELAINE: Yeah, Jerry, I have to conserve these sponges.

JERRY: But you like this guy, isn’t that what the sponges are for?

ELAINE: Yes, yes – before they went off the market. But I mean, now I’ve got to re-evaluate my whole screening process. I can’t afford to waste any of ’em.

–“The Sponge” [Seinfeld Season 7 Episode 9]

As an undergraduate reading Professor Dixit’s introduction, I felt supremely excited that an academic article was going to delve into the decision-making processes of one of my favorite fictional characters. However, the last sentence in the introduction gave me pause: “Stochastic dynamic programming methods must be used.” Dynamic programming? Suffice it to say that I did not grasp the methodological context or mathematical machinery embedded in the short and sweet paper. After a few read-throughs, I filed wispy memories of the paper away in some cluttered corner of my mind… Maybe one day this will make more sense to me…

Flash forward to August 2016. Professor David Laibson, the economics department chair, explains to us fresh-faced G1’s (first-year PhD’s) that he will be teaching us the first part of the macroeconomics sequence… Dynamic Programming. After a few days of talking about Bellman equations, I started to feel as if I had seen related work in some past life. Without all the eeriness of a Westworld-esque robot, I finally remembered the specifics of Professor Dixit’s paper and decided to revisit it with Professor Laibson’s lectures in mind. Accordingly, my goal here is to explain the simplified model set-up of the aforementioned paper and illustrate how basics from dynamic programming can be used in “solving for spongeworthiness.”

#### Act One [The Model]

Dynamic programming refers to taking a complex optimization problem and splitting it up into simpler recursive sub-problems. Consider Elaine’s decision as to when to use a sponge. We can model this as an optimal stopping problem–ie, when should Elaine use the sponge and thus give up the option value of holding it into the future? The answer lies in the solution to a mathematical object called the Bellman equation, which will represent Elaine’s expected present value of her utility recursively.

Using a simplified version of the framework from Dixit (2011), we can explain the intuition behind setting up and solving a Bellman equation. First, let’s lay out the modeling framework. For the sake of computational simplicity, assume Elaine managed to acquire only one sponge rather than the case of 60 (Dixit assumes she has a general m sponges in his set-up, so his computations are more complex than mine). With that one glorious sponge in her back pocket, Elaine goes about her life meeting potential partners, and yada yada yadaTo make the yada yada’s explicit, we say Elaine lives infinitely and meets one new potential partner every day t who is of some quality Qt. Elaine is not living a regular continuous-time life, instead she gets one romantic option each time period. This sets up the problem in discrete-time since Elaine’s decisions are day-by-day rather than infinitesimally-small-moment-by-infinitesimally-small-moment. If we want to base this assumption somewhat in reality, we could think of Elaine as using Coffee Meets Bagel, a dating app that yields one match per day. Ie, one “bagel” each day.

Dixit interprets an individual’s quality as the utility Elaine receives from sleeping with said person. Now, in reality, Elaine would only be able to make some uncertain prediction of a person’s quality based on potentially noisy signals. The corresponding certainty equivalent [the true quality metric] would be realized after Elaine slept with the person. In other words, there would be a distinction between ex post and ex ante quality assessments—you could even think of a potential partner as an experience good in this sense. (Sorry to objectify you, Scott Patterson.) But, to simplify our discussion, we assume that true quality is observable to Elaine—she knows exactly how much utility she will gain if she chooses to sleep with the potential partner of the day. In defense of that assumption, she does vet potential partners pretty thoroughly.

Dixit also assumes quality is drawn from a uniform distribution over [0,1] and that Elaine discounts the future exponentially by a factor of δ in the interval (0,1). Discounting is a necessary tool for agent optimization problems since preferences are time dependent. Consider the following set-up for illustrative purposes: Say Elaine gains X utils from eating a box of jujyfruit fruit today, then using our previously defined discount factor, she would gain δX from eating the box tomorrow, δ2X from eating it the day after tomorrow, and so on. In general, she gains δnX utils from consuming it n days into the future—thus the terminology “exponential discounting.” Given the domain for δ, we know unambiguously that X > δX >δ2X >… and on. That is, if the box of candy doesn’t change between periods (it is always X), (assuming it yields positive utility—which clearly it must given questionable related life decisions.) Elaine will prefer to consume it in the current time period. Ie, why wait if there is no gain from waiting? On the other hand, if Elaine wants to drink a bottle of wine today that yields Y utils, but the wine improves by a factor of w>1 each day, then whether she prefers to drink it today or tomorrow depends on whether Y—the present utility gain of the current state of the wine—or δ(wY)—the discounted utility gain of the aged (improved) wine—is greater. (Ie, if δw>1, she’ll wait for tomorrow.) If Elaine also considers up until n days into the future, she will be comparing, Y,  δ(wY), δ2X(w2Y), …, and δn(wnY).

In our set-up Elaine receives some quality offer each day that is neither static (as in the jujyfruit fruit example) nor deterministically growing (as in the wine example), rather the quality is drawn from a defined distribution (the uniform distribution on the unit interval—mainly chosen to allow for straightforward computations). While quality is observable in the current period, the future draws are not observable, meaning that Elaine must compare her current draw with an expectation of future draws. In short, everyday Elaine has the choice whether to use the sponge and gain Qt through her utility function, or hold the sponge for a potentially superior partner in the future. In other words, Elaine’s current value function is expressed as a choice between the “flow payoff” Qt and the discounted “continuation value function.” Since she is utility maximizing, she will always choose the higher of these two options. Again, since the continuation value function is uncertain, as future quality draws are from some distribution, we must use the expectation operator in that piece of the maximization problem. Elaine’s value function is thus:

This is the Bellman equation of lore! It illustrates a recursive relationship between the value functions for different time periods, and formalizes Elaine’s decision as a simple optimal stopping problem.

#### Act Two [Solving for Sponge-worthiness]

To solve for sponge-worthiness, we need to find the value function that solves the Bellman equation, and derive the associated optimal policy rule. Our optimal policy rule is a function that maps each point in the state space (the space of possible quality draws) to the action space such that Elaine achieves payoff V(Qt) for all feasible quality draws in [0,1]. The distribution of Qt+1 are stationary and independent of Qt, as the draws are perpetually from U[0,1]. (Note to the confounded reader: don’t think of the space of quality draws as akin to some jar of marbles in conventional probability puzzles—those in which the draw of a red marble means there are less red to draw later—since our distribution does not shift between periods. For more on other possible distributions, see Act Four.) Due to the aforementioned stationarity and independence, the value of holding onto the sponge [δEV(Qt+1)] is constant for all days. By this logic, if a potential partner of quality Q’ is sponge-worthy, then Q’ ≥ δEV(Qt+1)! Note that for all Q”>Q’, Q”>δEV(Qt+1), so some partner of quality Q” must also be considered sponge-worthy. Similarly, if a person of quality Q’ is not sponge-worthy, then δEV(Qt+1) ≥ Q’ and for all Q”<Q’, Q”<δEV(Qt+1), so any partner of quality Q” must also not be sponge-worthy. Thus, the functional form of the value function is:

In other words, our solution will be a threshold rule where the optimal policy is to use the sponge if Q> Q* and hold onto the sponge otherwise. The free parameter we need to solve for is Q*, which we can conceptualize as the all-powerful quality level that separates the sponge-worthy from the not!

