Economic Data Analysis

CSGnet Archive CSG2004
21

[From Bill Powers (2004.02.10.1349 MST)]

Rick Marken (2004.02.10.1210)–

If your model works properly, it should keep the simulated discount
rate

equal to the actual discount
rate.

No, to actual dCPI/dt, not discount rate.

I meant that the simulated discount rate would predict what the actual
discount rate was – isn’t that the point? In fact, the simulated
discount rate in the first figure seems to reproduce the actual discount
rate quite well for the first 350+ months, but after that the match gets
very bad.

What happened right after
month 350? Or is the good fit fortuitous?

The fit is as good as it can be based on dCPI/dt. The apparent lack of
fit

at the end comes only from how I arranged the offset for graphing
purposes.

I donb’t think we’re talking about the same figure. Here is the one I
mean, with annotations:

See the cc. I.m saving you the trouble. Hello, Zhang Huaxia, and I hope
your work is nearing its end.

15f0e2d.jpg
15f0e2d.jpg621×511 101 KB

Best,

Bill P.

22

[From Bill Williams 10 February 2004 2:45 PM CST]

[From Rick Marken (2004.02.10.1210)]

>Bill Powers (2004.02.10.0804 MST)--

> So this proposes a control system that keeps the difference between
> sim_discount and dCPI at a reference level of zero by varying

sim_discount.

> I think I'm with you.

Right.

> If your model works properly, it should keep the simulated discount rate
> equal to the actual discount rate.

No, to actual dCPI/dt, not discount rate.

> What happened right after month 350? Or is the good fit fortuitous?

The fit is as good as it can be based on dCPI/dt. The apparent lack of fit
at the end comes only from how I arranged the offset for graphing

purposes.

With a lower offset to simulated discount rates it look like the rates in
the early months are too low. It's the shape of the simulated discount

rate

curves that fits the shape of the actual discount rate curve. As I note
below, in the future I will evaluate the model using RMS deviation of

model

from actual data.

> I hope I see your logic correctly here. What you want to do is find the
> parameters of the model that will produce the same discount rate that

the

> Fed actually produced, under the hypothesis that they were controlling

with

> a certain gain and slowing factor to keep the discount rate equal to the
> inflation rate. But why use correlations? Why not just show the

predicted

> and actual discount rates?

I did.

> As we know, correlations give spuriously
> favorable impressions of how well one variable predicts another (I

expect

> that's why they're used). A correlation of 0.65 is really lousy. And

when

> the data are not normally distributed random variables, correlation is
> extremely misleading, as in this case.

Again, I was just testing to see what the _shape_ of the lagged

correlation

curve would be.

> What puzzles me is why the Fed would have any difficulty at all in

keeping

> the discount rate equal to the observed inflation rate.

I'm sure that inflation rate is only one consideration involved in the

Fed's

decision to raise or lower the discount rate. That is, the variable being
controlled by the Fed is surely more complex than a match of discount to
inflation rate. All the model shows is that a lot of the variability in

the

Fed's actions (changes in discount rate) can be accounted for by assuming
that the Fed is acting like it's in a pursuit tracking task, tracking
inflation rate with discount rate. The model also assumes that discount

rate

has no effect on interest rate. Of course, the Fed assumes otherwise. So

the

fact that a model that assumes no effect of discount rate on inflation

rate

works reasonably well suggests that discount rate may actually have

nothing

to do with inflation rate.

> Also, why would the Fed control for the discount rate to have any
> relationship to the inflation rate?

Because they think that discount rate will bring inflation down. I think
it's like being in a pursuit tracking task where you think that keeping

the

cursor even with the target will bring the target back to the center of

the

screen.

> Why not observe the inflation rate
> and adjust the discount rate so as to maintain inflation rate at

whatever

> level is desired?

That,I believe, is what the Fed is doing. But, since the discount rate has
no actual effect on inflation rate they end up just tracking inflation

rate.

You appear to be assuming that rising prices are
inflationary. However, Keynes p. 303 explains why this isn't so. It is a
neglected point in the Keynesian system, but never-the-less it is an
important one. Until you get the defintions straight-- everything is all
conflused.

