While many students will not have had differential equations, the intuition of the math should be accessible to most undergraduates.
This study is a great tool for teaching about multivariate regression in general and fixed effects in particular. Students will quickly recognize the difficulty in finding good data to answer this question. If you examine the correlation between internet speed and income you will undoubtedly find a positive correlation, but how can you possibly interpret this as a causal effect? Shouldn't we expect to find that high-income people opt for nicer things of all types...including internet service? That logic suggests a good part of this correlation is due to reverse causality with higher income leading to better internet speed.
The Analysis Group folks aren't foolish and so they don't simply look at the cross-sectional correlation. Instead, they create a panel of data which records internet service and GDP values for 2011 and 2012. They then run a regression with city and time fixed effects. For those of you not familiar with the terminology of "fixed effects models," this is just shorthand for saying that they included categorical dummy variables to capture city-specific and time-specific effects. The city-specific dummy variables effectively control for all of the factors about a city which are constant across time. What this means is that the fixed effects model looks only at the correlation between the change in high speed access and the change in GDP per capita. In other words, the analysis focuses entirely on cities which changed internet service status between 2011 and 2012 to see whether income growth in these cities differs from the economic experience of all other cities. The authors get it exactly right when they summarize their work: "We found that in [metro areas] where gigabit broadband service was introduced between 2011 and 2012, GDP per capita levels were significantly higher." The effect size was 1.1 percent with a standard error of 0.7 percent.
From a conceptual view, this sounds great. If economic growth is particularly strong in cities in the year(s) following an advance in internet service that would be stronger evidence than a mere correlation between the two variables. (Of course, we could still critique this approach. If you anticipated increased economic activity wouldn't that increase your willingness to invest in internet service? Isn't this forecasting exactly what we hope and expect firms and municipalities to be doing? If this is what is going on, then the fact that an advance in internet service precedes exceptional GDP growth should be of little surprise and hardly evidence for the benefits of computing technology.)
But from a practical view, the fixed effects approach is often problematic because it ends up resting the entire argument on a few, very odd cases. In this particular instance, Analysis Group reports that only 14 of 55 municipalities in their sample were in the high-speed group. They don't say whether this was in 2011 or 2012 and so I will assume it is the latter. But the really important question is: How many of those 14 were not high-speed in 2011? How many changed their internet service status? Given that they don't report how many areas were switched from slow to fast service, we can only guess. It seems reasonable to guess the number is less than 5. That means your entire argument rests on the experience of a small number of (by construction) highly unusual cities.
Is that really better than working from the admittedly biased results based on a cross-sectional analysis? I'd love to engage advanced students in debating this question as a means to a deeper appreciation of the power and limitations of fixed effects models.
I am preparing to lead an off campus study program this summer to study (among other things) the Industrial Revolution. (Note: I'll be posting less frequently over the next few months as a result.) In course prep I came across a great sentence. Joel Moykr (p. 21) is in the middle of an argument that what explains the Industrial Revolution is an Industrial Enlightenment. He argues that the great inventions of the annus miribalis (1769) are viewed that way only because of what happened next. After all, the history prior to the Industrial Revolution is replete with inventions which produced one-time increases in living standards without initiating persistent growth.
So, what is different about the late 18th century in Britain (and, to a great degree, Northern Europe)? In addition to favorable institutional changes which supported the rule of law, Moykr argues for an Industrial Enlightenment that valued the systematized sharing of scientific knowledge for the purpose of material improvement. This stands in contrast with earlier Aristotelian goals of mere understanding. He writes, "[T]he methods of scientific endeavor spilled over into the technological sphere: the concepts of measurement, quantification and accuracy, which had never been an important part of the study of nature, gradually increased in importance. The noted historian of science Alexandre Koyre (1968) argued that the scientific revolution implied a move from a world of 'more or less' to one of measurement and precision."
For me, that's the real crux of QR education. We are waging a war for progress based on the appreciation for the power that quantitative evidence lends to the cause of human advancement. It really does matter "what the numbers show"–not just in some narrow sense, but in a deep, philosophical way that entirely alters the way we live and approach problems. In essence, Moykr is arguing that the QR state of mind is at the center of why, after millenia of more or less stagnant living standards, we have arrived at an expectation of growth.
Recent proposals have suggested radical changes–elimination of mail service on Saturday's and/or Tuesdays. But interestingly, a more traditional solution may be more likely to work today than in the past: postage rate increases. While the regularity and annoyance of postage increases leads many to believe that stamps have seen a dramatic increase in price, in fact the price has more or less tracked inflation over the last 40 years. It may be reasonable to expect to pay more in inflation-adjusted terms given that the lost economies of scale. Estimates of the elasticity of demand–the percent change in quantity due to a one-percent change in price–suggest that the Post Office dales will fall 0.35% for each 1% increase in price. That means revenues will increase 0.65% for a 1% increase in prices.
What's more, this figure has dropped in recent years; we are getting less price sensitive in our mail demand. That makes sense if we suppose that those items which we still send through the mail are harder to replace with online alternatives.
To be sure, postage increases can't entirely fix the Postal Service's financial problems. Their deficit has been on the order of $5 to $15 billion on $66 billion of revenue. But a 10% increase in postage rates might raise over $4 billion.
Stuck on a plane, I found some interesting light reading in this month'sDelta Sky magazine. An article by Nancy Gohring entitled, "The Future of Intelligent Lighting" describes how new streetlights might be made "smarter" to improve city services while reducing costs. (The article also notes the ACLU's concerns about how these lights will be used–a fair point.) What caught my eye was a nice bit of "peripheral QR"–the use of quantitative evidence to enrich description. Specifically, I learned that the new LED lights will use about 15% as much electricity and last almost 20 times as long. The savings are made potentially large by the scope of the North American streetlight system which employs 1 billion lamps currently. (That's a great Fermi problem for those looking to give their students a little experience forming estimates!) Enlightening!