#### Act Three [What is Q*?]

When Q= Q*, Elaine should be indifferent between using the sponge and holding onto it. This means that the two arguments in the maximization should be equal–that is, the flow payoff [Q*] and the discounted continuation value function [δEV(Qt+1)]. We can thus set Q*=δEV(Qt+1and exploit the fact that we defined Q ~ U[0,1], to make the following calculations:

The positive root yields a Q* >1, which would mean that Elaine never uses the sponge. This cannot be the optimal policy, so we eliminate this root. In effect, we end up with the following solution for Q*:

Given this Q*, it is optimal to use the sponge if Q> Q*, and it is optimal to hold the sponge Q* ≥ Qt. Thus, as is required by the definition of optimal policy, for all values of Qt:

We can interpret the way the Q* threshold changes with the discount factor δ using basic economic intuition. As δ approaches 1 (Elaine approaches peak patience), Q* then approaches 1, meaning Elaine will accept no partner but the one of best possible quality. At the other extreme, as δ approaches 0 (Elaine approaches peak impatience), Q* then approaches 0, meaning Elaine will immediately use the sponge with the first potential partner she meets.

To make this visually explicit, let’s use a graph to illustrate Elaine’s value function for some set δ. Take δ=0.8, then Q*=0.5, a clear-cut solution for the sponge-worthiness threshold. Given these numbers, the relationship between the value function and quality level can be drawn out as such:

What better application is there for the pgfplots package in LaTeX?!

The first diagram illustrates the two pieces that make up Elaine’s value function, while the second then uses the black line to denote the value function, as the value function takes on the maximum value across the space of quality draws. Whether the value function conforms to the red or green line hinges on whether we are in the sponge-worthy range or not. As explained earlier, before the sponge-worthiness threshold, the option value of holding the sponge is the constant such that Q*=δEV(Qt+1). After hitting the magical point of sponge-worthiness, the value function moves one-for-one with Qt. Note that alternative choices for the discount rate would yield different Q*’s, which would shift the red line up or down depending on the value, which in turn impact the leftmost piece of the value function in the second graph. These illustrations are very similar to diagrams we drew in Professor Laibson’s module, but with some more advanced technical graph labelings than what we were exposed to in class (ie, “no sponge for you” and “sponge-worthy”).

#### Act Four [Extensions]

In our set-up, the dependence of the value function is simple since there is one sponge and Elaine is infinitely lived. However, it could be that we solve for a value function with more complex time and resource dependence. This could yield a more realistic solution that takes into account Elaine’s age and mortality and the 60 sponges in the valuable case of contraception. We could even perform the sponge-worthiness calculations for Elaine’s monotonically increasing string of sponge quantity requests: 3, 10, 20, 25, 60! (These numbers based in the Seinfeld canon clearly should have been in the tabular calculations performed by Dixit.)

For computational purposes, we also assumed that quality is drawn independently each period (day) from a uniform distribution on the unit interval. (Recall that a uniform distribution over some interval means that each value in the interval has equal probability.) We could alternatively consider a normal distribution, which would likely do a better job of approximating the population quality in reality. Moreover, the quality of partners could be drawn from a distribution whose bounds deterministically grow over time, as there could be an underlying trend upward in the quality of people Elaine is meeting. Perhaps Coffee Meets Bagel gets better at matching Elaine with bagels, as it learns about her preferences.

Alternatively, we could try and legitimize a more specific choice of a distribution using proper Seinfeld canon. In particular, Season 7 Episode 11 (“The Wink,” which is just 2 episodes after “The Sponge”) makes explicit that Elaine believes about 25% of the population is good looking. If we assume Elaine gains utility only from sleeping with good looking people, we could defend using a distribution such that 75% of quality draws are exactly 0 and the remaining 25% of draws are from a normal distribution ranging from 0 to 1.  (Note that Jerry, on the other hand, believes 95% of the population is undateable, so quality draws for Jerry would display an even more extreme distribution–95% of draws would be 0 and the remaining 5% could come from a normal distribution from 0 to 1.)

Regardless of the specific distribution or time/resource constraint choices, the key take-away here is the undeniably natural formulation of this episode’s plot line as an optimal stopping problem. Throughout the course of our six weeks with Professor Laibson, our class used dynamic programming to approach questions of growth, search, consumption, and asset pricing… while these applications are diverse and wide-ranging, don’t methods seem even more powerful when analyzing fictional romantic encounters!?

Speaking of power

#### References

As explained earlier, this write-up is primarily focused on the aforementioned Dixit (2011) paper, but also draws on materials from Harvard’s Economics 2010D sequence. In particular, “Economics 2010c: Lecture 1 Introduction to Dynamic Programming” by David Laibson (9/1/2016) & “ECON 2010c Section 1” by Argyris Tsiaras (9/2/2016).

# Anxious Optimization

Models

On the morning of my dynamic programming midterm, I tried to calm myself by recalling the golden rules of grad school that have been passed down through the generations[1]:

