Thursday, October 27, 2016

Parsing the macrohistory database ... for meaning


Adding to my expanding series (here, here, here) on the macrohistory database, I thought I'd discuss the possible meanings behind the principal components (pictured above) of the long and short term interest rate time series from the 1870s to the present being approximately equal to the US time series over that period. Let me begin a (probably not exhaustive) list:

Theory 1: The US has dominated the (Western) global economy since the 1870s

It is true that the US has played a large role in the (Western) global economy, but it doesn't have its commanding lead until the post-WWII period.

Theory 2: The principal component is actually a combination of the pre-WWII Europe and the post-WWII US

We'll use the UK in our example. Before WWII, the UK dominates interest rates; after, the US does. Since the UK dominates before WWII, the pre-WWII US interest rates are basically the UK rates. Since the post-WWII rates are dominated by the US, the UK's post-WWII rates are basically the US rates. Therefore either the US or UK would work as the principal component.

Theory 3: The principal component is actually just the post-WWII US

Before WWII, interest rates in the database seem to be fluctuations around a roughly constant level and the global Great Depression. Since there's nothing differentiating them, the only feature we're extracting is the rise and fall of interest rates in the post-WWII period when the US dominates the economy. The algorithm had to choose a country for the pre-WWII piece and the US works just as well as any.

Theory 4: There is a "global economy", and the principal component gives us its interest rate

This theory says that there is some underlying global signal and each nation's interest rate represents a particular measurement of it. Each nation taps into the global "pulse" in a different way, so the time series differ. However, looking at all the data you can get a glimpse of the economic heart beat. This theory could be interpreted as a generalization of theory 2 where no one economy dominates for very long.

...

These theories are all generically related by saying that the principal component PC is a linear combination of different numbers of pieces.

1: PC = A + ε

2: PC = a A + b B + ε

3: PC = a A + X + ε

4: PC = a A + b B + c C + ... + ε

In a sense, this isn't saying much. This is practically a definition of what a principal component analysis is. It organizes our thinking, though. And this allows us to make a surprising conclusion. Interest rates in a country we'll call D are explained by factors not domestic to D. Basically,

D = d PC + ε

Where PC is primarily other countries (and might even be just one). Therefore, if demographic factors are the cause of high interest rates in your model, they are demographic factors in A (using theory 1). If monetary factors are the cause, they are monetary factors in A.

Another way to put this is that the mechanism of interest rate "importation" (i.e. how the interest rate of A becomes the interest rate of D [1], and if/how the factors domestic to D have an effect) is almost more important than the mechanism for understanding the principal component interest rate. It also means that domestic factors are usually unimportant, except when you are looking at the principal component, in which case they are very important.

I can make this more clear using the IT model as an explicit model (just imagine your favorite stand-in model if you don't like it). Let's use theory 1 above (I'll leave it as an exercise to the reader how to generalize is). In country A, interest rates are given by

log(rA) = a1 log(NA/MA) + a0

However, in country D, they are given by

log(rD) = d0 (a1 log(NA/MA) + a0) + f(ND, MD, ...)

In country D, interest rates will seem to be governed by entirely different mechanisms than those in country A.

Speculation: Does this translate into economic theories in different countries? Does country A have more attempts at "scientific"/"fundamentals" -based theories (e.g. a purely monetary model), while other countries have more "social"/"relationships" -based theories? Does country A think economics is explainable while country D thinks economics is ineffable?

...

Footnotes

[1] An example of such a mechanism would be a country having lots of foreign currency denominated debt, such as Australia with US dollar-denominated debt.



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