Thursday, August 27, 2009

The Power of Mankiw

This week is Picture Week on This Young Economist. Every post tells a story, and every story begins with a picture.

Here is a partial screenshot from my Google Analytics account:

This graph displays the number of pageviews of my Mankiw versus Krugman poll for each day for the month after Greg Mankiw linked to it.

The graphic tells two stories:

1. Links from popular blogs (Greg Mankiw's blog, Marginal Revolution, and Paul Krugman's blog) bring in a lot of visitors. As the graphic demonstrates, one link from Mankiw's blog brought approximately 7,500 pageviews to my little corner of the blog-o-sphere in one month. For a blog as small as mine, that's huge. I am grateful for the additional exposure.

2. On a more economic/mathematical note, the shape of the distribution of visits is interesting. For the first couple of days, the number of new pageviews declined (but slowly). After about day three, the number of pageviews declined more rapidly. The result is what looks like the right hand side of a bell curve (but a little fatter in the middle, or platykurtic for you math nerds).

To me, the graph looks like one of my favorite statistical distributions, the Weibull distribution, which according to Wikipedia:

[... was] named after Waloddi Weibull who described it in detail in 1951, although it was first identified by Fréchet (1927) and first applied by Rosin & Rammler (1933) to describe the size distribution of particles.

This is interesting because one common application of Weibull distributions is in "survival analysis," or to put it more bluntly, the statistical analysis of how long it takes for something to die. Usually, people use Weibulls to ask how long one can really expect that lightbulb to last, or in a more econometric setting, how long someone's unemployment will last.

The case of Mankiw versus Krugman similarly asks how long it takes for something to die. In this case, that something is interest in a jousting match between Mankiw and Krugman. Based on the graph, it took longer than a week for collective interest in the topic to die, which is great given that my poll only lasted a week.

More generally, I expect the distribution of pageviews for posts on popular topics to look similar to the Mankiw post on my blog. That is, there's a period of discovery, but after most people have read the post, new pageviews decline rapidly.

Here's a question to ponder/discuss:

If I wrote a more timeless post, such as some great tips for aspiring economists, or an excellent piece on how to write well, how would the distribution of visits/pageviews be different?