Weather risk and the farmer

The 19th century farmer had much less control of the environment in which his crops were growing compared to modern farmers. But did weather risk get translated into different rents? After all, you'd expect a farmer who was wanting to rent land in an area where the weather was very changeable to try to negotiate a lower rent. It seems that the amount of rainfall in July matters a large amount for a grain crop such as wheat or barley. The coefficient of variation is a useful (and somewhat overlooked statistic). It is the standard deviation of a set of observations divided by their mean. So there are no units: it is just a percentage. Perfect for measuring "changeability" of weather. Malcolm kindly got me the CoV for July rainfall for 10 weather stations. I used GIS to interpolate between the stations, and then get the stretched values into the observations for our parishes. Then I ran a regression and --- wonderful news! --- CoV has a strong negative effect on rents. Greater CoV means lower rents. Below is a map of the southwest, showing the parishes and a raster of stretched CoV values. The highest CoVs are in the extreme southwest---that is Cornwall, well known for wet summers.

The pinkish bits have the lowest CoVs and it is no coincidence that wheat is grown there. The very wet areas are suitable for livestock and so that is where cattle and sheep raising went on.

Rent and distance from railway station

I am still working on the Railways Paper, trying to quantify the difference that an extra kilometre of railway track had on agricultural rents. The draft is very nearly finished, and I am hoping I can get the article into a journal such as Economic Geography.

So far I have found a significant relationship using two measures of the availability of railway track. One method is what I call the 'nearest station' method, which involves the measuring of the distance from the farm to the nearest railway station on an annual basis. As the railway was being built, it approached the farm. This meant that the farmer could put his animals into wagons for transport to market. He saved on the costs involved in droving the animals along roads (loss of weight, expenses and risk). So a reduction in distance to nearest station increased the rent...which is what we found. The other measure is the 'buffer' measure, which involves counting the total kilometres of railway track within a 40km radius of the farm. More track nearby raises the rent---it is easier to get your stuff to market. Greater "connectivity" in modern parlance.

Here are a couple of interesting graphs:

We have the rent rolls for 31 large estates. The graph shows the average rent and distance from nearest station. As theory predicts, rent is a declining function of distance. Now take a look at this one:

This is the distance between estate and nearest station over time. By 1860 or so, all the estates were within 10km of the nearest station. That accounts for the clustering around the 10 km mark in the first graph.

Surplus extraction!

Elasticity is a term used in economics to quantify the relationship between two variables in terms of percentages. Typically we use the price elasticity of demand. This means: “how many percent does demand change for a one per cent change in price?” If gas goes up ten per cent, how many per cent does demand change?

I am using elasticity to find how much agricultural rents changed for a change in price. This gives me an indication of how closely rents were oriented to market conditions. If landowners were setting their rents without really wanting to “squeeze” their tenants, then we would expect the elasticity to be small. Prices could change a lot, but the rent wouldn’t change very much. As the elasticity increases, this shows that landowners are beginning to set rents more competitively.

We can find elasticity using regression, if we first transform the variables to their natural logarithms. The coefficient is then the elasticity. I got a rent series for 1760 to 1840, and a price series, then did the transformation and the regression. Because I want to see the change in the coefficient over time, I used a technique called a ‘rolling’ regression. Here is the result:

You can see that the elasticity climbs up, reaching unity at about 1840. This is fascinating: landowners who were stuck with long leases during the time of big price increases during the Napoleonic Wars (ended 1815) got excluded from the windfall profits. So they renegotiated their leases to shorter ‘rack rent’ leases to scoop up the surplus. Greedy fellows, but we caught up with them!

The Ricardian method

The so-called Ricardian method has become quite popular in the last ten years as a way of trying to estimate the potential damage (or gains) to agriculture through climate change. It is usually a cross-sectional regression on land values (price of land per hectare or rent per hectare) and a bunch of exogenous variables. Records such as past wheat yields aren’t included. Then we can measure the impact of a change in a variable such as temperature or precipitation. Control variables, such as strength of the local economy are usually added.

I’ve been doing the same with the arable rents for the southwest of England in the early 19^th Century, but with recent meteorological data. There were no weather measurements taken then, and even if climate change has occurred in the period between 1835 and now, the change is likely to have been relative. The regression output is below, but here are some interesting points:

I include variables of interest, such as MARAIN (March rainfall) with their squares. That’s because there is a non-linear relationship. So for March rain, the regular unsquared variable has a negative sign, while the square is positive. The result of the combination on arable rents is a upward curve, meaning more rain was good in March. That is true: farmers want water in the ground to get the plant through to the summer.

