A Preliminary Analysis of the Spread of the Depression

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A preliminary analysis of THE SPREAD OF THE DEPRESSION

W. R. Tobler

July 1975 WP-75-76

Working Papers are not intended for distribution outside of IIASA, and are solely for discussion and information purposes. The views expressed are those of the author, and do not necessarily reflect those of IIASA.

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"The progress of business cycles was surprisingly slow, a little over half a mile daily on the average."

A. Losch

A preliminary analysis of THE SPREAD OF THE DEPRESSION

w.

R. Tobler

The closure of banks at the time of the depression can be regarded as an economic innovation which diffused through- out our society, culminating in the national bank holiday.

The propagation of such events would seem likely to reveal the structure of the system. One may postulate that the general organization of the society has not changed in the last forty years, although the banking industry has been

modified in its details. One would expect that technological innovations in today's society spread in a manner analagous to bank closures in that earlier period, probably at a some- what accelerated rate.

The data, listed in the appendix, include the date of closure of individual banks, and the latitude, longitude,

and population of the towns in which these banks were located, as reported during a six month period. There are thus 714 observations. This is quite inadequate, but even this was difficult to obtain, the normal scientific situation.

The extensive geographical literature on innovation diffusion suggests two types of hypotheses. There is the neighborhood contact process so adequately described by Hagerstrand. Then there is the pattern of spread through the central place hierarchy. Probably both processes are

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... 2 ...

involved. In the first instance, one attempts to estimate the parameters of a stochastic version of the classical diffusion equation,

There is also epidemiological literature which takes this tack and which may be relevant; each bank closure may be considered an event in the spread of an, "epidemic^{II •} There are many possible analogies here: only the worst cases are reported, there is probably an incubation period, etc. Un- fortunately, the population at risk is not well known.

Apparently nobody bothered to count the number of banks in the United States. In many cases the data do include the date of reopening of the banks. One might thus wish to test a version of the wave hypothesis:

The idea being that the financial shock wave passes on with some finite velocity. Examination of the data reveals a pattern of simultaneous bank closures on most days which tends to complicate the analysis.

The hierarchical model asserts that events propagate

from high order central places to their lower order neighbors.

The most detailed models are those suggested ?y Hudson.

Evidence for this hypothesis might be revealed, inter 'alia, by the occurance of bank closures at larger places before closures at smaller neighboring places. Presumably this would correspond, at least roughly, to the relations within the banking industry.

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- 3 ~

Only crude tests of both types of hypotheses are pre~

sented here. Figures I and II show that the preient data, with the detailed locations of the banks, covers only a small portion of the event. The next figures illustrate the geographical spread. These maps do not,show a strong directional movement during the short time period for which we have data.

Viewing the same data on a cathode ray tube in the correct temporal sequence -- a simulated movie, or dynamic cartogra- phy -- also does not leave one with the impression of simple spatial spread. A linear regression suggests a westward

movement of 0.84 km per day, and a northward movement of 0.40 km per day, consistent with Losch's statement, but the corre- lations are too low to be important (r² = 7%, approximately, in both cases). Nor is any trend relating city size and the date of bank closure discernable. A similar conclusion is reached for the 156 banks for which both opening and closing dates are observed. The only strong correlation which emerged was that the earlier a bank closed, the longer i t stayed

closed. This strong (r²

=

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=

¹⁵⁶⁾ linear reiation presumably measures the marginality of these enterprises. The data have not been examined for any particularistic effects as might be observed from looking at the detailed inter-industry connections, nor has a test for spatial randomness been applied.

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LITERATURE

Anon. The Banking Situation in the United States. New York:

Industrial Conference Board, 1932.

Bailey, N. The Mathematical Theory of Epidemics. New York:

Hafner, 1957.

"Stochastic Birth, Death, and Migration Processes for Spatially Distributed Populations", Biometrika 55

(1968), pp. 189-98.

Beatty, M. A. Bank Failures in the District of Columbia in

- - --

^" ^{, -}

the Twentieth Century. Washington: Catholic University of American Press, 1949.

Bremer, C. D. American Bank Failur~s. New York: Columbia University Press, 1935.

Brown, L. Diffusion Processes and Location. philadelphia:

Regional Science Research Institute, 1968.

Casetti, E., and R. Semple. "Concerning the Testing of Spatial Diffusion Hypotheses", Geographical Analysis, 1 (19 69), pp. 254 - 59.

Galbraith, J. K. The Great Crash: 1929.