### “grades don’t matter… nothing matters.”

However, I quickly realized that by adopting this perspective I was simply subbing out test anxiety for existential anxiety. And, come to think of it, the latter didn’t seem to be helpful, while the former could actually aid in my short-term goals–namely, jotting down lots of equations into a collection of small blue booklets.
In considering the roles that angst can play in day-to-day life, I started to become curious about whether I could model optimal choices of anxiety using dynamic programming techniques. Allow me to channel my inner Ed Glaeser[2] using David Laibson-esque framework[3] and wax poetic on the specifics of something you could call (using very flexible terminology) an “economic model”…
Let’s assume that anxiety has some negative cost (say to my overarching mental health), however, its presence in my life also often gets me to achieve goals that I do genuinely want to achieve. Therefore, anxiety factors into my personal utility function in both positive and negative ways. In other words, it is not some force in my life that I want to erase entirely since it can lead to incredibly positive outcomes.
Let’s say, for the sake of model simplicity and for the sake of accuracy since I’m in academia now[4], that my utility function is simply equated to my academic success. Imagine that academic success is some definable and quantifiable concept–we could define this as some weighted average of number of papers published in quality journals, number of good relationships with faculty members, etc. Let’s also assume that this type of success that is a function of (and increasing in) two items: idea creation and execution of ideas. This seems reasonable to me. The next piece is where the real controversial and strict assumptions come in with respect to anxiety: I assume that idea creation is a function of (and increasing in) existential anxiety, while execution is a function of (and increasing in) time/test anxiety. Assume that the functions with respect to the anxiety types have positive first derivatives and negative second derivatives–this is equivalent to assuming concavity. [Note: In reality, there is most definitely some level of both angsts that stops being productive… noting that this is the case calls for more complex assumptions about the functional forms beyond assuming simple concavity… suggestions are welcome!]
Then, given these assumptions and the framework of dynamic programming, the optimization problem of interest is equivalent to solving a maximization problem over the lifecycle.
Explicitly solving this optimization problem requires more assumptions about functional forms and the like. Ed, I’m open to your ideas! Sure, it’d be much simpler to somehow make this a one variable maximization problem–a transformation we are often able to achieve by exploiting some budget constraint and Walras’ law–however, I do not believe that anxiety measures should add to some value beyond human choice. Other potential questions: Do we think our state variables follow an Ito process? Ie, I could see the existential anxiety variable following geometric Brownian motion since drift maybe should rise exponentially with time?
Back to reality, an implication of my model build that comes straight out of my assumptions (don’t even need first order conditions for this) is that I should not be thinking about how “nothing matters” when there’s an upcoming test. A test falls into the category of execution tasks, rather than the realm of idea creation. The existential anxiety that grows out of repeating the mantra “nothing matters” to myself over and over would only be helping come up with ideas… In fact, this whole model idea and post did come from continuing down the path of some existential thought process! So, perhaps the real question should be: is my blogging engrained in weighted average measure for “academic success”? If so, I’m feeling pretty optimized.
##### Footnotes

[1] Thank you to the G2’s (second-year’s) for the soothing (yet still terrifying) words in your recent emails.

[2] Microeconomics professor of “verbal problem” fame

[3] Macroeconomics professor for the “dynamic programming” quarter of our sequence

[4] I kid, I kid. I’m off to a frisbee tournament for this entire weekend, so clearly my utility function must be more complex.

###### © Alexandra Albright and The Little Dataset That Could, 2016. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts, accompanying visuals, and links may be used, provided that full and clear credit is given to Alex Albright and The Little Dataset That Could with appropriate and specific direction to the original content.

Words, words, words
##### Intro

While I usually use this blog to work on casual pet projects, I wanted to take an opportunity to use the medium to discuss academic research. Writing is an instinctive mechanism for me to process my thoughts on a topic, but it is one that I use sparingly to discuss the meta-narrative of my own decisions and behavior. The impetus for this self-reflection is the following exciting news: I’ll be pursuing my PhD in economics at Harvard starting this fall! The decision has naturally prompted me to think about my adventures thus far in the academic sphere and the scope of my ambitions and interests.

Think of this as a more organized and open outlet for many of the words (written, spoken, and silently thought) that have bounced around my head throughout the (now 100% finished!) applications process. This post contains a mixture of excerpts from academic personal statements from PhD applications as well as even undergraduate ones (turns out the overwhelming majority of my college application essays involved math in some way, shape, or form).[1] The purpose of this piece is multi-pronged: I’m hoping to (Part I) introduce my interest in economics research on a personal level, (Part II) clearly outline research questions and topics that I have worked on, and (Part III) describe potential eventual research ambitions.[2]

##### Part I: The number friends

A framed piece of legal paper hung in my parents’ room for nearly a dozen years. The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 were etched onto the page. Each held a shade or two of color, leaked from a gifted box of gel pens, within its skinny outline. A speech bubble burst from each number so it could introduce itself or articulate feelings that might be beyond its self-quantification. ‘9’ philosophizes that “it is hard to be odd,” while ‘1’ grumbles over lonesomeness. Atop this paper is the simply written title “The Number Friends.”[3]

Many of my childhood memories are inseparably intertwined with numbers. Learning the exponents of 2 while poking my head into the ice cream freezer at our local deli. Multiplying numbers by wicking my finger against moisture on my grandmother’s 1980 Volvo. Calculating and writing up the winning percentages of baseball teams on the white board in our living room. (It’s an understatement to say that the 2000 subway series was an exciting time in my early life.) To cut to the chase, I was always fond of numbers. My numbers—those I played with as though they were a set of stuffed animals in my living room—hardly resemble those many people groan about—their dusty gray, corporate counterparts.

Despite my interest in the numbers that were stacked on top of each other to fill the standings in the sports section, I grew up ignoring a word that often found itself on adjacent pages of the inky paper— “economics.” The word always seemed to be coming from the lips of men in suits who carried leather briefcases and drank dark, serious coffees. It was a word that I did not associate with anything but Mr. Monopoly—that is, until my senior year of high school when I took an economics class for the first time. Carrying the weightless tools of microeconomics outside of the classroom, I quickly found myself internally modeling the grumpiness of my classmates based on the outside temperature, the day’s schedule type, the quality of their chosen lunch, and the morning delays (or, hopefully, lack thereof) on their regular subway line; explaining my teenage decisions to my parents by implicitly highlighting our very different utility functions; and even debating how one could “optimally” match up students for prom.[4] Imagine my joy in 2012 when Alvin E. Roth won the Economics Nobel for work that redesigned the mechanism for students to select into my exam high school (Stuyvesant High School[5])! The eventual knowledge that groundbreaking work in game theory and market design had implicitly played a role in my presence at that school and, accordingly, in my first foray into economics was incredibly exciting and inspiring. My innate adoration of mathematics and logic combined with my attention to the dynamics of the human world around me molded me into a young economist.[6]

##### Part IIa: Early research exposure

In my undergraduate studies, I eagerly continued formulating arguments and theories using the building blocks of microeconomic theory and began to seek out academic opportunities to explore these interests. In particular, my fondness for behavioral economics was solidified when I earned a job as a Research Assistant to Professor Sarah Jacobsen my junior year and discovered how assumptions of rational choice do not necessarily hold in human decision-making.  In helping evaluate the results of experimental economic studies, I was intrigued by the gap between seemingly concrete theory and the realities of human behavior.[7] I dived deeper into economics research by working on campus at Williams that following summer as a 1957 Research Fellow for Professor Yung Suk Lee, focusing on a project about the expansion of exam schools and opportunities to attain academic achievement. In this role, I used knowledge of exam cutoffs for admission into specialized New York exam schools and compared academic outcomes for students that were at the margin (both above and below cutoffs) to investigate the much-debated impact of these schools on later academic success. As well as exposing me to statistical methodologies such as regression discontinuity design, the summer taught me how to work independently and probe assumptions and logical frameworks at the core of well-respected studies.

