Correlation and The Skyscraper Theory

I was recently inspired by a Planet Money podcast that discussed the Skyscraper Bubble Theory (full podcast and transcript here). In short, the theory posits that there is a correlation between the number of skyscrapers that are built and the bursting of economic bubbles. Several factors encourage the building of skyscrapers: an increased demand for office spaces and low interest rates. Both of these are strongest right before a bubble bursts, and thus herald the onset of an economic depression.

I thought I would go ahead and graph the data myself to see if my analysis would support the hypothesis. A simple correlation graph shouldn't take too long, and it would be interesting to examine the results myself, since plenty of articles cited the theory, though few provided actual graphical evidence for it. The first dataset that I explored described tall building completion rates over time. If we look at the number of buildings completed per year that measure more than 200m, we are presented with this graph, courtesy of The Skyscraper Center:

Apologies for the dual y axis. We are presented with the first problem in analyzing this dataset: completing a skyscraper is a multi-year process, with the average time taken to complete a skyscraper ranging from 2 to 5 years. So does the theory posit that skyscrapers would start being built during a boom, or finish being built right before a boom? Either way, given that the periods of time between bubbles bursting could be less than a decade, this makes it harder to draw any definite conclusions.

If we look at the grey bars that represent the number of skyscrapers that were completed in each of these years, we also see that there is a strong increasing trend. As time goes on, additional tall buildings are being built. If we wish to see whether additional skyscrapers are built before economic depressions, we would need to identify a divergence from the average number of skyscrapers that are built over the course of a decade. This makes our analysis significantly more difficult, as we are attempting to find cycles within an increasing time series. Given our limited dataset, this is a difficult task.

I poked around some more to see if I could find visual representations of data that supported the Skyscraper hypothesis. One of the most convincing graphs that I found was this one:

Plot by Eric Ross, full blog article available here. This graph illustrates 'super-tall buildings' (not just the tallest ever built), as well as economic crashes. However, we can clearly see some inconsistencies. First, the selection criteria is unclear. As the first chart showed us, dozens of buildings greater than 200 m have been built between 2000 and the present day. Is the graph only showing the top 3 or so tallest buildings? Secondly, GDP and building height over time are both increasing time series -- which means of course that are data sets are not independent and identically distributed, and we cannot look at simple correlation (for a great dicussion of this with some excellent visualizations, check out this article).

In short, it's possible that there is a correlation between the two, but we cannot find it by simply drawing a line of correlation between the two unprocessed time series. We'd have to use some more complex model than a simple linear regression, such as vector autoregression, which Mizrach and Mundra undertook, and did not find changes in height predicted changes in GDP, though GDP did seem to predict changes in height (check out the full article here).