Pasture yields

This concerns the 'Devon Rents' paper. The analysis we have done for 648 parishes in six counties in south-west England has used only the arable rent and the wheat yield. But many of the parishes were right in the middle of prime sheep and cattle-raising areas, and in fact livestock farming would have been more important in 1836 than wheat farming. I haven't analysed the livestock sector for the parishes because a lot of the data is missing for livestock: we have livestock yields and livestock rents only for one county, Devon. We don't have livestock yields for the other counties. It is very tricky to calculate livestock yields, so that is probably why  the Inspector didn't bother. But we do have livestock rents, which for the Inspector would have been much easier to record; he would just have written them down.

So we aren't currently making use of the livestock rent data...which seems a shame. Hate to waste data! This morning I was out running and I thought of a way that we would use the livestock rent data. We know the livestock yields AND the livestock rent for Devon (n =96). Could we use the mathematical relationship that we know for Devon yields and rents to construct a simulation for the other counties? We know the soil, the rainfall, distance to market town----perhaps this is enough to calculate the relationship between rent and simulated yield for our other 600+ parishes? This would be a significant contribution to the literature. And the applications to developing countries are obvious.

A distance to market mystery!

I have been working on the geographically-weighted regression tool, exploring the spatial distribution of the various explanatory variables in the 'Devon rents' paper.  One variable is distance to the nearest market town of the parish. When I was doing 'ordinary' regression this particular variable caused me some grief because it wasn't always significant. It kept changing its sign depending on the size of the dataset. The theory holds that the sign should be negative. Greater distance to market should lower the rent. Below is a map of the signs and coefficients of the market distances for the parishes. Some areas, notably to the west and the northeast (Devon and Herefordshire) are respectably negative, but Somerset and Dorset are positive. How can being  further from the market increase your rent?

 Red and ochre colour are positive for market distance, blue and dark blue are (respectable and what we like!) negatives. I can only think that this result is connected somehow with transport to market over longer distance, or integration into the wider market. If you are putting cattle and wheat onto railways and canals, the distance to the nearest market town doesn't matter. Next step is to control for soil and climatic conditions. Fascinating!

Five railway 'panels' significant

Malcolm just sent me the lengths of railway track for the fifth estate---Tavistock. Tavistock is away down in the south-west of England in Devon. I was interested to test for this estate because it took longer for the railway to reach down into this relatively remote part of England. Below is a graph showing track mileage for Tavistock and for Dalemain.

Track mileage for Dalemain (in the north-east) and Tavistock (in the south-west)

I'm pleased to say that the results remain highly significant, regressing rent per acre against wheat and cattle prices, and length of track. This regression is 'longitudinal' over the years 1832-1899 with five 'panels', one for each estate. Next step is to add one further estate (Badminton) and then adjust the track amounts with some new data for 1872. I also want to include some data specific to each estate, such as yields, but there are no consistent and reliable time-series for this. It might be possible to 'control' for climatic conditions, such as average rainfall, but this might not be worth the work. With at least one more estate we already have a good outcome.

Now I am working on the structure of the paper and I will post a draft on Google docs for you to read and comment on very shortly.

Geographically Weighted Regression

I finally found out how to do geographically weighted regression! This allows us to look at local changes in a statistical relationship. I tried out the technique by regressing the natural log of arable rent against the natural log of wheat yield. The coefficient on wheat yield will give us the elasticity: the percentage that arable rent changes for a certain percentage of wheat yield. Elasticity is a commonly-used measurement in economics....often used for price and demand. So if a 100% percentage decrease in price for some item caused the demand for that item to double (go up 100%) , we could say that the elasticity was one, or unitary.  I have used elasticity to try to show how much the landlord keeps from the rent. Here is a map indicating the coefficient for the natural log of wheat yield, or the elasticity. To the west, the elasticity is lowest, but rises gradually as we move to the east, towards London. Just why we should see this very clear trend is highly interesting. Any ideas?

Cartogram of arable rents and wheat yields

I have been learning how to use some free software called Geoda. Frankly, it is not easy! So far I have constructed two cartogram of arable rent and wheat yields. Cartograms aren't really maps: they represent quantities of interest. Here they are:

The top one is wheat yield and the bottom one is rent. I find it interesting that the red dots don't match: red represents a large positive outlier, green represents normal. So we have quite a few instances of high rents, but rather fewer of high yields. So some landlords were extracting high rents when the yields were only normal. Now, let's not get too carried away with blaming landlords: there might have been other factors, such as closeness to the market. Anyway that is something to test.

The parishes and Thorndon added to panel data

Two advances today:

1. Finally worked out how to join the dataset that Malcolm has been so patiently preparing to the map of the locations of the parishes. The result is below. Looks a bit as though south-west England is suffering from chicken-pox! We have the data on arable rents, yields, distances to nearest market-town and elevations for these parishes, nearly 800 of them. We have already done the basic statistics and found that there is a very strong relationship between rent, yields, distance and elevations. We also found that the elasticity of rent to what the farmer took home increased markedly as we moved east towards London. I don't know why that should be, but I suspect it might be connected to the amount of 'enclosure' that went on in the area. I'll work on that idea. Next step is to use some free software called Geoda to calculate the 'spatial lag', which is the grouping together of rents. Here's the map and then below some notes on Thorndon.

The 800 (or so!) parishes in south-west England: data from the 1836 Tithe Files

 2. The 'railways' paper: Malcolm calculated the amount of track laid on an annual cumulative basis for Thorndon, the fourth of the estates. Thorndon is in Essex, right over on the east coast, not far north of London. As a result, they had railway track early on. I added Thorndon to the other three estates in the panel data set, and I'm delighted to say that the results remain highly significant. It is clear that landlords were extracting the savings from their tenants----but hey! what else is new? Mi has found me useful information on yields which is part of the estate-specific information I will begin adding to the dataset. Think of it this way: we want to isolate the impact of just one factor---track---so we need to hold steady anything else that might have an effect on rents. This is what we can do with panel-data regression and that's why it is such a powerful tool. So much is done with regression....learn it whenever you get a chance. It will be really useful to you. I'll teach you if you like.

Population growths

Mi has helped me to calculate the annual population total for three counties: Cumberland (where the Dalemain estate lies), Norfolk (Holkham Hall) and Sussex (Petworth). There is a graph below. Since the area of the county, didn't change, we can use the population figures as representing population densities. I tried including population density in the panel data regression, but it wasn't significant. I think we'll try the population size of the nearest market town to the estate. That worked well for the 'Devon' data. Take a look at the graph: can you see that the population of Sussex more than doubled in half a century? This huge growth meant many more mouths to feed and so required agriculture to increase its yields. The area of cultivatable land is fixed and so the only way to increase output is to increase the yields. This is a close parallel to the world situation today: food prices are climbing because the global population is swelling. That's one reason why the work we are doing has relevance.
I'll spend today at UBC getting more maps of railway construction: the Victorians helped solve their food problem by transporting agricultural output more efficiently. Lessons to be learned!