##### Part IIb: Wine economics as senior thesis

At the end of my junior year, I was lucky enough to be awarded the Carl Van Duyne Prize in Economics and received funding to pursue a senior honors thesis; this opportunity was the catalyst for the start of my self-directed economics research. My project focused on the intersection of applied econometrics and behavioral economics and examined the dynamic response of prices in the wine market to wine critic reviews. Since consumers have often not experienced a given wine ex ante when considering what to buy, reviews and ratings of quality play a consequential role in shaping consumer and market dynamics. My fascination with this subject was derived from the knowledge that, though ratings measure quality, they also influence consumers independent of their accuracy; for this reason, my curiosity about how researchers could disentangle the concepts of hype and quality grew.

While other economists have studied similar topics, no previous work had defined hype and quality as unobserved concepts. Given the fact that I defined these two dimensions of a product as unobserved, a naive cross-sectional regression would not have sufficed in comparing the respective roles. Therefore, I instead used a panel structural vector autoregression methodology to approach this topic from a new angle. (For more on this method, see Pedroni 2013.) I exploited knowledge of the dynamics of an online wine community (CellarTracker) as well as the behavior of the consumer rating mechanism in order to construct short-run restrictions to identify structural shocks. Therefore, by combining both substantive knowledge of wine and the wine drinking community with statistical techniques, I was able to work on a novel approach to a continuously intriguing problem.

I continue to work with my advisor Professor Peter Pedroni on translating the concepts beyond the scope of wine to broader research pertaining to high-end goods. In fact, I’m going to the American Association of Wine Economists Meeting in Bordeaux to present on this in June![8] In preparing a paper for conference submission, we treat information from expert reviews of high-end goods as a part of a broader signal extraction problem tackled by consumers of such goods. (More to come on this soon…) During June 2015, I presented this ongoing work at the interdisciplinary Connected Life Conference at Oxford University, which fostered collaboration with computer scientists, sociologists, and other researchers.[9]

##### Part IIc: Working at the intersection of law and economics @ Stanford

Since graduating from Williams, I have worked with Professor John Donohue at Stanford Law School as a Research Fellow.[10] In this pre-doctoral role, I work on projects at the intersection of law and economics, with a particular focus on the economics of crime and related econometric and statistical methodologies. For instance, I got to play a large role in developing and reviewing the paper “The Empirical Evaluation of Law: The Dream and the Nightmare” (published in the Journal of American Law and Economics Review).[11] This paper charts the enormous advances in estimating causal effects of laws and policies in the past few decades and points out the frequency of conflicting studies on identical questions. Given the conflicting nature of many studies, it can be hard to know what should be believed and the media, think tanks, and others often exploit this difficulty to promote certain studies for private political or social agendas. Accordingly, in discussing the methodological soundness of various approaches, this article seeks to begin a discussion about how we want to manage the translation between research and media coverage especially when it comes to politically contentious topics.

On a related note, I am currently working on a project that uses a statistical technique called synthetic controls (see Abadie & Gardeazabal 2003 and Abadie, Diamond, & Hainmueller 2009) to look at the impact of right-to-carry laws on crime in the United States. The impact of right-to-carry gun laws on crime has been debated within both the academic community and the public sphere for decades. To address some of the inherent weaknesses of panel data models, we are using the aforementioned synthetic controls methodology, a methodology that generates counterfactual units by creating a weighted combination of similar (in terms of the pre-treatment period) control units. Panel data studies are often extremely sensitive to minor changes in choices of explanatory variables. Therefore, by working on new approaches to these sorts of questions, we seek out methods that generate robust results that have the potential to help guide policy decisions in pivotal areas, where slicing and dicing numbers can be done to fit virtually any policy agenda. The broader impacts of creating robust decision-making processes for analyzing the impact of controversial policies is one of the aspects of economics about which I am most passionate.

##### Part IIIa: Potential research ambitions in economics

During PhD visits, it is common to pitch your interests to professors. At the macro level (and using some slick economics jargon), I am most interested in behavioral economics, and applied microeconomics. Applied microeconomics is a lovably large umbrella term that easily contains both urban economics, and law and economics, and, therefore, the previous sentence adequately articulates both my interest in the effects of psychological/social/cognitive/emotional factors on decision making as well as the application of microeconomic theory to the study of crime, cities, law, and education. (That undoubtedly leaves space for a lot of potential research topics!)

While I have a number of continuing interests, such as the reputational influence of experts in networks as investigated in the wine project (in the behavioral realm), or economics of crime topics at Stanford, I believe one of the ripest and most important areas for economic research is actually a union of behavioral economics with the economics of crime. That is, further investigating how people find themselves participating in crime.

I am often struck by how often individuals, myself included, buy into illusions of choice. It is tempting to view one’s accomplishments as essentially a function of personal social/academic merit. This is especially true among the more privileged among us—those of us who grew up benefitting from the financial success of family members, the color of our skin, and overall, positive reenforcement in most facets of our lives. I became aware of the influence of environmental behavioral factors while observing my own behaviors in a school context. In high school, I was lucky enough to be a beneficiary of overwhelmingly positive forces (driven/ambitious peers and thoughtful/encouraging teachers). The profound influence of positive classrooms like my own can be easily seen in a recent study by Card and Giuliano. The study found that participation by “non-gifted” students in a “gifted” classroom lead to significant achievement gains for the minority students (gains of 0.5 standard deviations in reading/math). Incredibly, the authors did not attribute the gains to teacher quality or peer effects, but to “the effects to a combination of factors like teacher expectations and negative peer pressure that lead high-ability minority students to under-perform in regular classes but are reduced in a GHA classroom environment“!

While education topics are increasingly receiving a behavioral treatment in the literature (due in part to the ability to fashion experiments in classrooms and, potentially, due to the less politically contentious nature of education), the current state of the economics of crime is still deeply entrenched in Beckerian ideas of deterrence–criminals make cost-benefit calculations in their minds and then use these to inform decisions. This type of reasoning (which is not incorrect, as much as it is lacking in dimensions of the human experience) over the past decades has lead to piles and piles of papers trying to separate out the impact of sentence enhancements (seen around the time of the 1990’s crime decline) into an incapacitation effect (people are off the street in prison and thus incapable of committing crimes) and a deterrence effect (people are scared off of committing crimes because of the greater cost). What with our improved notions of behavioral mechanisms and the current well-deserved focus on incarceration levels, policies from the 1990’s (specifically, the 1994 crime bill), and interactions between police and disadvantaged communities, there is no doubt that further studies of the social interactions in crime networks (see the classic Glaeser 1996 paper) as well as environmental factors (think Reyes’ work on lead exposure) are warranted to better inform policy as well as our core human understanding of how peoples’ lives diverge so starkly. Illusions of choice are powerful (as well as enticing to those at the helm of the ship) and are accordingly worth a hefty dose of skepticism from the community at large. (There are many more ideas to develop and papers to cite in these paragraphs, but I’ll let this marinate as it is for the moment.)