Bill Williams

23

[From Bill Powers (2004.02.10.1633 MST)]

Rick Marken (2004.02.10.1210)--

Thinking over that first figure, I think it would be interesting to do a
little detective work. But first, try this: compute the RMS error for
12-month periods starting at month 1, month 2, and so on to 12 months
before the last data. I suspect we will see a medium-to=-small error up to
month 375 or so, followed by an abrupt increase to a much larger number --
indicating that the model works up until then and then stops working.

Then look at the financial news for the dates in question. I had a feeling
some time ago that the Fed had stopped trying to control inflation by
raising interest rates. Maybe you've caught them in the act.

Best,

Bill P.

24

[From Rick Marken (2004.02.10.2050)]

Bill Powers (2004.02.10.1349 MST)--

Rick Marken (2004.02.10.1210)--

I meant that the simulated discount rate would predict what the actual discount rate was -- isn't that the point? In fact, the simulated discount rate in the first figure seems to reproduce the actual discount rate quite well for the first 350+ months, but after that the match gets very bad.

Good eye!! I've just looked at the correlation between simulated and actual discount rate before and after various time points. I've also looked at the RMS error in the same way.

The correlation between simulated and actual discount rate before ~1987 peaks at about .95; after 1987 the correlation goes to .31. The RMS deviation of simulated from actual discount rate before 1987 is .07 discount units. After 1987 the RMS error goes up to.21 discount units. So you are right. A policy change seems to have occurred at about the point in the graph you mention, point 350. This point happens be near early 1987, where the fit of the inflation tracking model of discount rate variations starts to deteriorate.

What happened in 1987 is that Alan Greenspan took over as Fed chairman from Paul Voelker, the "inflation fighter".

See the cc. I.m saving you the trouble. Hello, Zhang Huaxia, and I hope your work is nearing its end.

Please say hello to dear Zhang from me, too!

Best regards

Rick

···

---
Richard S. Marken
marken@mindreadings.com
Home 310 474-0313
Cell 310 729-1400

25

[From Bill Powers (2004.02.11.0515 MST)]

Rick Marken (2004.02.10.2050) --

What happened in 1987 is that Alan Greenspan took over as Fed chairman
from Paul Voelker, the "inflation fighter".

No kidding! So maybe that peak of inflation was really like the "reversal"
effect. a positive-feedback runaway followed by some kind of higher-level
switch! I see there were two peaks, like an oscillation, and then the
discount rate got disconnected permanently from inflation and the inflation
died away. Makes a good story -- I wonder if it's true. It's always
possible that the inflation was caused by something else and the discount
rate simply followed it, with no great effect either way. But that sure
looks like an exponential rise to me, followed by a quick drop, followed by
another exponential rise.

Try another one: discount rate versus unemployment rate. Same idea, except
try some reference levels for unemployment of around 6%. Greenspan once
said that there is an optimum level of unemployment, It seems pretty sure
that there's an indirect effect of discount rate on unemployment. It is, of
course, a considerable advantage for the composite producer to have a
significant part of the workforce hungry for a job, and therefore docile
with respect to wages. Or slo it would seem -- provided _somebody_ still
has enough money to buy the product.

How about writing to Greenspan (on RAND stationery) and asking him just
when it was that he decided that the former policy of fighting inflation by
increasing the discount rate wasn't working. It would be nice to get the
time accurate to the month.

The mysterious comment about a cc to Zhang was an artifact of the
clipboard. Somehow when I pasted the graphic into the text of the post,
that bit of text came along with it, left over from a post to Alice. I
didn't notice it.

Best,

Bill P.'

26

[From Bill Powers (2004.02.11.0616 MST)]

Rick Marken (2004.02.10.2050)--

The correlation between simulated and actual discount rate before ~1987
peaks at about .95; after 1987 the correlation goes to .31. The RMS
deviation of simulated from actual discount rate before 1987 is .07
discount units. After 1987 the RMS error goes up to.21 discount units. So
you are right. A policy change seems to have occurred at about the point
in the graph you mention, point 350. This point happens be near early
1987, where the fit of the inflation tracking model of discount rate
variations starts to deteriorate.

What happened in 1987 is that Alan Greenspan took over as Fed chairman
from Paul Voelker, the "inflation fighter".

