## Sunday, July 1, 2012

### Continuation of "Real GDP vs. Total Work: Historical Data from the US"

Note that this post is just a continuation of the previous post on "Real GDP vs. Total Work: Historical Data from the US." In this post, I'm including data analyzed back to 1965. So, I'm including similar graphs as presented previously, but this time I'm analyzing the time period from 1965 to 1985 and the full time period from 1965 to 2011.

In this case, the average growth rate of Total Work was greater than the average real growth rate of the GDP (though, not by much...3.5%/yr vs. 3.2%/yr, respectively.) Given the uncertainty in both measuring GDP and calculating Total Work, this is pretty close. The problem is more that there are periods of time where the GDP and Total Work don't track each other all that well, such as 1965 to 1973 and 1977 to 1980. The problem with the 1965 to 1973 time period may have to do with the difficulty of calculating GDP and Total Work during a major war (i.e. the Vietnam War.) The correlation coefficient between the real US GDP increase and the growth rate of Total Work is only 0.65 from 1965 to 1985. This is less than the value of 0.80 given previously for 1985 to 2011. However, it should be noted that the correlation coefficient is 0.83 for the time period from 1973 to 1985, and the correlation coefficient from 1973 to 2011 is equal to 0.80. That's pretty good considering that there are inherent errors, as mentioned above regarding the calculation of real GDP [\$2005] and total work per year [TWh/yr]. Below is the full data set from 1965 to 2011.

The average growth rate of the GDP and the Total Work were 2.9%/yr and 2.7%/yr over this time period. That means that GDP and Total Work track each other nearly perfectly on average over the time period between 1965 and 2011. However, this doesn't mean that there is a year-to-year tracking  between the variables. For example, the correlation coefficient between the real GDP and Total Work between 1965 and 2011 is 0.71. Note that the data between 1965 and 1972 causes the correlation coefficient to decrease from 0.80 to 0.71. One question is whether there are any secular (i.e linear) trends in the data. There does appear to be a general trend in the data in the downward direction, as seen below, but it should be noted that the correlation coefficient between the data and the best linear-fit is only 0.25 for the Total Work data and only 0.06 for the real GDP data. A correlation coefficient of 0.06 essentially means that the data and the linear-fit are uncorrelated.

And now, I'd like to make some the general comments about what I see when I look at the data. In general, I see a lot of fluctuations. So, I decided to conduct a frequency analysis of the growth rate data. Below is a plot of the absolute magnitude of a sinusoidal fluctuation as a fucntion of the frequency of the oscillation. This is an FFT analysis in which the growth rate data is fit by sine-functions of varying frequency. No one frequency is that much greater than the others. (Note that the large value for the first data points is an artifact of the fact that there is a secular trend in the data, as discussed above.)

If there were a "business cycle," there would be a peak in frequency space at the given frequency. The plot below points out what should be obvious to anybody who hasn't been indoctrinated by economists. There is no such thing as a business cycle.  The magnitude of any oscillation is nearly the same, regardless of whether the oscillation has a period of 2 year or 10 years. Though, with that having been said, the absolute magnitude of oscillations with a frequency of 0.5/yr is a little bit larger than for the range of frequencies between 0.1 [1/yr] and 0.4 [1/yr]. Note that the x-axis is the frequency of a given oscillation, i.e. the inverse of the period of the oscillation. An oscillation with a period of 2 years goes along with what I was stating in the last post...that when there is a downturn, people often realize that they have made bad choices and then start finding better places to invest their money. However, the amplitude of this 2-year oscillation is not that much larger than the amplitude of oscillation with longer periods.

So, now I'd like to step back and discuss the seemingly random data for growth rates in the US.
The causes of the drips in growth rate in the US were mostly due to the price shocks in the price of oil in 1973 and 1979. Of the major dips in economic growth rate between 1965 and 2011, most are due in some part of oil  [1973, 1979, 1991 (Gulf War I), and 2008.] A few were due in part to human delusion [1989 Stock Market crash, 2000 dot-com crash, and 2008 financial meltdown.] And terrorism in 2001 seemed to play role in prolonging the 2000 dot-com crash.

The moral of the story here is that a lot of things can cause an economy to go into recession, such as oil embargoes, war, terrorism, natural disasters, and human delusion. And there are a lot of things that can cause a society to grow economically, such as finding new sources of cheap exergy, investing in power plants, and growing the population. Except for population growth, most of the factors that affect the economy either positively or negatively are quite random. This is why I don't try to predict the future in any of my posts. Growth rates can not be calculated using a simple formula because the real world can't be described by simple formulas. Yearly growth rates appears to be chaotic, i.e. not periodic and not completely random. In a future post, I'll analyze this same data, but I'll use a non-linear analysis rather than a linear FFT analysis as in the last graph.