But look at July rain. The signs are the opposite way round. The result is a curve, shown above. The recorded range of July rainfall in mm is on the x axis. The y axis is the rent. Some July rain is good, but then at about 52mm, that’s enough, thanks. The plant gets waterlogged and the forthcoming harvest is ruined.

Days of airfrost is fascinating: see the positive sign? Farmers wanted more days of airfrost back in 1835, because that is what killed the pests. No Roundup etc then. For soil, I put in dummies for different levels of clay. The negative signs mean that more clay lowers the rent. This seems counter-intuitive until one realises the connection with rainfall. Heavy clay soils tend to hold the water, generally good, unless you farm in a poorly drained area. Much of the southwest was just that. 

Agricultural production functions

Different types of agriculture have different manpower needs---at least they did in the early 19^th century. For a farm of any given size, less workers are required for livestock than for arable. Arable requires a lot of labour for sowing, weeding, harvesting, threshing and all the rest of it. So we might expect to see the number of workers per farmer increasing with an increasing share of arable. Now, here is the interesting thing. The ratio between arable and livestock changed with proximity to London, at least it did from the perspective of the southwest of England. The closer the farm was to London, the more arable. Cornwall, Devon , Dorset and Somerset were heavily into livestock.

So, how about we plot the ratio between arable and livestock against distance from London AND the ratio between number of labourers to farmers?  I have used lowess smoothing to get a single trend line from a mass of points. I have to say that I was really deeply surprised by the closeness of the two lines. And the best thing is that the data sources were entirely independent. The farmer to labourer ratio came from the 1851 Census records, and the arable to pasture ratio came from the 1836 Tithe Commission Files. The 'kink' at around 200km from London is the beginning of the heavily pastoral country, eastern part of Somerset. 

Von Thunen and intensification

JH von Thunen was a German farmer and economist who lived about 200 years ago (which makes him even older than me!). In the Devon rents paper, we successfully tested his theory that rents decline with distance from the market. He had another, less well-known theory. He argued that the intensity of agricultural production would increase the closer the farm was to the market. The rent would be higher, and so the farmer would 'work' his (or her!) land harder.

Amy and Malcolm,  you helped me to calculate the ratio between farmers and agricultural labourers, using data from the 1851 census. I built a shapefile using the locations and the ratios and then 'kriged' the shapefile to get an interpolated surface. I put the ratio values for each location into the observations for our 609 parishes in the southwest of England. Finally I plotted the ratio for each parish against its distance from London. The result is the graph below.

Isn't this fascinating? You can see quite plainly that the ratio decreases with increasing distance from London. The farmer employs less labour the further away he is from the market. The furthest distance represents Cornwall at the extreme west. There the ratio is very small, so probably most of the farmer's family were involved in work on the farm. Looks like von Thunen was right!

Direction for the railways paper

The focus of the ‘railways’ paper is a quantification of the amount of money saved by agriculture.  We are going to try to calculate the savings as a share of Gross National Product in the years 1850-1870.  Some previous studies (e.g. Hawke, 1970) conclude that the savings made by farmers using railways are “insignificant.”  Let’s test this!

Our methodology

1.      The graph shows the coefficient of the regression of rent against track length.  The coefficient provides the rent-per-acre increase for every extra kilometre of track within 40 km. of the estate.  The landlord is “extracting” this amount, equal to what the tenant farmer saves by using the railway.

2.      If we multiply the coefficient by number of acres by the length of track (year by year), this will give us the total amount saved. For example, take the year 1860. If a landowner had 1,000 acres, and in (say) 1860 200 km of track became available, then he would be able to gain an extra 1000*200*0.0002 = 40 pounds for that year and going on into the future. (I got the 0.0002 from reading off the graph).  But the point is that this saving is cumulative. We could (and we will!) go back to 1850, find the savings and then add that to the saving for 1851, and so on. The landowner gets the cumulative savings year after year. 

3.      At this point, we don’t care whether it was the landowner or the tenant who got the money.  It was saved, that’s enough.

4.      The result from paragraph 2 gives us the savings for our estates – now we need to extend this to the whole country.

5.      This isn’t too hard: Malcolm and I can calculate total track year by year, and Amy and I can find (where?!) total amount of pastoral land and cattle.

6.      The next step is to divide the total savings by the yearly GNP.

7.      Trying to get this done by the end of February!