The modeling process seems to have shown when a change of policy happened.
But there is still the relationship between inflation rate and actual
discount rate to examine, which would not depend on policy. How about
applying the same treatment to the correlation between discount rate and
inflation? By the way, if you smooth data before comparison you should
apply exactly the same smoothing formula to all the data. I guess you know
that.

It looks to me as though there is about the same correlation between actual
discount rate and inflation through the whole data set, though that's a
little harder to see by eye alone.

Best,

Bill P.

27

[From Rick Marken (2004.02.11.1030)]

Bill Powers (2004.02.11.0515 MST)]

Rick Marken (2004.02.10.2050) --

What happened in 1987 is that Alan Greenspan took over as Fed chairman
from Paul Voelker, the "inflation fighter".

No kidding! So maybe that peak of inflation was really like the "reversal"
effect. a positive-feedback runaway followed by some kind of higher-level
switch! ...

How about writing to Greenspan (on RAND stationery) and asking him just
when it was that he decided that the former policy of fighting inflation by
increasing the discount rate wasn't working. It would be nice to get the
time accurate to the month.

I might just do that. Alan and I are actually connected in some interesting
ways. We're both Jewish, of course, in that same non-religious way that was
popular before the Middle Ages came back to America in the 1970s, and we
(well, just me; I don't know if Alan kept his) have a picture of Linda (the
shiksa) with Alan (and a few other Fed execs) that was taken when Linda was
working at the LA Fed. That, plus the RAND stationary should get his
attention.

Bill Powers (2004.02.11.0616 MST)--

The modeling process seems to have shown when a change of policy happened.
But there is still the relationship between inflation rate and actual
discount rate to examine, which would not depend on policy. How about
applying the same treatment to the correlation between discount rate and
inflation?

I think you're talking about determining the "forward" relationship from
discount rate to inflation. Is that right? If so, I don't think I understand
how you propose to determine this.

Best

Rick

···

--
Richard S. Marken
MindReadings.com
Home: 310 474 0313
Cell: 310 729 1400

28

[From Bill Powers (2004.020947 MST)]

Rick Marken (2004.02.11.1030) --

I think you're talking about determining the "forward" relationship from
discount rate to inflation. Is that right? If so, I don't think I understand
how you propose to determine this.

No, just looking at the correlations or RMS differences over various parts
of the whole period. The discount rate produced by the model shows a large
departure from the actual discount rate for the last 1/3 of the data,
though it fits very well for the first 2/3, showing that a change of policy
occurred. But if the inflation rate has the same relationship to the
discount rate over the whole period, the discount rate during the final 1/3
should still correlate with the inflation rate, about the same as in the
first 2/3. This would (if true) support the idea that it was the policy,
and not the relationship of discount rate to inflation, that changed.

Best,

Bill P.

29

[From Rick Marken (2004.02.11.2000)]

Bill Powers (2004.020947 MST)--

Rick Marken (2004.02.11.1030) --

I think you're talking about determining the "forward" relationship
from
discount rate to inflation. Is that right? If so, I don't think I
understand
how you propose to determine this.

No, just looking at the correlations or RMS differences over various
parts
of the whole period. The discount rate produced by the model shows a
large
departure from the actual discount rate for the last 1/3 of the data,
though it fits very well for the first 2/3, showing that a change of
policy
occurred. But if the inflation rate has the same relationship to the
discount rate over the whole period, the discount rate during the
final 1/3
should still correlate with the inflation rate, about the same as in
the
first 2/3. This would (if true) support the idea that it was the
policy,
and not the relationship of discount rate to inflation, that changed.

In fact, the correlation between inflation and discount rate is .76
over the first 2/3 of the observed time period and .28 during the last
1/3 (starting in about 1987).

By the way, in the graphs I presented, inflation and growth are
measured as they are reported by the Fed and by the media, as
percentage change. So, for example, when the inflation rate on the
graph is 2 that means that the inflation "rate" was 2%, ie. Inflation
rate = [CPI(t)-CPI(t-1)]/[(CPI(t)+CPI(t-1)/2] .