On herd behavior in particular: I have no qualms in asserting that I have benefited immensely from herding behaviors that harm others who simply gained consciousness in a different social/economic environment. The same strains of herd behavior, which pulses through networks (those of academics, and those of drug traffickers alike), lead to disparate outcomes based on the starting point and environment in which they occur.

Beyond behavior and crime, some other developing research interests on my eventual topic wishlist include:

##### Part IIIb: Things are about to get meta

On a somewhat meta note, I feel strongly about making economics research and, more generally, research that is data-driven replicable and accessible to the public. I believe that open sourcing datasets and code for projects not only facilitates how different projects can build off of one another but also encourages a more diverse group of individuals to explore quantitative methods.[12] By making work publicly accessible, researchers can challenge themselves to defend their ideas and assertions to any interested individuals, rather than limiting themselves to discussion in academic bubbles. I strongly believe that this renders research dynamics fundamentally more efficient, as public-facing projects allow for a faster and smoother exchange of ideas, which can lead to superior projects in the long-run. This sort of openness on the part of researchers often allows for great collaborations—my wonderful friend/public speaking inspiration Sarah Michael Levine and I originally bonded via Twitter (!) and then ended up writing a paper together on the shortcomings of mainstream data science when applied to social good projects (which we got to present at the Bloomberg Data for Good Exchange 2015). In my personal experience, making work and ideas available to a larger audience has led to a number of incredible opportunities to work with talented people on a range of captivating questions that engage the public and illustrate the fundamental creativity that is inherent to but often ignored in quantitative work.

##### Endnote

In reviewing this writing, I am acutely aware of the fact that I tend to over-narrativize my own experiences, injecting meaning into the twists and turns that may just be segments of a random walk. However, while there might not be some grand meaning in an individual’s path towards the degree that we call a PhD, I do strongly believe in the profound nature of social science research more generally—self-awareness is fundamentally human and our ability to study our own machinations is something that we find irresistible.[13] The letters we desire to have traipse behind our names are trivial in the long run, but the questions we ask in pursuit of them ultimately stem from the core of personhood—consciousness and the curiosity that comes with it.[14][15]

##### Footnotes

[1] Concretely describing motivations, processes, and goals for research is an element of communication in academia that I believe can be much improved by embracing non-traditional/technologically-driven mediums of discussion. So, why not take the time to try and practice communicating with the transparency and openness that I often crave from other researchers? (Warning: this is going to be long! I am working through caches of thoughts that have managed to build themselves into some pretty hefty structures over the years.)

[2] In thinking about that oft-cited 2 x 2 matrix that contains four quadrants dedicated to simple/complex ideas vs. simple/complex writing, the dream is to eventually make it into that slick complex ideas & simple writing quadrant.

[3] Oh, the trials and tribulations of being an only child… (“Some imaginary friends you never outgrow.”)

[4] Think utility maximization problems. If the application of mathematical concepts to questions of romance is interesting to you: check out the marriage problem.

[5] Go Vixens!/Go Phoenix!/Go Renegades! (The last one was a much needed improvement from the softball team’s previous mascot—the Chipmunks.)

[6] In this vein of personal narrative, see also Claudia Goldin’s “The Economist as Detective.”

[7] In technical terms, I ran paired t-test and signed-rank regressions in order to analyze a survey participant’s level of consistency in terms of his or her risk-taking decisions.

[8] Hopefully, I will soon have some slides that can help in communicating the relevant ideas.

[9] Check out the call for papers!

[10] I originally found out about Prof Donohue through reading Freakonomics (a commonly cited catalyst for people’s realization that economics can be clever and creative!) my sophomore year since the abortion and crime chapter is based on one of his articles “The Impact of Legalized Abortion on Crime” with Steven Levitt of UChicago.

[11] I saw the journal that contained this article (and my name typed within it) in the flesh a few weeks ago at Harvard before some meetings. That experience immediately quashed some hefty feelings of impostor syndrome.

[12] Papers, data, and methods should be available to the public rather than only available to those at institutions of higher education…or, even worse only available through asking nicely via email with shiny credentials. (Once, a professor I emailed once for data responded that he was retiring and moving across the country, so he had thrown out all his papers, and, thus, could not help me. I often feel more like an investigative reporter when tracking down data than an academic!)

[13] Research in this context should not be solely interpreted as academic research! In fact, I would argue that every individual conducts casual research in the day-to-day, while the PhD is an example of an institutionalized and formal medium for research.

[14] Listen to this recent episode of Radiolab for the following relevant quote and much more: “Consciousness—for some reason, for some reason one animal on the planet and only one that we can know seems to string into this very elaborate sense of self-awareness—we don’t know how it happened we don’t know why it happened it just did”

[15] Insightful discussions that stem from that very curiosity should not be limited to only those with a PhD. So, social network, let’s talk.

# How I Learned to Stop Worrying and Love Economics

Words, words, words
##### Intro

Many months ago, in October, the Economics Nobel prize was awarded to Angus Deaton. Beyond experiencing sheer joy at having beaten my friend Mike at predicting the winner, I also was overwhelmed by the routine, yearly backlash against the discipline in the form of articles shared widely across any and all social networks. Of particular interest to me this year was the Guardian’s piece “Don’t let the Nobel prize fool you. Economics is not a science.” The dialogue surrounding this article made me incredibly curious to investigate my own thoughts on the discipline and its place in the realm of “the sciences.” In a frenzy of activity that can only be accurately explained as the result of a perfect storm of manic energy and genuine love for an academic topic, I wrote up a response not only to this article, but also to my own sense of insecurity in studying a discipline that is often cut down to size by the public and other academics.

In my aforementioned frenzy of activity, I found myself constantly talking with Mike (in spite of my status as the superior Nobel forecaster) about the definition of science, hierarchies of methodologies for causal inference, the role of mathematics in applied social science, and our own personal experiences with economics. Eventually, I linked the Guardian article to him in order to explain the source of my academic existential probing. As another economics researcher, Mike had a similarly strong reaction to reading the Guardian’s piece and ended up writing his own response as well.

So, I am now (albeit months after the original discussion) using this space to post both responses. I hope you’ll humor some thoughts and reactions from two aspiring economists.

##### Alex responds

I developed a few behavioral ticks in college when asked about my major.  First, I would blurt out “Math” and, after a brief pause of letting the unquestioned legitimacy of that discipline settle in, I would add “and Econ!”–an audible exclamation point in my voice. I had discovered through years of experience that the more enthusiastic you sounded, the less likely someone would take a dig at your field. However, nonetheless, I would always brace myself for cutting criticism as though the proofs I attempted to complete in Advanced Microeconomics were themselves the lynchpin of the financial crisis.

