четверг, 24 апреля 2008 г.

Дискуссия Кристофера Рупа с читателем

Читатель под ником Whewt, спрашивает, Кристофер под ником  Cheapbastud отвечает
 
Q:
Cheap. Awesome post. I have been trying to get my head around the significance of this ever since I saw it. With your explanations I am getting closer, but one thing that would help me is if I could see actual data for two of the points. Can you post the numbers used for the last two points? I think if I can say...oh the GDP(t) was this and GDP(t-4) was this.....and the Debt(t)....and so on, I will be able to digest it.

I really appreciate your work.

 A:
Whewt, very interesting what has happened during the last two data points.

I'll start with the most recent:

(Numbers in billions)
GDP2009Q4 = 14461.7
GDP2008Q4 = 14347.3
Debt2009Q4 = 52416.7
Debt2008Q4 = 52542.9

DeltaGDPQ4 = 14461.7-14347.3 = 114.4
DeltaDebtQ4 = 52416.7-52542.9 = -126.2

DeltaVelocity = 114.4/-126.2 = -0.91 (which corresponds to the Unsmoothed chart above)

now for the Q3 data:
GDP2009Q3 = 14242.1
GDP2008Q3 = 14546.7
Debt2009Q3 = 52549.1
Debt2008Q3 = 52082.5

DeltaGDPQ3 = 14242.1-14546.7 = -304.6
DeltaDebtQ3 = 52549.1-52082.5 = 466.6

DeltaVelocity = -304.6/466.6 = -0.65

So, you can see that the Denominator was negative in the most recent data point but the numerator was negative for the Q3 data point. This is to be expected as part of the dynamics of debt saturation. Eventually, I expect a violent snap back to the positive as part of this dynamic. It doesn't mean that we're in the clear at that point just that an oscillation in the data sets up as the system tries to cleanse itself. 

Q:
Cheap and Nate. How would you explain my hypothetical?

GDP2009Q4 = 14461
GDP2008Q4 = 14460
Debt2009Q4 = 52416
Debt2008Q4 = 52415

DeltaGDP=14461-14460=1
DeltaDebt=52416-52415=1
DeltaVelocity=1

GDP2009Q4 = 14460
GDP2008Q4 = 14461
Debt2009Q4 = 52416
Debt2008Q4 = 52415

DeltaGDP=14460-14461=-1
DeltaDebt=52416-52415=1
DeltaVelocity= -1

By changing the debt numbers by one unit, I can cause this indicator to flip from +1 to -1 which would appear to be an EXTREME shift. I will look at this more tonight, but something appears to be fundamentally wrong.

A:
Whewt, remember that this is looking at impacts at the margin.

So in your first example you have perfect efficiency of transfer of that extra dollar of debt into a dollar of GDP.

In the second example, the effect (who knows why?) of one extra dollar of debt translated into a contraction of GDP. Perhaps this is indicative of debt saturation or not.

For example, immediately after WWII the .gov stopped borrowing immense amounts of money while the smaller private sector sprang to life. GDP took a hit in 1946. In this case the marginal decline in contribution to GDP from the .gov was larger than the marginal increase in contribution from the private sector. The contribution from the private sector soon overtook the .gov contribution so that we exited that recession quickly. GDP and thus Marginal Velocity took a hit in 1946 but it was not indicative of debt saturation. The private sector was freed from the constraints of sacrifice for the war effort and there was enormous pent-up demand for private sector credit.

Such is not the case today.

A:
Cheap.



Whewt, remember that this is looking at impacts at the margin.

So in your first example you have perfect efficiency of transfer of that extra dollar of debt into a dollar of GDP.

In the second example, the effect (who knows why?) of one extra dollar of debt translated into a contraction of GDP. Perhaps this is indicative of debt saturation or not.



I question the value of a metric that swings from a perfectly efficient value of "1" to a perfectly inefficient value "-1" with a $2 swing in the numbers.

I find it significant that in history, DeltaGDP has always correlated with DeltaDebt. Also significant that this correlation has reversed over the last two quarters. The thing I don't agree with is assigning a metric that can swing from one extreme to another on such small changes and then drawing major conclusions based on the metric. Especially if you look at examples like ARRA funds.

Of the 787 Billion in funds, less than 40% have been spent. If I am not mistaken, the full $787B counts in the DeltaDebt, but only $303 Billion would be expected to have an impact on GDP. In other words, there may be a time lag factor between the realization of GDP growth and DeltaDebt that, if not accounted for in your metric, may lead to false conclusions

Q:
Whewt, I think we are talking past each other here. I am not calculating the velocity of debt. I am calculating the MARGINAL velocity of debt. Bear with me because I can't really think of any other way of explaining it.

If there is an increase or decrease of ONE dollar in GDP and Debt, you can see that the velocity barely budges. Do it on your hypothetical examples above.

For increasing GDP
2009Q4 Velocity = 14461/52416 = 0.275889

2008Q4 Velocity = 14460/52415 = 0.275875

So here you can see that the velocity measure barely increases but the MARGINAL contribution was efficient translation of that extra dollar of debt into GDP.

