An Empirical Study of Price Correlations: 2. The Decrease in Price Correlation with Distance and the Concept of Correlation Length
The dependence of the correlation between wheat price fluctuations on different markets with respect to the distance between those markets is investigated. It is shown that the decrease in the correlation is exponential and is governed by a characteristic distance which is called the correlation length for wheat prices. This is a measure of the level of market integration in a given area. The magnitude of the correlation length is compared for different cereals: wheat, rye, and oats, and the evolution of the correlation length during the 19th century is studied. In particular, it is observed that subsistence crises are characterised by a collective behaviour of the economy which results in a sudden peak in the correlation length. Last, the part played by the spatial correlation between precipitations is investigated. It appears to be rather small; consequently, the price-correlation length is primarily the result of economic factors.
Wheat Prices and Rainfall in Western Europe.
IN an article on “Weather and Harvest Cycles” in the Economic Journal of December last Sir William Beveridge gave index-numbers showing the fluctuation of wheat prices in each year from 1500 to 1869, and made a preliminary mathematical and arithmetical analysis of these figures with a view of discovering periodicity in the yield of harvests, which might be attributed to periodicity in the weather. In a paper read to the Royal Statistical Society on April 25, he has now given the results of a much fuller analysis, involving a test of the same figures by harmonic analysis, for the discovery of practically all possible periods between 2 and 84 years' length. The following is a summary of the paper.
A Spatial Analysis of Gravity Flows
Curry L. (1972) A spatial analysis of gravity flows, Reg. Studies 6, 131–147. Since Wilson gave theoretical substance to the gravity model, it is possible to treat it analytically. His derivation is discussed and calibration problems examined. In particular, the general constraints on the maximum entropy solution he obtains can be particularized. Here the association between the spatial distribution of jobs and homes is investigated using a spatial regression operator which is interpreted as the impulse response function of a second order difference equation. By using Z transforms, the regression and gravity operators are applied in paralle. Feedback from the resulting trip pattern allows the job-home relation to be changed sequentially. Measures of spatial entropy and joint information are introduced and related to travel entropy.