Guest Post by Michael Cain
Back in this post the subject of states that are net federal tax donors and tax recipients came up in the comments. D. C. Sessions pointed at the Wikipedia article  on the topic and James Hanley made a remark about how it would be nice if I turned the data into a map. I do crank out cartograms from time to time, but the tax donor thing has always been hard. Nevertheless, I decided to take another crack at it. I think the results are mixed, at best, but you can make your own decision about that.
For those not familiar with the concept, cartograms are maps where the usual divisions have been resized to reflect something other than physical area. It’s almost always a good idea to include a “flat” map  with the same divisions when presenting cartograms – even when it’s a well-known map, people often have a poor recollection of the detailed proportions. Hanley’s post included a non-contiguous cartogram illustrating the portion of each state owned by the federal government that incorporates a flat map directly. I’ve included a flat reference map here.
I prefer to use contiguous cartograms when I can. There are tools for generating cartograms like the open-source ScapeToad and assorted plug-ins for commercial map packages like ArcGIS. I was never happy with those; instead, over the last few years I’ve accumulated some useful open-source components and written a bunch of Perl code to paste them together so that I can generate cartograms fairly easily. I think my own version of the federal land-holding statistic done as a contiguous cartogram where the size of each state reflects the absolute size of the federal land holdings is a more impressive illustration of the point .
On to the tax donor cartogram, then. The cartogram uses both area and color to represent the relevant data (2013 revenues and expenditures from the Wikipedia page). The size of each state represents its population and the color represents the per capita “tax donor” status. Shades of green indicate states that generate more federal tax revenue than they receive in expenditures; shades of red the opposite. Darker shades indicate higher values. Maryland’s expenditures are larger than its taxes, but not by a lot per capita. Michigan pays more taxes than the federal expenditures in the state, but again not by much. Delaware and North Dakota are the two extremes. The color scales are non-linear in order to make distinctions clearer.
Let me make a few “regional” observations. The Southeast portion of the country is a net tax recipient, and is the only region that is clearly a recipient. The states west of the Mississippi are overwhelmingly net tax donors, much to the surprise (I expect) of easterners. Conventional wisdom is probably that the three Pacific Coast states are tax donors; more surprising is that the states west of the Mississippi form a tax donor region even when the Pacific Coast is excluded. The western states with large federal land holdings (the yellow states in the first cartogram) are net tax donors as a group; this is true even when California is excluded. (If it’s not obvious, I’m a westerner and biased.)
Tax donor status is a complicated thing. The Wikipedia article notes that the numbers do not include interest on the national debt or Department of Defense spending, since those are deemed to be spending related to the country as a whole rather than individual states or residents thereof. One of the things that should jump out at the reader is that overall the green seems to dominate the red. Aren’t we running deficits? Yes, but once DoD and interest are subtracted out, the remaining expenditures are smaller than the tax revenue. Even where expenditures can be accurately attributed to a specific state, there can be problems. New Mexico is the site for the Waste Isolation Pilot Plant, where nuclear wastes associated with weapons production – a DoE function, not DoD – are stored. New Mexico is in the process of trying to collect a $54M fine from the DoE for violating operational safeguards at WIPP. Should that fine count as expenditures “for” New Mexico? Or perhaps, should it count as expenditures “for” all of the states that don’t have to host WIPP?
People who are interested in more examples of continuous cartograms should visit the WorldMapper project’s site. They maintain a large collection of cartograms based on the countries of the world. They have an actual budget, and minionsgraduate students to do much of the data collection and organization. I have hopes that someday I’ll have a Web site where people can submit US state and/or county data and get cartograms back.
 The Web site referenced by the Wikipedia article responds, but as of this writing none of the links on the page for actually accessing data seem to work.
 There’s a whole lot of details involved in calculating the projection of a portion of the surface of a sphere onto a plane such that the relative sizes of different areas are preserved. Fortunately, cartographers have spent centuries worrying about that problem and there’s a bunch of open-source software that deals with it nicely. Technically, my maps use Lambert Azimuthal Equal Area projections.
 “But wait,” you say, “what about Alaska and Hawaii?” Contiguous cartograms present a number of difficulties in practice. Hanley’s cartogram included Alaska and Hawaii, neither one shown on the same scale as the rest of the map and neither of them shown in the proper position relative to the other states. That pretty much defeats the purpose of contiguous cartograms. Fortunately for me, in most of the situations where I want to apply cartograms I can say, “Alaska and Hawaii are such outlier cases that they are excluded.”