In the court of public opinion, economics is often misunderstood as the get-rich-quick major synonymous with Finance. The basic assumptions of self-interest and rationality that the discipline gives its theoretical actors are stamped onto its practitioners and relabeled as hubris and heartlessness. Very few students are seeking out dreamy economics majors to woo them with illustrations of utility functions in which time spent together is a variable accompanied by a large positive coefficient. (The part where you explain that there is also a squared term with a negative coefficient since the law of diminishing marginal utility still applies is not as adorable. Or so I’ve been told.)

It can be hard to take unadulterated pride in a subject that individuals on all sides of the techie/fuzzy or quant/qual spectrum feel confident to discredit so openly. Economics is an outsider to many different categories of academic study; it is notably more focused on quantitative techniques than are other social sciences but its applications are to human phenomena, which rightfully ousts it from the exclusive playground of the hard sciences. I admit I have often felt awkward or personally slighted when accosted by articles like Joris Luyendijk’s “Don’t let the Nobel prize fool you. Economics is not a science.” which readily demeans contributions to economics simply by both appealing to the unsexiness of technical jargon and by contrasting these with the literature and peace prizes:

Think of how frequently the Nobel prize for literature elevates little-known writers or poets to the global stage, or how the peace prize stirs up a vital global conversation: Naguib Mahfouz’s Nobel introduced Arab literature to a mass audience, while last year’s prize for Kailash Satyarthi and Malala Yousafzai put the right of all children to an education on the agenda. Nobel prizes in economics, meanwhile, go to “contributions to methods of analysing economic time series with time-varying volatility” (2003) or the “analysis of trade patterns and location of economic activity” (2008).

While comparing strides in economic methods to the contributions of peace prize recipients is akin to comparing apples to dragon fruit, Luyendijk does have a point that “[m]any economists seem to have come to think of their field in scientific terms: a body of incrementally growing objective knowledge.” When I first starting playing around with regressions in Stata as a sophomore in college, I was working under the implicit assumption that there was one model I was seeking out. My different attempted specifications were the statistical equivalent of an archeologist’s whisks of ancient dust off of some fascinating series of bones. I assumed the skeleton would eventually peek out from the ground, undisputedly there for all to see. I assumed this was just like how there was one theorem I was trying to prove in graph theory–sure, there were multiple modes of axiomatic transport available to end up there, but we were bound to end up in the same place (unless, of course, I fell asleep in snack bar before I could really get there). I quickly realized that directly transplanting mathematical and statistical notions into the realm of social science can lead to numbers and asterisks denoting statistical significance floating around in zero gravity with nothing to pin them down. Tying the 1’s, 3’s, and **’s  down requires theory and we, as economic actors ourselves who perpetually seek optimal solutions, often entertain the fantasy of a perfectly complex and complete model that could smoothly trace the outline and motions of our dynamic, imperfect society.

However, it is exactly Luyendijk’s point that “human knowledge about humans is fundamentally different from human knowledge about the natural world” that precludes this type of exact clean solution to fundamentally human questions in economics–a fact that has and continues to irk me, if not simply because of the limitations of computational social science, then because of the imperfection and incompleteness of human knowledge (even of our own societies, incentives, and desires) of which it reminds me. Yet, as I have spent more and more time steeped in the world of economics, I have come to confidently argue that the lack of one incredibly complex model that manages to encapsulate “timeless truth[s]” about human dynamics does not mean models or quantitative methods have no place in the social sciences. Professor Dani Rodek, in probably my favorite piece of writing on economics this past year, writes that,

Jorge Luis Borges, the Argentine writer, once wrote a short story – a single paragraph – that is perhaps the best guide to the scientific method. In it, he described a distant land where cartography – the science of making maps – was taken to ridiculous extremes. A map of a province was so detailed that it was the size of an entire city. The map of the empire occupied an entire province.

In time, the cartographers became even more ambitious: they drew a map that was an exact, one-to-one replica of the whole empire. As Borges wryly notes, subsequent generations could find no practical use for such an unwieldy map. So the map was left to rot in the desert, along with the science of geography that it represented.

Borges’s point still eludes many social scientists today: understanding requires simplification. The best way to respond to the complexity of social life is not to devise ever-more elaborate models, but to learn how different causal mechanisms work, one at a time, and then figure out which ones are most relevant in a particular setting.

In this sense, “focusing on complex statistical analyses and modeling” does not have to be to “the detriment of the observation of reality,” as Luyendijk states. Instead, emulating the words of Gary King, theoretical reasons for models can serve as guides to our specifications.

In my mind, economics requires not just the capability to understand economic theory and empirics, but also the humility to avoid mapping out the entire universe of possible economic interactions, floating coefficients, and greek numerals. Studying economics requires the humility to admit that economics itself is not an exact science, but also the understanding that this categorization does not lessen the impact of potential breakthroughs, just maybe the egos of researchers like myself.

via xkcd. WHERE IS ECONOMICS?

##### Mike responds

Economics is an incredibly diverse field, studying topics ranging from how match-fixing works among elite sumo wrestlers to why the gap between developed and developing countries is as large as it is. When considering a topic as broad as whether the field of economics deserves to have a Nobel prize, then, it is important to consider the entire field before casting judgment.

Joris Luyendijk, in his article “Don’t let the Nobel prize fool you. Economics is not a science,” directs most of his criticisms of economics at financial economics specifically instead of addressing the field of economics as a whole. We can even use Mr. Luyendijk’s preferred frame of analysis, Nobel prizes awarded, to see the distinction between finance and economics. Out of the 47 times the economics Nobel has been awarded, it was only given in the field of Financial Economics three times.  And in his article, Mr. Luyendijk only addresses one of these three Nobels. I would argue that since financial economics is but a small part of the entire economics field, even intense criticism of financial economics should not bring the entire economics field down with it.

A closer look at the Nobels awarded in financial economics reveals that the award is not “fostering hubris and leading to disaster” as Mr. Luyendijk claims. The first Nobel awarded in financial economics was presented in 1990, for research on portfolio choice and corporate finance and the creation of the Capital Asset Pricing Model (CAPM). Far from causing financial contagion, to which Mr. Luyendijk hints the economics Nobel prize has contributed, optimal portfolio theory examines how to balance returns and risk, and CAPM provides a foundation for pricing in financial markets. More recently, the 2013 Nobel was again awarded in financial economics, for advances in understanding asset pricing in the short and long term, applications of which include the widely used Case-Shiller Home Price Index.

The second Nobel awarded for financial economics, to Merton and Scholes in 1997, does deserve some criticism, though. However, I would argue that the Black-Scholes asset pricing model gained traction long before the 1997 Nobel Prize, and continues to be used long after the collapse of the hedge fund Merton and Scholes were part of, because of its practical usefulness and not because of any legitimacy the Nobel prize might have endowed it with. The quantification of finance would have happened with or without the Nobel prize, and I find it hard to believe that the existence of the economics Nobel prize causes profit-driven financiers to blindly believe that the Black-Scholes formula is a “timeless truth.”

