An Analysis of Alfred Adler’sSome Long Term relations among Money Supply,

Price Levels, and Economic States

Phase Relations, Holonomy, and the Underlying Curvature of the Commodity Price - Money Supply Space:

Gaston Phillips101 345 730

US Money Supply (In Billions)

0

200

400

600

800

1000

1200

1400

1825 1875 1925 1975

Annual Average Commodity Price Index

y = 1.5751x - 2922.7R2 = 0.5596

-100

0

100

200

300

400

500

1825 1875 1925 1975

WPILinear (WPI)

y = 0.3367x + 39.928R2 = 0.9457

050

100150200250300350400450500

0 200 400 600 800 1000 1200 1400

U.S. Money Supply (In Bllions)

Annual Average WPI

y = 0.3367x + 39.928R2 = 0.9457

1

10

100

1000

0.01 0.1 1 10 100 1000 10000

US Money Supply (In Billions)

Annual average WPI

M1 vs WPI

Holonomy 1

• Consider a Triangle whose sides are on great circles of a sphere.

• The three vertices are all right angles

Holonomy 2

• Draw a vector (here in yellow), on the surface of the sphere.

Holonomy 3

• As the vector moves to the second vertex, it remains parallel to the first side and perpendicular to the second.

Holonomy 4

• As the vector moves to the third vertex, it remains perpendicular to the second side, so it’s parallel to the third.

Holonomy 5

• Now as it moves back to the first vertex it remains parallel to the third side, so it ends up perpendicular to the first, rotated 90 degrees from its original orientation.

Log-Scaled Commodity Price

c(t) = 0.0061t - 9.8634R2 = 0.709

0

0.5

1

1.5

2

2.5

3

1825 1850 1875 1900 1925 1950 1975 2000

c(t)Linear (c(t))

Periodicity Modulo 55

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

1825 1850 1875 1900 1925 1950 1975 2000

c(t)G(t)

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

1825 1845 1865 1885 1905 1925 1945 1965 1985 2005

G(t)

Phase RuledG/dt > 0 and dm/dt > dM/dt then dc/dt = dG/dtdG/dt > 0 and dm/dt = dM/dt then dc/dt = dG/dtdG/dt > 0 and dm/dt < dM/dt then *

dG/dt = 0 and dm/dt > dM/dt then dc/dt = dG/dtdG/dt = 0 and dm/dt = dM/dt then dc/dt = dG/dtdG/dt = 0 and dm/dt < dM/dt then *

dG/dt < 0 and dm/dt > dM/dt then dc/dt = F(t) dm/dtdG/dt < 0 and dm/dt = dM/dt then dc/dt = dG/dtdG/dt < 0 and dm/dt < dM/dt then dc/dt = dG/dt

Log-Scaled Money Supply

Lm(t) = 0.0238t - 44.424R2 = 0.9935

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

1825 1845 1865 1885 1905 1925 1945 1965 1985 2005

Year

m(t) - log of money supply

M(t) - Long Term Trend of m(t)

Change in log-scaled Money

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

1825 1875 1925 1975

dm/dtdM/dt

1860-1865 G(t) Ascending and m(t) ascending

1865-1870 G(t) Declining and m(t) declining

1870-1887 G(t) Declining and m(t) neutral

1887-1895 G(t) Declining and m(t) declining

1895-1908* G(t) Ascending and m(t) ascending

1908-1915 G(t) Ascending and m(t) declining

1915-1920 G(t) Ascending and m(t) ascending

1921-1933 G(t) Declining and m(t) declining

1933-1950* G(t) Declining and m(t) ascending

1950-1963* G(t) Declining and m(t) declining

1963-1975 G(t) Ascending and m(t) neutral

1976-** G(t) Declining and m(t) ascending

1860-1908 G(t) and m(t) are in phase

1908-1915 G(t) and m(t) are out of phase

1915-1933 G(t) and m(t) are in phase

1933-1963 G(t) and m(t) are out of phase

1963-1975 G(t) and m(t) are in phase

1976- G(t) and m(t) are out of phase

Year My Analysis

Adler’s Analysis

1976 IN OUT

1963*-1967, 1970, 1974 OUT IN

1937-1938, 1947-1949, 1952, 1958,

IN OUT

1915*, 1920, 1923, 1925 OUT IN

1909*, 1911-1912 IN OUT

1860, 1864, 1870-1872, 1880-1883, 1886-1887, 1889-1890, 1892, 1895-1896, 1907-1908

OUT IN

-6

-4

-2

0

2

4

6

8

10

1825 1875 1925 1975

TEST STATERROR

Test Statistic

Error by Phase

-1

0

1

2

3

4

5

6

7

8

1825 1875 1925 1975

In ErOut Er

To Do

• Hypothesis Test

• Determine Power of Experiment

• Explain Holonomy Better

• MSE, S2, &c