The Promising Future of Mathematical Sociology

I strongly believe sociology, especially mathematical sociology, has an extremely promising future. The current trends in information technology clearly indicate a growth in quantitative modeling. Among other things, we are currently witnessing a tsunami of data from a globally-connected world (in fact, big data is the techno-geek buzzword), exponentially faster computing power (Markov Chain Monte Carlo simulations of complex models are now increasingly commonplace), and a rapid uptick in the volume and range of high-quality statistical programs (a great deal of which are open-source).

However, why would I think quantitatively-oriented sociologists are especially well-placed to gain from these structural developments?

The primary reason is that the underlying epistemology of modern quantitative sociology — grounded in complex predictive models, relational and nested data structures, and a folk-Bayesian approach to research design — represents the cutting edge and future direction of modeling in a shockingly vast array of fields. For example, multidimensional scaling, social network analysis, log-linear modeling, and finite mixture models (i.e., latent class analysis) are now at the forefront of disciplines ranging from machine learning to computational genetics (for example, see here, here, here, and here). However, most promising is the growing popularity of Bayesian multilevel models, which sociologists have in effect been using for several decades now. For instance, Bayesian multilevel models are now used by physicists to measure the mysterious properties of dark energy, geneticists to unlock the basic patterns of genomic population differentiation, and neuroscientists to describe the deepest structures of the brain. It is no exaggeration to claim that a human-level form of artificial intelligence, if it is ever developed, will probably be based on multilevel models of the type currently familiar to most quantitatively-oriented sociologists.

A secondary reason why the future looks so promising for mathematical sociology is that a vacuum has been created in the social sciences due to the rise of an alternative approach to quantitative modeling, frequently promoted by mainstream economists. According to this approach, the main goal of quantitative research is to estimate population-averaged causal effects, either by setting up a randomized (controlled) experiment or applying a small suite of techniques to observational data, such as instrumental variables regression, so-called “fixed” effects (rather than “random” effects) regression, difference-in-differences design, and so forth.

This approach is appealing because it promises the extraction of causal estimates with minimal theoretical insight, but it comes at enormous costs. For example, the assumptions of causality are rarely, if ever, satisfied for any particular model fit to observational data (as painfully but clearly outlined by the counterfactual model of causality, and evinced by the growing ranks of not-really-exogenous-but-we’ll-use-it-anyway instrumental variables). Furthermore, although it’s well-known randomized experiments are inferior to controlled experiments, the latter require strong theory that is often absent (and even then experiments in the social sciences often lack generalizability to other populations). Finally, an enormous amount of substantively-rich information is usually discarded when observational data are used primarily  for extracting causal estimates, so if we don’t believe our causal estimates then we’re left with a rather meager description of the data at hand (the worst offender is the so-called “fixed” effects technique, which can be viewed as a special case of a Bayesian multilevel model in which the groups are assumed, rather unreasonably, to have infinite variance between them).

Of course, both economics and sociology are large fields, encompassing a wide range of viewpoints, so I caution that my comments embody ideal types. Yet the dominant trends of a globally-networked world, combined with the rise of a distinctive approach to quantitative modeling popularized by economists, has created the conditions for a promising future for sociology more generally, and mathematical sociology in particular.

Devaluing the Feminine + Econ 101

…talk therapy is often considered a “junk discipline” and is very badly-paid in part because it comes from the “feminine” domain of relationship management and emotional management.

I hear this sort of argument quite a lot and I think it has some truth to it, but also misses something.

Many sociologists have already digested a lot of economics, they might want to skip this post.  Let’s assume, for the sake of the argument, that the disproportionate number of talk therapists who are women, or the perceived femininity of the practice, causes talk therapy to be viewed as low-status.  Will this also cause it to be paid more poorly?  In a supply and demand framework, the reason for thinking a low-status occupation will earn less money is the demand side.  Fewer customers are willing to pay as much money for it as they would be willing to pay in a world where talk therapy was not perceived as feminine.  But don’t forget the supply-side.

It seems reasonable to assume that because talk therapy is considered feminine, fewer men are willing or able to go into the field.  This is a restriction on the supply, which means that talk therapists face less competition which means they can charge higher prices and still keep their customers.  So does the perceived femininity of talk therapy cause talk therapists wages to be lower?

This basic economic analysis is silent on whether the reduction in demand will affect wages more or less than the reduction in supply.  At this point, I’d put my theory aside for a while and start thinking about how to collect empirical evidence.  Theory is less ambiguous on something else though, if femininity depresses both supply and demand then we can be sure the overall size of the market, the amount of people getting talk therapy, will be smaller.

Keep in mind that there are a lot of reasons labor markets aren’t perfectly competitive so the analysis above can be made more realistic by considering that it takes time for supply and demand to equilibrate, and that norms and especially governments, can stop supply and demand from adjusting.

Though I’m questioning whether the low-status of an occupation causes it to be low-paid, there is a much more straight-forward way in which women were historically forced to accept low wages.  Social norms meant that women were only allowed certain occupations… if they weren’t low-wage already, they became low-wage because there was a large supply of women who couldn’t work in other jobs and therefore had reduced bargaining power.

Picking on our disciplinary rivals

Jeremy Freese notes:

In a case in which the other shoe took a very long time to drop, Marc Hauser, the Harvard psychology professor renowned for his work on moral judgment, apparently has resigned after a protracted dispute regarding “scientific misconduct” that included retraction or post-publication-revision of three papers because of data problems.

Q: Is any schadenfreude sweeter for the mainstream sociologist than evolutionary psychology schadenfreude? (A: Economist schadenfreude. But just barely.)

Well Jeremy, check out Andrew Gelman’s hard questions for pop-economics:

I think I’m starting to resolve a puzzle that’s been bugging me for awhile.

