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!

Track around 3 estates significant and elasticities

Two interesting advances today:

 1. For the 'railways and rents' paper:  I have built a 'panel' dataset using annual total railtrack in a 40km radius of three estates: Dalemain, Holkham Hall and Petworth. I regressed the rent against the track, cattle and wheat prices. The three independent variables---track, wheat and cattle---are all significant and with the 'right' signs. This is very satisfying. I'd like to get more data specific to each estate, such as yields etc. Mi is working on this. Soon we will develop a clear picture of how agricultural rents were set in the 19th century. This is something no one has tried before. The techniques will have analytical uses in developing countries where data is --- like 19th century Britain --- a bit sparse.


2. For the 'Devon rents' paper: I built a variable which represents the amount of money a farmer would get after he had paid his farming expenses. I regressed this, together with population of nearest market town and elevation, against rent. The results are highly significant. Then I built four 'windows' moving from west to east, so that I selected only the farms inside the windows. For each window I calculated the 'elasticity', which is the percentage change in rent for a percentage change in farmer's take-home money. I think (!) that this is a measure of the 'surplus extraction' of the landlord: how much he can 'squeeze' out his tenant. What is remarkable is that the elasticity changes as we move east towards London. It more than doubles over two hundred miles. This is a fascinating result, but at the moment I am at a loss as to how to explain it! I have put the elasticities into the relevant counties in the map below....not quite the same as the moving window but I can't see how else to show you.

It has been a good day. Thank you!

Distances to Market Decreasing With Longitude

I have been analysing data from about 700 parishes in the southwest of England, looking for patterns of how rent was set in the 1830s. The relationship between arable rent and wheat and barley yields is very strong, as we would expect. I started off the analysis with 96 parishes in Devon, in the far southwest of England. Here the relationship between rent and distance to market is very clear....further from market the lower the rent. Over the holidays, Malcolm helped me to increase the dataset, moving east towards London. The larger dataset was initially puzzling, because distance to market was no longer significant and had a positive sign. This morning I regressed distance to market against longitude and found that distance to market decreases as we move east towards London. In other words, there is a higher population density and so the farmer doesn't have to cart his produce so far to sell it. Here is a scatter plot with the regression trend line:

Now, I'll be the first to agree that this looks pretty much like wasps around a honey jar: BUT the relationship is statistically highly significant although with very little explanatory power (r-squared is small). I think this negative relationship goes towards explaining my initially confusing results. [Obvious when you think about it, which is (probably) what Newton thought after the apple landed on his head. ]

I did some more probing and found that the sign for market distance changes from negative and significant to either positive or not significant at about longitude= - 3.25. This is close to the eastern borders of our two western counties. Next step is to go to the 1841 census files and get population densities for the six counties we have been analysing. Clearly it wouldn't be a huge surprise if distance to market correlated with population density.

Dalemain Results

Malcolm has calculated the track for Dalemain, an estate in the north of England noted for sheep and cattle raising. The results look significant: the graph below shows the actual rent and the rent predicted by the regression model. Not bad....but I need to use some deflated prices and more localised variables, such as population density.

Google ngram as a research tool

There is a highly useful Google tool here:
http://ngrams.googlelabs.com/

which allows you to search for a word or phrase through all those books that Google has been scanning and also track the rise and fall of the word or phrase over time. You can select by language and bracket by years. And at the bottom of the graph there is a clickable link to the original books. Naturally I immediately tried 'agriculture','railway' for 1800-1870 and found some useful source documents. Might help you.