Distance coefficients---positive?!!

Finally got it! I did two regressions:
Arable rent = arable yield + distance from London (and a bunch of other variables)
Pasture rent = pasture yield + distance from London

Agricultural location theory (and common sense) would tell us that the sign for yield should be positive (rent goes up for better land) and negative for distance from the main market. The further away you are, the more your transport costs, so your rent is less. So why was I getting negative signs for pasture (meaning livestock) and positive signs for arable? Seems contradictory. The pasture sign is fine---the animals had to walk all the way to London, so you would expect a negative. But arable?

I finally got it at about three this morning. Couldn't sleep. Wheat was produced in the eastern counties and the western counties were importers from the east. They could not produce enough to feed themselves. So those western producers who could grow wheat were in a sense protected by the distance. So the further you are away from London (which is close to the wheat-producing counties) the greater your arable rent.

I checked this by getting averages of wheat prices in 1820 for all counties (no data at the county level available for 1836). The map below shows that the west (darker colour for higher wheat prices) did have higher wheat prices. In effect Cornwall acted as a main market, which is why the prices are highest there. Here is the map.

London is the red dot to the east. The 588 parishes are coloured by their r-squared values. You can see there is patch of dark red (high r-squared) in north Devon/Somerset. Now I also made a graph of the regression coefficients for distance from London against distance from London. Here:

You can see that at the point closest to London (ie further from Cornwall) the regression coefficient is 0.00002. As we move towards Cornwall, the coefficient goes down to 0.000008, a reduction of 2.5 times. Notice the interest shape of the curve (which I think I can model). The 'straightest' or most linear section is between about 200,000 metres and 300,000 metres (marked with vertical red lines). It happens that our high r-squared values lie between these distances. The r-squared values are high because distance is being accurately incorporated.

It seems that the size of the coefficient is a function of distance. So if I can get the equation of the curve above, I can use integration to get the total cost of any journey....then plug that back into the regression. Hey the sun is finally shining!

Capitalisation in the southwest

Agriculture in the 1830s was very much in a state of change (does that make sense!), and one way of detecting rates of change on a regional basis is by calculating the ratio of farmers to the agricultural labourers employed. A higher ratio of employees to employer implies a greater degree of capitalisation. A smaller ratio means that much of the labour would have been supplied by the farmer and his family. Malcolm has found me the XY coordinates for 138 datapoints, and Amy and I have calculated the ratios. The datasource for the numbers of farmers and labourers is the 1851 census. Together we have created a 'surface' which interpolates between the 138 datapoint. The result is below. The surface is draped over an outline map of the southwest.

The darker the blue, the greater the ratio (goes from 0.97 to 14). There is an obvious pattern. The closer we go towards London, the higher the ratio. Similarly, the very low ratio in Cornwall seems to imply almost peasant subsistence. 

Update on the Devon rents paper

I haven't posted anything for about six months---so here is an update of the Devon rents paper. Here we have the data on 488 parishes in the southwest of England for the year 1836. We are trying to test the following five hypotheses:

H1: farmers were integrated into the national economy, even before the railways reduced transport costs
H2: agricultural rents were set  at levels predictable by agricultural location theory
H3: farmers considered weather risks when negotiating rent
H4: some landowners reduced rents in exchange for votes from their tenants
H5: the practice in the county of Devon of leasing agricultural land by auction increased rents in that county, other factors (such as land quality) being equal

I have finally managed to get a working regression, of arable rent against grain yield, elevation, distance to London and pasture rent for adjoining land. The coefficient of determination (r-squared) is a tad over 0.7, which is not at all bad (although of course I'd like it higher). I then used geographically-weighted regression to discover any regional differences in the regression coefficients. The result is below.

The colours represent different levels of r-squared, with red (in the green rectangle) being the highest. This means that for some reason the rents in the red parishes were set more closely in accordance with what agricultural location theory would predict. Why is this? Possible answers are:

1. There is a misspecification in the model, perhaps I've omitted a variable or two
2. John Knight bought 15,000 acres of Exmoor Forest in 1819, and that corresponds very closely to the green rectangle. Because he was a newcomer, the rents may have been set at more realistic levels
3. Agricultural leases in Devon were set by auction, in contrast to elsewhere. In this case we would expect the level of rent to reflect market conditions more closely than rents set arbitrarily.
4. More---I am working on this....but weather risk is an interesting possibility.

Just to keep you up to date. We are nearly there!