## Saturday, August 31, 2013

### FPI and Christensen-Fitted Debt

Couple weeks back I looked at the calculations behind Lars Christensen's Market Expectations Index. He did some nifty stuff with averages and standard deviations, to "fit" one line to another on a graph, to make visual comparison easier.

I saw an opportunity to practice that calculation, to compare the movements of TCMDO debt to Fixed Private Investment.

But first I took the easy way out, and in Graph #3 of the 25th I "fitted" TCMDO to FPI by eye. After looking at the unfitted graph, I wanted to scale the debt numbers up by a factor of 3. Then after seeing the result of scaling, I decided to subtract 20 from the debt numbers to shift the debt line down and get it close to the FPI line.

But it was all just ballpark.

So I downloaded the numbers from FRED for Graph#2 of the 25th, sat down to work, and applied Christensen's calculations to the debt numbers.

 Graph #1: TCMDO Debt (red) Christensen-Fitted to Fixed Private Investment (blue)

For comparison, here's the "no finesse" graph I showed on the 25th:

 Graph #2: TCMDO Debt (red) Fitted by Eye to Fixed Private Investment (blue)

Pretty good, for no finesse.

Funny thing. When I was doing the "no finesse" graph and writing that post, I was careful not to talk about the one line being "higher" than the other. It's okay to talk about something happening first in the one line and later in the other. And it's okay to observe the one line changing more rapidly than the other. But you can't say one is "higher" or "lower" or even that it changes from higher to lower (or the reverse) because the relative positions, higher and lower, depend on how much you subtract as part of the "Christensen Fit" calculation.

Actually I was disappointed when I sat down to do the calculation Lars's way. I had forgotten that Christensen's calculation includes an arbitrary up-and-down adjustment term. That term puts the same ambiguity into his calc that I had in my finesse-free version: It makes the relative positioning of the two lines completely arbitrary.

That may be necessary when the calc combines two datasets for comparison to one, as Christensen's does. I don't know. But intuition tells me that if I take just one dataset (like TCMDO) and tweak it by the average and the standard deviation values for that dataset, then I shouldn't also need an arbitrary up-and-down adjustment.

I'm not linking to my spreadsheet this time, because the calc isn't clear in my head. Maybe I've got a mistake in it, that looks okay because of the up-and-down adjustment I made. I have to work through this calc and get more familiar with it.

Meanwhile, I still think it's an interesting technique.

Jazzbumpa said...

Right - higher/lower than means absolutely nothing.

The only purpose I can see for an up-down adjustment is to overlay the lines, and the only purposes for that are to detect relative motions, and pick out leads and lags.

The movements look close to concurrent through the mid 70's. After that, FPI clearly leads TCMDO, except for the drop into the the '01-2 recession.

There's an almost total absence of contrary motion.

What are we to make of all this?

Cheers!
JzB

The Arthurian said...

JzB: "There's an almost total absence of contrary motion.
What are we to make of all this?"

Sounds like FPI and new uses of credit tend to move in the same direction. One could generalize and say that not just FPI buy all spending tends to move in parallel with new uses of credit.

To me, this confirms the view that people borrow money in order to spend it. (People don't usually borrow money and sit on it.) I think this view is compatible with ...

"...with endogenous money theory, which implies that economic activity – itself caused by a myriad of factors - automatically generates the level of ‘MV’ necessary for the QToM equation to hold"

as Unlearning Economics recently wrote.

//

I agree, about the purpose for up-down adjustment. Still, if you subtract from Series A the average value of Series A, and then divide by the standard deviation for Series A, and then multiply by the standard deviation for Series B, and then add the average value of Series B... at that point no further up-down adjustment should be needed for comparing A and B.

And yet Lars Christensen subtracts an arbitrary 1.5...

Jazzbumpa said...

What are we to make of all this?"

Makes me suspicious of cause and effect here.

More likely, common cause, where both are reacting to the general economic conditions.

jim said...

Hi Art,

I usually just let FRED take care of the scaling and shifting the graph by putting one graph scale on the left and one on the right. .
For instance, for percent change in FPI and TCMDO

http://research.stlouisfed.org/fred2/graph/?g=lZp

The Arthurian said...

Ha! Your method produces a strikingly familiar result, Jim. Good graph. Excellent point.

Jazz, Not sure I can separate money, debt, and spending from general economic conditions.