So if economics is not finance, then what is it? I would argue that an identifying feature of applied economics research is the search for causality. Specifically, much of economics is a search for causality in man-made phenomena. To model human behavior in a tractable way requires making assumptions and simplifications. I have to agree with Mr. Luyendijk that economics needs to be more forthright about those assumptions and limitations – economists may be too eager to take published findings as “timeless truths” without thinking about the inherent limitations of those findings.

Failing to realize the limitations of such findings can come back to bite. For example the Black-Scholes model assumes that securities prices follow a log-normal process, which underestimates the probability of extreme events, such as the ones that led to the collapse of Long-Term Capital Management. But the failure of some to pay attention to well-known limitations of important findings should not diminish economics as a whole.

Applied economics is also distinct from other social sciences in that it attempts to apply the tools of the hard sciences to human problems. I agree with Alex and Mr. Luyendijk that knowledge about the physical and human worlds is inherently different. The heterogeneity of human behavior creates messy models, and these models require the creation of new mathematical and statistical methods to understand them. This “mathematical sophistication” that Mr. Luyendijk bemoans is not just math for math’s sake, it is using tools from the hard sciences to explain real-world phenomena (and what’s wrong with pure math anyways?).

Despite the occasional messy solution, the ideal study in applied economics is still a controlled experiment, as it is in many hard sciences. In the human world, however, this experimental ideal is difficult to implement. Much of applied economics thus relies on quasi-experimental methods, trying to approximate experiments with observational data by finding natural experiments, for example, when controlled experiments are not feasible. Still other branches of economics use actual economic experiments, such as randomized control trials (RCTs). The idea behind economics RCTs is the same as that behind clinical drug trials, where people are randomly separated into treatment and control groups to test the effect of an intervention. RCTs have become increasingly popular, especially in development work, over the past decade or so. Given Mr. Luyendijk’s concern about how divorced from the real world economics has become, he would be impressed by the amount of practical, detailed planning required to successfully implement RCTs, and be taken aback by how different this fieldwork is from the academics spending all day thinking of complex and impractical models that he envisions.

A Nobel prize in economics will probably be awarded for advances in the methodology and applications of RCTs, the closest economics can come to the hard sciences that Mr. Luyendijk so reveres, sometime in the next decade. What will he say then?

##### Endnote

Mike and I were Research Assistants at Williams College together during summer 2013. Mike is currently on a Fulbright in China working with Stanford’s Rural Education Action Program, which conducts RCTs in rural China. We are both happy to hear any feedback on the linked articles and our responses, as we are both genuinely interested in thinking through where economics (and computational social sciences on the whole) should belong in scientific dialogue.

# This Post is Brought to You by the National Science Foundation

##### Intro

I have officially finished applying for my PhD. While the application process included many of the same elements that I had previously encountered as a fresh-faced* 17-year-old (think standardized testing without the #2 pencils and lots more button clicking), I am no longer applying as a (relatively) blank slate–a future liberal arts student who will float and skip between disciplines until being neatly slotted into a major. Instead, we PhD applicants have already zeroed in on a particular area of study–in my case, economics. Consequently, each PhD discipline is unlikely to exhibit the same carefully crafted demographics boasted in the pie charts that plaster undergraduate brochures across the country to provide tangible evidence for optimistic, bolded statements about diversity. In formulating responses to a slew of university-specific prompts about diversity in “the sciences,” I grew curiouser and curiouser about two particular questions: What do demographic compositions look like across various PhD disciplines in the sciences? & Have demographic snapshots changed meaningfully over time?

As I continued working to imbue a sense of [academic] self into pdfs composed of tightly structured Times New Roman 12 point font, I repeatedly found myself at the NSF open data portal, seeking to answer these aforementioned questions. However, I would then remind myself that, despite my organic urge to load rows and columns into R Studio, I should be the responsible adult (who I know I can be) and finish my applications before running out to recess. Now that the last of the fateful buttons have been clicked (and a sizable portion of my disposable income has been devoured by application fees and the testing industrial complex), I’m outside and ready to talk science!**

##### NSF data and sizes of “the sciences”

In this post, I am focusing on the demographics of science PhD degrees awarded as they pertain to citizenship and race/ethnicity, but not gender. In an ideal world, I would be able to discuss the compositions of PhD fields as broken into race/ethnicity-gender combinations, however, the table that includes these types of combinations for US citizens and permanent residents (Table 7-7) only provides the numbers for the broader categories rather than for the desired discipline-level. For instance, social science numbers are provided for 2002-2012 without specific numbers for economics, anthropology, etc. This approach, therefore, would not allow for an investigation into the main topic of interest, which is the demographic differences between the distinct disciplines–there is too much variety within the larger umbrella categories to discuss the fields’ compositions in this way. Therefore, I limit this discussion to demographics with respect to citizenship and race/ethnicity and, accordingly, use Table 7-4 “Doctoral degrees awarded, by citizenship, field, and race or ethnicity: 2002–12” from the NSF Report on Women, Minorities, and Persons with Disabilities in Science and Engineering*** as my data source.

Before getting into the different PhD science fields and their demographics, it’s worth noting the relative sizes of these disciplines. The following treemap depicts the relative sizes of the sciences as defined by NSF data on doctoral degrees awarded in 2012:

The size of each squarified rectangle represents the number of degrees awarded within a given field while the color denotes the field’s parent category, as defined by the NSF. (Note that some studies are, in fact, their own parent categories. This is the case for Biological Sciences, Psychology, Computer Sciences, and Agricultural Sciences.) In the upcoming discussion of demographics, we will first discuss raw numbers of degrees earned and the relevant demographic components but will then pivot towards a discussion of percentages, at which point remembering the differences in size will be particularly helpful in piecing together the information into one cohesive idea of the demographics of “the sciences.”****

##### A decade of demographic snapshots: PhD’s in the sciences

The NSF data specifies two levels of information about the doctoral degrees awarded. The first level identifies the number of degree recipients who are US citizens or permanent residents as well as the number who are temporary residents. Though “[t]emporary [r]esident includes all ethnic and racial groups,” the former category is further broken down into the following subgroups: American Indian or Alaska Native, Asian or Pacific Islander, Black, Hispanic, Other or unknown, and White. In our first exploration of the data, we specify the raw number of degrees awarded to individuals in the specific ethnic and racial categories for US citizens and permanent residents as well as the number awarded to temporary residents. In particular, we start the investigation with the following series of stacked area charts (using flexible y-axes given the vastly different sizes of the disciplines):

In this context and for all following visualizations, the red denotes temporary residents while all other colors (the shades of blue-green and black) are ethnic and racial subsets of the US citizens and permanent residents. By illustrating the raw numbers, this chart allow us to compare the growth of certain PhD’s as well as seeing the distinct demographic breakdowns. While overall the number of science PhD’s increased by 39% from 2002 to 2012, Astronomy, Computer Science, Atmospheric sciences, and Mathematics and statistics PhD’s clearly outpaced other PhD growth rates with increases of 143%, 125% 84%, and 80%, respectively. Meanwhile, the number of Psychology PhD’s actually decreased from 2002 to 2012  by 8%. While this was the only science PhD to experience a decline over the relevant 10-year period, a number of other disciplines grew at modest rates. For instance, the number of Anthropology, Sociology, and Agricultural Sciences PhD’s experienced increases of 15%, 16%, and 18% between 2002 and 2012, which pale in comparison to the vast increases seen in Astronomy, Computer Science, Atmospheric sciences, and Mathematics and statistics.