.

Boston: Houghton- Mifflin, 1955.

Griliches, Z. "Hybrid Corn: An Exploration in the Economics of Technological Change", Econometrica 25 (1957), pp.

501 ... 22.

Hagerstrand, T. Innovation Diffusion as a Spatial Process.

Chicago: Univ. of Chicago Press, trans~ation, 1967.

"A Monte Carlo Approach to Diffusion", in B.

Berry

&

D. Marble (eds), Spatial Analysis, New York:

Prentice-Hall, 1968.

Hagerstrand, T. The Propagation of Innovation Waves._, Lund, Lund Series in Geography, Series B, No.4, 1952.

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Harvey, D. W. "Geographic Processes and the Analysis of Point Patterns: Testing a Diffusional Model by Quadrat Sampling", Transactions and Papers, Institute of British, . - Geographers, 40 (1966), pp. 80 - 95.

Hotelling, H. "A Mathematical Theory of Migration", M. A.

Thesis, Seattle: University of Washington, 1922.

Hudson, J. "Diffusion in a Central Place System", Geograph- ical Analysis, 1 (1969), pp. 45 - 58.

Geographical Diffusion Theory. Evanston: Dept.

of Geography, Northwestern University, 1973.

Lieberson, S. , and Schwirian, K. , "Banking Functions as an Index of Inter-City Relations", J. of Regional Science,

- -

IV, 1 (1962) , pp 69

-

^81.

Losch, A. The Economics of Location. New York: Wiley, 1967.

Morrill, R. "Waves of Spatial Diffusion", Journal of Regional Science, 8 (1969), pp. 1 - 18.

Nadler, M. and J. I. Bogen. The Banking Crisis. New York:

Dodd, Mead, & Co., 1933.

Pred, A. "Large City Interdependence and the Preelectronic Diffusion of Innovations in the U.S.", Geographical Analysis, 3 (1971), pp. 165- 81.

Pyle, G. F. "The Diffusion of Cholera in the United States in the Nineteenth Century", Geographical Analysis, 1 (1969), pp. 59 - 75.

Rashevsky, N. Looking at History Through Mathematics. Cambridge:

MIT Press, 1968.

Rodkey, R. G. "State Bank Failures in Michigan", Michigan Business Studies, VII, 2, (1935).

Tobler, W. R. "Geographical Filters and Their Inverses", Geographical Analysis, 1 (1969), pp. 234 - 53.

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Tobler, W. R., "A Computer Movie Simulating Urban Growth in the Detroit Region", Economic Geography, _26~ 2 (1970), pp. 234 - 240~

"Of Maps and Matrices", Journal of Regional Science, 7 (1967), pp. 275 -

8d.

Tobler, W. R. and B. Barton. "Spectral Analysis of Inno- vation Diffusion", Geographical Analysis, 3 (1971), pp.

182 - 201.

Upham, C. B., and E. Lamke. Closed and Distressed Banks.

Washington: The Bookings Institution, 1934.

Utterback, J. M., "Innovation in Industry and the Diffusion of Technology", Science, 183 (15 Feb. 1974), pp. 620 - 626.

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DATA APPENDIX

Dates and locations of bank closings are taken from;

Polk Co., Monthly Bulletin, supplemental to Polk's Bankers Encyclopedia, Polks Bank Information Service, 75th ed., no 6, (August 1932), pp.

4 - 21; "Reported Conpolidations, Liquidations, Changes of Title, etc."

This source was locatyd by H. Woods Bowman of the Federal Reserve Bank of Chicago, and to whom I wisn tq acknowledge this debt. Copies covering other time periods have not been located.

Latitude and longitude and 1930 census populations were added and the detail coding was done by H. Dupree and J. Kahimbaara,

students at the University of Michigan. Bank closures without dates, or in towns which could not be located were omitted.

Partial support was received under National Science Foundation Grant GS 34070X.

KEY

A) Number of days from 1 January 1931 to closing of bank B) Number of days closed, if reopening date known.

C) Number of days from 1 Jan. 1931 to reopening. 900 = reopening not noted.

D) 1930 population

E) Arbitrary sequence number, corresponds to position in Polk F) X, Y map projection coordinates in kilometers

G) Latitude and longitude, in decimal degrees H) Date of bank closing

I) Date of bank reopening, if known J) Name of town, state

(3I3, I7, 13, 2F6.0, F6.3, F8.3, 2(A2,A4), 5A4, 13)

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