Difference in wheat market prices by distance

I came across a really special dataset that has wheat (and other grain) prices by the week from 1760 to 1820 for every one of the 40+ English counties. Think of the work some dedicated soul did in copying out all those numbers! I used this dataset in a recent post to show that wheat prices varied quite a lot, especially by 'demand', ie whether the destination market was in surplus or deficit.

Malcolm's map showing wheat origins

Malcolm has kindly provided me with a set of measurments from the two major wheat producing counties (Cambridgeshire and Lincolnshire) to each of the counties. See Malcolm's map on the right. We know the price difference between the wheat exporting county and county of importation; the distance between the two; the mean elevation of the journey, and the standard deviation of the elevation of the journey. The last measurement is to proxy the 'roughness' of the journey. I figured that greater changes in the standard deviation would be more expensive for the horse and cart operators of that time, and so they would increase the prices accordingly. We only have about 35 observations, but the results are interesting. After some experimentation, I found that regressing the natural log of the price difference against the natural log of the distance produced an acceptable result (p=0.02). The scatter plot of log price difference on the x axis with log distance on the y axis is shown here, together with a trend line of predicted values.

Regression of log price diff against log distance

If we use logs in the regression, then we also have a measure of the elasticity. The coefficient from the regression is 0.47, which means that a one percent increase in distance increases the price difference by 0.47 per cent. (See how useful logs and elasticities are!). This is quite a lot, and more than I had expected. The other measurements, such as roughness of the journey, didn't seem to matter as much. Now I am going to move on to 'control' for other variables, such as whether or not the county was industrial/agricultural, or on the coast. Why should coastal be interesting? Quite a lot of wheat was shipped by coastal vessels, probably a lot cheaper than by land. More later.