While it is tempting to use this chart to delve into the demographics of the different fields of study, the use of raw numbers renders a comprehensive comparison of the relative sizes of groups tricky. For this reason, we shift over to visualizations using percentages to best get into the meat of the discussion–this also eliminates the need for different y-axes. In presenting the percentage demographic breakdowns, I supply three different visualizations: a series of stacked area graphs, a series of nightingale graphs (essentially, polar stacked bar charts), and a series of straightforward line graphs, which despite being the least exciting/novel are unambiguous in their interpretation:

One of my main interests in these graphs is the prominence of temporary residents in various disciplines. In fact, it turns out that Economics is actually quite exceptional in terms of its percentage of temporary residents, which lingers around 60% for the decade at hand and is at 58% for 2012. (In 2012, out of the remaining 42% that are US citizens or permanent residents, 70% are white, 11% are asian or pacific islander, 3% are black, 3% are hispanic, 0% are american indian or alaskan native, and 13% are other or unknown.) Economics stands with Computer science, Mathematics and statistics, and Physics as one of the four subjects in the sciences for which temporary residents made up a higher percentage of the PhD population than white US citizens or permanent residents consistently from 2002 to 2012. Furthermore, Economics is also the science PhD with the lowest percentage of white US citizens and permanent residents–that is, a mere 30%.  In this sense, the field stands out as wildly different in these graphs from its social science friends (or, more accurately, frenemies). On another note, it is also not hard to immediately notice that Psychology, which is not a social science in the NSF’s categorization, is so white that its nightingale graph looks like an eye with an immensely overly dilated pupil (though anthropology is not far behind on the dilated pupil front).

Also readily noticeable is the thickness of the blue hues in the case of Area and ethnic studies–an observation that renders it undeniable that this subject is the science PhD with the highest percentage of non-white US citizens and permanent residents. Following this discipline would be the other social sciences Anthropology, Sociology, and Political science and public administration, as well as the separately categorized Psychology. However, it is worth noting that the ambiguity of the temporary residents’ racial and ethnic attributes leaves much of our understanding of the prominence of various groups unclear.

Another focal point of this investigation pertains to the time dimension of these visuals. When homing in on the temporal aspect of these demographic snapshots, there is a discouraging pattern–a lack of much obvious change. This is especially highlighted by the nightingale graphs since the polar coordinates allow the 2012 percentages to loop back next to the 2002 percentages and, thus, facilitate for a simple start-to-end comparison. In most cases, the two points in time look incredibly similar. Of course, this does not necessarily mean there has been no meaningful change. For instance, there have been declines in the percentage of white US citizens and permanent residents in the subjects Area and ethnic studies, Psychology, Sociology, Anthropology, and Political science and public administration, which have then been offset by increases in other groups of individuals. However, the picture is incredibly stagnant for most of the disciplines, especially the hard sciences and the unusually quantitative social science of economics. In pairing the stagnant nature of these demographic snapshots with consistent calls for greater faculty diversity in the wake of campus protests, it is clear that there is a potential bottleneck since such lagging diversity in PhD disciplines can directly contribute to a lack of diversity at the faculty-level.

##### Endnote

When the public discusses the demographics and diversity of “the sciences,” 1.5 dozen disciplines are being improperly blended together into generalized statements. To better understand the relevant dynamics, individuals should zero in on the discipline-level rather than refer to larger umbrella categories. As it turns out according to our investigation, the demographic breakdowns of these distinct subjects are as fundamentally different as their academic methodologies–methodologies which can be illustrated by the following joke that I can only assume is based on a true story:

As a psychological experiment, an engineer, a chemist, and a theoretical economist are each locked in separate rooms and told they won’t be released until they paint their entire room. They are each given a can of blue paint which holds about half the paint necessary to paint the room and then left alone. A few hours later the psychologist checks up on the three subjects.

(1) The engineer’s walls are completely bare. The engineer explains that he had worked out that there wasn’t enough paint to cover all the walls so he saw no point in starting.

(2) The chemist’s room is painted in faded, streaky blue. “There wasn’t enough paint, so I diluted it,” she explains.

(3) In the economist’s room, the floor and the ceiling are completely blue, and there’s a full can of paint still sitting on the floor. The experimenter is shocked and asks how the economists managed to paint everything. The economist explains, “Oh, I just painted the rational points.”

And with an unwavering appreciation for that bit, I hope to be one of the ~20-30 (who knows?) % of white US citizens/permanent residents in the economics PhD cohort of 2021.

PS-Happy 2016 everyone!

##### Footnotes

* I had yet to take a driving test at a DMV. I did this successfully at age 21. But, I will not drive your car.

** The NSF divides subjects up into S&E (science and engineering) and non-S&E categories. In this context, I am only discussing the subjects that fall under the umbrella of science. It would be simple to extend the approach and concept to the provided numbers for engineering.

*** This table explains that the exact source for this information is: National Science Foundation, National Center for Science and Engineering Statistics, special tabulations of U.S. Department of Education, National Center for Education Statistics, Integrated Postsecondary Education Data System, Completions Survey, 2002–12.

**** In particular, the tiny size of the group of History of Science PhD’s allows for much more variability year-to-year in terms of demographics. Only 19-34 degrees were given out on an annual basis from 2002-2012. In this case, size of the program is responsible for the wildly evident changes in demographic composition.

##### Code

Data and R scripts necessary to replicate visualizations are now up on my github! See the NSF_Demographics repo. Let me know if you have any questions or issues with the R script in particular.

##### Further directions for work
• Create gif of treemap using years 2002-2012 to replace the static version for just 2012
• Or use a slider via some D3 magic
• Follow-up by comparing the gender compositions
• Look into the development and change history of the US Office of Management and Budget for racial and ethnic categories
• Just curious as to the timeline of changes and how categorization changes affect our available data