## Climate Cycle, Meet Business Cycle-Preliminaries

I’ve been wanting to write something up for a while about my thoughts on the idea of “cyclical” climate variations, and in particular to express extreme skepticism about them, but one element in particular. Many, with some degree of enthusiasm, have noted that there is a claimed “cycle” in economic activity with (very roughly) the same periodicity claimed to exist in climate: The Kondratiev Wave.

I’ll be perfectly frank. I don’t think the Kondratiev Wave exists. I don’t think it is an actual, real thing. I think it is complete and total bull crap.

But before I can write up a long ass post explaining why it is complete and total bull crap, I want to just post up some fun things.

As before, I will use US GDP data, with the portion representing Government spending removed, to represent actual meaningful production. Except this time, I really want more data than just back to 1890, so I use simple method to estimate the state and local spending from the federal spending: from 1890-2013, there is a correlation between a change in federal spending as a fraction of GDP and a change in federal spending as a fraction of total spending-the correlation is better in later years, so one should be a little bit weary of extending it back in time. But let’s proceed with reckless abandon nonetheless. The main purpose is to properly restrict what are mostly war spikes to increases in federal spending. I can use this relationship to estimate how much of the total government spending before 1890 was made up of federal spending and how much state and local spending. One can then use the estimated fraction, federal/totgov, with the actual federal spending, to get an estimate of total government spending in years before 1890. Anyway, this is what that fraction looks like, with the estimated portion highlighted:

Note that with this, I can extend the total government as a percent of GDP back to 1792. However, the GDP data go back to 1790. After converting from percent of GDP to billions of dollars-and deflating the series to constant 2013 dollars-I observe that the first couple of years saw a slight declining trend. I simply assume 1791 was about 2.2% higher than 1792, and the same for 1790 relative to 1791, to extend the data backwards. This is less than satisfactory, but I wanted to be able to have a reasonable estimate for every year. Anyway, I then subtract those values for total government spending from GDP. For those of you who haven’t taken an undergraduate macro course: well, first of all, don’t, if you are at almost any University in the US. Second, GDP is defined as the sum of all final expenditures by: Consumers (C) Government (G) Investors (I) and the difference between Exports and Imports (“Net Exports”) (NX). So we are basically talking about GDP – G, or C + I + Nx. As measures go, this has a few things to recommend it over GDP including G. But it depends what you are trying to “measure.” And it still suffers from a number of defects. Nevertheless, as a measure of economic growth and fluctuation, I find it nigh infinitely superior.

Anyway, frequently, economists refer to fluctuations in GDP as representing an “output gap”-this basically refers to the percent departure of the GDP from a long term trend curve. There are lots of ways to calculate a long term trend curve, and how you do so determines a great deal about what you will conclude about cyclical variations in output. It’s also questionable whether the entire thing is a very meaningful concept, or more specifically, what meaning to attach to the long term trend curve. My current think is somewhere between that it is meaningless data torture, and that it represents just a proxy for progress. Again, let’s proceed with reckless abandon regardless.

My method for removing the long term trend line has as a goal not removing anything that might conceivably represent a short term variation. So I want a highly aggressive filter. Oh say, I’ve got that. Specifically, I take the following steps: I take the growth rate year over year, for each year relative to the previous. I then lag that back one year. For all years but the first and last, I average those two series. For the first and last, I take the average of the next two, and previous two years, respectively. Then, I iteratively smooth it: I take three point centered averages, with the first and last points double weighted to extend the centered averages to the end of the series, 1110 times-that is 10*(years-2)/2 (since years happens to be 224, an even number). I then use this final smoothed series of “long term growth rates” to create a compound growth curve starting at 1 in 1789. I multiply this by a factor suggested by regression against GDP-G. I then take the ratio GDP-G/TREND1, This seemed to consistently under estimate values in the first half of the data. So I did the smoothing on that ratio 1110 times, and multiplied TREND1 by that factor, which was the new estimate of the long term trend. Then I take the ratio of the actual GDP-G to the trend curve, to estimate the “output gap”:

Hm, I’m rambling quite a bit. Why was I writing this again? Oh, right, I just wanted to describe the data I’d be using for my post on the (non) existence of the Kondratiev Wave. Anyway, we’ll revisit that later. For now, there are several interesting things for readers to ponder.

Also this was a great opportunity for me to ramble on about economics on what is ostensibly a science blog. 😉