Pop economists (or, at least, pop micro-economists) are often making one of two arguments:

1. People are rational and respond to incentives. Behavior that looks irrational is actually completely rational once you think like an economist.

2. People are irrational and they need economists, with their open minds, to show them how to be rational and efficient.

I understand why Gelman finds these types of arguments somewhat contradictory, but its possible they can each be true in different cases. After noting the tension between the two, what needs to be done is to identify a representative sample of such cases and see in what share of the cases the analysis is correct. Admittedly this isn’t an easy task, but it doesn’t seem to me much of substance has been shown based on Gelman’s observations (interesting though they may be).

Krugman on Useful Macroeconomic Models

Brad Delong reposts an essay by Paul Krugman, which I believe was written before the crisis.  In this short piece, Krugman attempts to summarize useful macroeconomic models and laments that they have fallen out of fashion.

If you are interested primarily in modeling outside of economics, this Krugman is more useful, but both are definitely worthwhile.

The Credibility Revolution in Econometrics

Angrist and Pischke are on a tear.  They’re bringing econometrics to the masses with their new book, and the editors of the Journal of Economic Perspectives have seen fit to publish a debate around their article assessing the state of econometrics.  A&P claim, and I more or less agree, that microeconometrics has undergone an inspiring “credibility revolution.”

The best summary I’ve found of their article is by Austin Frakt, here.  Arnold Kling comments here.  Andrew Gelman reviewed their textbook positively and constructively here.

Angrist’s website gave ungated links to most of the comments on his paper:

Michael Keane, Edward Leamer, Aviv Nevo and Michael Whinston, Christopher Sims, and James Stock

Added 6/3:

Austin Frakt reviews the Mostly Harmless Econometrics.

Mostly Harmless Econometrics has a blog!

Just Give Them the Money

In the 1950’s and 1960’s, a Michigan town used urban renewal projects to destroy black neighborhoods.  Today, they are compensating some surviving victims by building them affordable housing. Though it is obviously coming too late, this may seem the most fitting and just response.  Unfortunately, it isn’t the best way to help people.

Michigan doesn’t need to build new low-income housing, they don’t have enough people for the housing they’ve got which results in it falling into disrepair.  A major reason the economy is so messed up is that we, as a society, invested too much of our scarce resources in housing.  This just exacerbates it.

What they should have done, is taken the money they used to build housing and just give it to the people they were trying to help.  They’ll spend it more wisely than we would on their behalf.  For insight into how, and why, government has historically liked to control aid to the poor, I recommend Viviana Zelizer.  The work I’m most familiar with is The Social Meaning of Money but it could be that some of her other work is even more relevant.

Biased in favor of your null hypothesis

Another great post on orgtheory.  I think the takeaway is that when it is really hard to prove something conclusively people fall back on their personal and disciplinary biases.  Rafe Stolzenberg has more than once reminded me how economists’ strong theory is a double-edged sword.  Economists need to be reminded that even if the data you’re currently analyzing can’t reject every possible rational choice model doesn’t mean you shouldn’t take alternative models seriously.  In fact, placing such a heavy burden of proof on alternative models seems quite irrational to me.

In hindsight, how would you have prevented the financial crisis?

Arnold Kling was asked:

With regard to the recent financial crisis and current economic recession – if you were given the power to go back in time and change only one thing in an effort to prevent the crisis and recession, what year would you choose, and what one thing would you change?

He answers here. You also might want to check out his new book with Nick Schulz called Poverty to Prosperity: intanigible Assets, Hidden Liabilities and The Lasting Triumph over Scarcity.  Much of it consists of interviews with highly noted economists.  I’ve only had the chance to read a few chapters so far but I’ll definitely look at it again when I have a little more time.

Sethi on Insights from Ecology

Economist Rajiv Sethi has a great blog.  In this post, Sethi, and Thoma, whom he quotes, seem to acknowledge that the financial crisis should lead them to consider new ideas for economic models.  Later on in the post, Sethi points out that behavioral economics has mined psychology for insights, but that economists would do well to look beyond the level of the individual:

If one is to look beyond economics for metaphors and models, why stop at psychology? For financial market behavior, a more appropriate discipline might be evolutionary ecology. This is not a new idea. Consider, for instance, this recent article in Nature. Or take a look at the chapter on “The Ecology of Markets” in Victor Niederhoffer’s extraordinary memoir. Or study Hyman Minsky’s financial instability hypothesis (discussed at some length in an earlier post), which depends explicitly on the assumption that aggressive financial practices are rapidly replicated during periods of stable growth, eventually becoming so widespread that systemic stability is put at risk. To my mind this reflects an ecological rather than psychological understanding of financial market behavior.

Reading people like Sethi, I’m confident economics will come around.  Sociologists have never overemphasized rational actors, but we too can learn from approaches in other disciplines like ecology.

What Protestant Ethic?

Davide Cantoni of Harvard Economics offers this job market paper:

The Economic Effects of the Protestant Reformation: Testing the Weber Hypothesis in the German Lands [pdf]

Many theories, most famously Max Weber’s essay on the ‘Protestant ethic,’ have hypothesized that Protestantism should have favored economic development. With their considerable religious heterogeneity and stability of denominational affiliations until the 19th century, the German Lands of the Holy Roman Empire present an ideal testing ground for this hypothesis. Using population figures in a dataset comprising 276 cities in the years 1300-1900, I find no effects of Protestantism on economic growth. The finding is robust to the inclusion of a variety of controls, and does not appear to depend on data selection or small sample size. In addition, Protestantism has no effect when interacted with other likely determinants of economic development. I also analyze the endogeneity of religious choice; instrumental variables estimates of the effects of Protestantism are similar to the OLS results.

Hat Tip to Tyler Cowen.