For decreasing GDP
2009Q4 Velocity = 14460/52416 = 0.275869

2008Q4 Velocity = 14461/52415 = 0.275894

Here, the velocity barely decreases yoy but the MARGINAL contribution was an inefficient translation of that extra dollar of debt into GDP.


Like I said above, I think that CONTEXT is key to interpreting what the metric means. But the marginal calculation and metric is widely used in science, business, economics, etc.

Q:
Look at what Fatso said. He was referring to this.

DeltaGDPQ4 = 14461.7-14347.3 = 114.4
DeltaDebtQ4 = 52416.7-52542.9 = -126.2

If I understand you correctly, you are suggesting that getting a marginal gain in GDP of 114.4B with a marginal reduction of Debt of 126.2B is "worse" than....

DeltaGDPQ3 = 14242.1-14546.7 = -304.6
DeltaDebtQ3 = 52549.1-52082.5 = 466.6

...a marginal reduction of GDP by 304B and a marginal gain in debt of 466B. Huh?

I may not understand the finer points of economics, but this does not pass the smell test. In fact, I would argue that in order to recover we need to shrink the marginal debt every quarter and grow the marginal GDP. This would produce a "negative" metric value, but it would be the good kind of "negative" in that marginal debt would be decreasing while the marginal GDP increases.

A:
Whewt, I can only guess, but I think you are getting hung-up on thinking that this relationship is linear.

That is y = A*x + B

where y = GDP and x = debt. A and B are constant

So then yes, marginal product calculations that show a decline in debt producing a positive change in GDP in one instance and then a rise in debt producing a decline in GDP in another instant and then a rise in debt producing a rise in GDP in yet another instant DOESN'T MAKE ANY SENSE.

But 'A' is not constant. Velocity is variable too.

The relationship is NONLINEAR.

y = v*x

I'm gonna go drink a beer and hang out with the fam now

Q:
Cheap. I appreciate your patience on this and all the work you have done. I am just trying to make sense out of this.

One thing that I am wondering is if the use of quarterly data for the last few years along with the time delay I pointed out with the ARRA example of debt making it into the economy, causes severe distortions in the data. On something as fuzzy as GDP, the Debt to GDP transfer may historically have registered in the same year due to the nature of the debt, its use, and the one year timeslice. However if you take on huge chunks of debt on certain days during the quarter and then funnel it into banks where it is parked or used in novel ways (not buying bullets, or planes, or missiles) the effects on GDP may get delayed (or postponed permanently?). If you carry this year to quarter comparison even further, you can see where it breaks down. Imagine tracking Debt and GDP on a daily basis. Obviously you would not expect the GDP to grow the same day the debt is incurred. So maybe looking at it quarterly is also unreasonable? To test this, you could probably just use the previous four quarters rolling average and see if that smooths out the negative values.

Again. I am not pretending to be an economist. I am just coming at it from a scientific standpoint and trying to understand what the limits are and find out where and why the correlation appears to break down.

A:
Quote:

However if you take on huge chunks of debt on certain days during the quarter and then funnel it into banks where it is parked or used in novel ways (not buying bullets, or planes, or missiles) the effects on GDP may get delayed (or postponed permanently?)



Yes, exactly. If I take a loan from the bank and sit on it, then the marginal velocity is zero for the amount of that loan since it doesn't contribute to GDP.

Now lets say that I take an additional loan in the next period and use it along with the original loan taken out in the first period and spend both loans on something. Then the marginal velocity will be higher in this next period than it would be if only the second loan were now contributing to GDP.

Remember, GDP has a nonlinear response to the amount of debt taken in any period. Velocity itself can be thought of as a nonlinear function of what is done with the money supply in the economy.
- Is it used for acquiring productive capital?
- Is it used for consumption?
- Is it being stuffed into the mattress?
- Have improvements in technology allowed the economy to produce more and different goods than existed before?
- Is the debt self-liquidating because it is being paid back?
- Is the debt being defaulted on?

The answers to questions like these make up the nonlinear function, velocity.

However, your ARRA funds example doesn't really apply since those funds are borrowed and spent as needed. The Treasury isn't sitting on the remainder of the 787billion in its vault because it hasn't been borrowed yet.

Quote:

To test this, you could probably just use the previous four quarters rolling average and see if that smooths out the negative values.



The very first chart above is a 4 quarter moving average.

Quote:

I am not pretending to be an economist.



Neither am I

Quote:

....and find out where and why the correlation relation appears to break down.



It isn't breaking down. People are getting confused by the idea especially of a decline in debt resulting in a rise in GDP. That's why I struck out 'correlation' in your statement above. Because the vast majority of the time the implication is that 'correlation' is 'linear correlation' as is common practice in statistical analysis.

However, the economy is always trying to become more efficient. Capital is constantly redeployed into other, more productive projects. That's how markets work. So it shouldn't be surprising to see from time to time a gain in GDP even though the money supply is shrinking.