When I use the true in inflation rate values, ie. Inflation rate =
[CPI(t)-CPI(t-1)]/12, as inputs to the model, I get virtually the same
results as when I used the percentage change numbers. I think the
results using inflation measured as percentage change are more
appropriate for models since the Fed Chair (and Board) perceive
inflation in this way. That is, the Fed Chair reports (and presumably
perceives) inflation at 2%, not $ 0.20 per year and GDP growth rate at
8%, not $8,345,548,445 per year .

Best regards

Rick

···

---
Richard S. Marken
marken@mindreadings.com
Home 310 474-0313
Cell 310 729-1400

30

[From Bill Powers (2004.02.13.0559 MST)]

Rick Marken (2004.02.11.2000)--

This would (if true) support the idea that it was the
policy and not the relationship of discount rate to inflation, that changed.

In fact, the correlation between inflation and discount rate is .76
over the first 2/3 of the observed time period and .28 during the last
1/3 (starting in about 1987).

This says that the real discount rate doesn't follow the inflation rate,
either during the last third. Well, I guess that makes sense if Voelker did
use the inflation rate to guide the discount rate, and Greenspan didn't, or
ast least changed the policy shortly after 1987..

By the way, in the graphs I presented, inflation and growth are
measured as they are reported by the Fed and by the media, as
percentage change. So, for example, when the inflation rate on the
graph is 2 that means that the inflation "rate" was 2%, ie. Inflation
rate = [CPI(t)-CPI(t-1)]/[(CPI(t)+CPI(t-1)/2]

It's d(CPI)/CPIavg ? OK, that make it appropriate for an exponential rise,

When I use the true in inflation rate values, ie. Inflation rate =
[CPI(t)-CPI(t-1)]/12, as inputs to the model, I get virtually the same
results as when I used the percentage change numbers.

Dividing by twelve would correct the yearly rate to the monthly rate. But
if you have CPI numbers for every month, you don't need to do that: t is
already in months. What you have to do to get the equivalent yearly rate is
to compute

(1 + monthly fractional inflation) ^ 12 - 1, or

exp(12*ln(1 + MonFractInfl)) - 1.

I think the results using inflation measured as percentage change are more
appropriate for models since the Fed Chair (and Board) perceive
inflation in this way. That is, the Fed Chair reports (and presumably
perceives) inflation at 2%, not $ 0.20 per year

oops, 0.02 per year (fractional rate), and not dollars.

and GDP growth rate at
8%, not $8,345,548,445 per year .

Yes, I agree, especially about growth rate! But I think it's safest to use
fractional growth rates and convert to percentages only for plotting.
Otherwise you get those factors of 100 and 0.01 in there and they can be
confused with values like gain.

Best,

Bill P.

31

[From
Bjorn Simonsen (2004.02.23,17:30 EuST)]

[From
Rick Marken (2004.02.21.0930)]

[From
Rick Marken (2004.02.22.1040)]

Could you do me a favour and send me
(in a spreadsheet) the Norwegian data on gross

private investment and growth in GDP (or GNP) going back as far as you can go.

(I got back to 19653). I used quarterly data but I’ll take what I can get. What
I

would like is real (not inflation adjusted) GDP (or GNP), inflation adjusted
GDP (or GNP)

and real (not inflation adjusted) gross private investment (I don’t think they
report

inflation adjusted investment, I presume because they assume it will be
measured

as a proportion of GNP, which would also have to be in real dollars). If you
can get

me gross government investment as well that would be great (in the US they
report

defence and domestic investment as separate parts of government investment).

I
send you private the spreadsheets-You will find 1) The Norwegian data Grossed
fixed capital formation at current price, Ip, General government
investment (Ig), and the GDP. The data is partial quarterly data and yearly
data. And 2) a Norwegian CPI table 3) A Simulated Change in Discount and
Correlation coefficients and 4) An Analysis of Norwegian Discount relative to
CPI.

If
any other is interested, give me a mail

I
don’t know if it is

               .

…a wonderful birthday present (my birthday is next Saturday, 2/28).

But,
Happy Birthday. I shall have my birthday on Friday 2/27, and I leave the same
day for our cottage in the mountain.
I am back again Monday.

Did you do these calculations using
Visual Basic? In my calculations, the value of

sim_discount that is used in the
calculation of p is the value of output calculated

on the prior iteration of the following
loop (lines stating with an apostrophe are remarks.

If
you go to 3) A Simulated Change in Discount and Correlation coefficients and
4) An Analysis of Norwegian
Discount relative to CPI you will see that the calculations are very simple. I
have just made the formulas in a cell and dragged the Cell in accordance to the
CPI and the date columns. You will understand when you open the spreadsheets.

I
know you use Visual Basic, but I think functions in the spreadsheet also work
well.

If
you look at 3) A Simulated Change in Discount and Correlation coefficients you
see I still get the correlation coefficient like 1. In the same spreadsheet you
will see that I have not used your formula for the output

F16+0.01*(8*(0-(F16-C15))-F16),
I have used = F16+$D$8*($D$9*($D$10-(F16-C15))-F16).

I
have substituted 0.01 with $D$8 and substituted 8 with $D$9 and your reference
0 with $D$10. This is Simply and
you have maybe done it yourself. I thought it was exciting having a Simulated
Discount graph and changing the values in D8, D9 and/or D10. Then I could see
how the graph changed when I clicked F9.

I
didn’t understand your comments about my correlation coefficient =1.00. If you
see a mistake, please tell me.

I
did the same wit the US Simulated Discount data. And I got the Correlation
coefficient almost =1.00 also there.

I see that you did do an analysis of
Federal Gross Investment and Discount Rate

(something I did not do). Was this for the
Norwegian data? If so, then you can

apparently get the data I want: Norwegian
Gross Federal and Gross Private

Investment as well as Norwegian Real and
Inflation Adjusted GDP.

I
did it also with the US data. I send it to you as 5) US Investment relative to
Discount

bjorn

···
32

[From Rick Marken (2004.02.23.0950)]

Bjorn Simonsen (2004.02.23,17:30 EuST)--

I send you private the spreadsheets-You will find 1) The
Norwegian data Grossed fixed capital formation at current
price, Ip, General government investment (Ig), and the GDP.
The data is partial quarterly data and yearly data. And
2) a Norwegian CPI table 3) A Simulated Change in Discount
and Correlation coefficients and 4) An Analysis of
Norwegian Discount relative to CPI.

The data of greatest interest to me are in the sheet called "investing
related to GDP 1.xls" It looks like you have quarterly data on investment
(capital formation) but not on GDP (GDP seems to be called "gross capital
formation"). It looks like you have yearly data only or all variables from
1970 and quarterly data for investment from 1980 to to present. You only
have yearly data for "gross capital formation" from 1970 to 2003.

If "gross capital formation" is really GDP then I'm close to being in
business, for a yearly analysis, anyway. It would really be nice to get the
quarterly GDP numbers back to 1980, if possible. I assume that the "gross
capital formation" or GDP values are _not_ inflation adjusted, since you use
them to measure investment (Ig and Ip) as a proportion of GDP. If this is
true, then I think I can get the inflation adjusted yearly GDP values by
dividing the GDP numbers by the yearly CPI numbers. Is that right? Or can
you get me yearly (or, better, quarterly) inflation adjusted GDP numbers? I
see that the CPI numbers go back to 1865 so it looks like Norway has been on
top of things economic for quite some time.

I don�t know if it is

                 . a wonderful birthday present (my birthday is next
Saturday, 2/28).

But, Happy Birthday. I shall have my birthday on Friday 2/27, and I leave the
same day for our cottage in the mountain. I am back again Monday.

Unbelievable!! No wonder you're such a great guy. Maybe there's something to
this astrology thing after all. Of course, all the people on my "delete,
don't read" list are probably Pisces as well;-)

The data you sent are indeed a wonderful birthday present. I'll start
working on them ASAP. Have a wonderful time in your mountain cottage (sounds
lovely). Have a very happy birthday!

I'll also check out the calculations you described. I (like you) would like
to do the model calculations using cell formulas (without Visual Basic) but
my first quick attempt to duplicate the Basic loop calculations in cells
didn't work correctly. So I still suspect that the use of cell computations
is the basis of the 1.0 correlation you get. But, again, I'll check it out
ASAP.

Best regards

Rick

···

--
Richard S. Marken
MindReadings.com
Home: 310 474 0313
Cell: 310 729 1400