Railways and rent

So far we have twelve estates with kilometres of railway track counted up. In the regression we get very satisfactory results, which go to show that railway construction did indeed cut costs for farmers---but those savings were transferred to their landlords in the form of higher rents. However, in my readings I am finding some interesting differences between landlords. Some landlords had political ambitions and wished to be able to direct the votes of their tenants. As a result they under-rented...so the next research step is to try to find out which of our landlords had political ambitions, and then include this variable as a dummy variable. Then we can see the effect of politics on rent.

Coastal counties got cheaper wheat

I coded the counties with a dummy variable (0 = interior, 1 = coastal) so that I could test whether there was
any difference in the 'mark-up' according to whether a county importing wheat was on the coast or not.  A lot of wheat was shipped by coastal routes because that mode was often easier than using a horse and cart. I want to test for that. So

was the regression equation I used. On the left-hand side we have the dependent variable, the difference in wheat price between any one county and the source of the wheat, which was either Cambridgeshire or Lincolnshire. On the right-hand side is the intercept, then the coefficient for distance between the counties; the coefficient for amount of surplus or deficit in wheat for that county; and finally the dummy variable for 'coastal'.

As you can see from the output below, all the explanatory variables are statistically significant at the 95% level (p < 0.05). The coefficient for distance is positive, meaning that the further away, the higher the price difference. In effect this is giving us the transport rate for hauling wheat. It should be positive, makes sense doesn't it? Surplus/deficit has a negative sign. That means that the more surplus the county has, the smaller the price difference. Again, that makes sense. Why would a county pay more for wheat if they already have lots of it? The coastal dummy is the most interesting. It has a negative sign. So if you lived in a county on the coast, you paid less for wheat "other things being equal". We are 'controlling for" distance and surplus. So if we happened to have two counties, both the same with respect to distance and surplus, the one on the coast would pay less for wheat. Because they got more of their wheat through coastal shipping would seem to be a reasonable explanation! Can you see the power of these techniques? We can learn a huge amount just with a few bits of data scraped off the floor.

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.

Wheat price differentials surplus/deficit areas

Earlier I calculated the 'wheat flow' from counties where they grew more than they ate to counties which grew less wheat and more livestock. Recently I found extraordinarily detailed data which lists the wheat price by county only by year but by week within the year! I thought that the difference in wheat price between counties might be explicable just by some function of the distance between them. Turns out not to be so simple as that, but more interesting. The difference between counties is much more pronounced when there is a bad harvest. When the harvest is bad, the wheat exporting counties really take advantage and the prices in the importing counties surge. Sounds like the sort of behaviour we see over tickets to hockey games, doesn't it! So I worked out which counties had the most surplus (Lincolnshire and Cambridgeshire) and which had the biggest deficits (Lancashire and Middlesex). Then I subtracted Lincolnshire from Cambridgeshire...because if my theory os correct, the gap between the two surplus counties shouldn't change much. Then between the biggest surplus county (Lincolnshire) and the highest deficit county (Lancashire). If things are going my way, then the difference between these two should be accentuated in years of bad harvests. Sure enough, the red line really jumps in years when we know from old books that the harvest was poor. The years 1816/17 are a good example of this. 1800 looks dramatic, but we were at war with the French then (remember Napoleon?) and so there were all sorts of other factors involved. These results have a modern-day significance in terms of food security. Especially now as the world looks like it is running out of food. The events in Eqypt were basically triggered by high food prices. Learn from history! Next step is to try to quantify the effect. This is fun!

Relationship between flow and price in wheat

Negative relationship between surplus/deficit

In my last post I presented a map showing counties which were in surplus or deficit. I am convinced there is a relationship between price and surplus or deficit, with the price difference between counties being due to transport costs. I regressed (there you are again!) the flow against the wheat price, and found a strong statistical relationship (p=0.007). Here is a scatterplot which admittedly looks---well, scattered! But you can tell by eye that the relationship is negative. The greater the deficit, shown by having a negative sign on the y axis, the more you pay for wheat, price of wheat on the x axis. Now I need to try somehow to build a mathematical relationship between flow, distances travelled, and wheat prices. If I can find this relationship, then I can set it to zero on one side of the equation to find the 'limit of cultivation'. If that limit happens to be the border between Devon and Somerset----problem solved and game over!

Wheat price betrween farm and market

Wheat movements

England is rather regional in wheat production. But of course consumption of wheat (typically in the form of bread) is not regional. Everybody likes a toasted bagel! So that meant that wheat had to be moved (by horse and cart usually) from areas where production exceeded consumption to areas where they ate more than they grew. I've added surplus and deficit to the map...so red areas exported wheat to areas in deficit. I have looked at wheat price records for 1760-1820 trying to associate surplus/deficit with difference in price. Sure enough, areas with surplus had a lower wheat price than areas with a big deficit. The graph below shows the wheat price for Lincoln and Norfolk (big surplus) and Lancashire and Devon (deficit). As you can see, surplus areas were pretty much always cheaper than deficit areas. Isn't it interesting how correlated the prices are? The gap between them is remarkably consistent. So, it might be reasonable to suppose that this gap is due to the cost of moving the grain from one county to another. If this was the case, then we could work out the distance and from that get the transport costs per unit of distance. We would do this by (our friend!) regression, something like this:

difference in prices between two counties = intercept + beta1*distance

beta 1 would be the transport costs.

(Now, I've linked the word 'regression' here to a Youtube video I've done in case you need a little revision). Take a look!

Remarkable price correlations

Why do we want to know this? Look at Devon. It's wheat cost is very high and it is also furthest from the big wheat producing areas. We have also found that 'distance to market' sign changes around the Devon/Somerset border. It could just be that this is the point where wheat brought in from Norfolk etc is just too expensive because of transport costs. This leaves the local farmers in control of their own market, so distance to market becomes important. Just a thought!

Wheat Prices and Geography

Mean wheat price 1760-1820

Last post, I showed how the prices of wheat in the counties of interest (Cornwall, Devon, Dorset and Somerset) all seemed pretty much in lock-step over the period 1760-1820, although Somerset seemed marginally higher. Now I've calculated the mean for the whole period for most English counties and plotted them on the map. The darker the green, the higher the price. Originally I thought this might be connected somehow with London, but it isn't. The big wheat growing areas in England then and now are the flat areas in the east (Norfolk, Essex, Cambridgeshire). Our counties of interest didn't really produce much wheat. So you can see that the greater the local wheat production, the lower the price. Or put it another way, if you live far away from the area of production you pay more because of the cost of that horse and cart. The area within the red pencilled bit is the wheat-growing heartland. See how the price of wheat goes up the further away you are. Except for Cornwall! Those people down in the extreme south-west have always gone their own way!

Wheat price coordination

Wheat price yearly averages for four counties

In a recent post about the theory of agricultural location, I missed out the definition of 'P' in Dunn's equation...thanks Mi for pointing this out. P is the price of the commodity (e.g. wheat) at the market. I've corrected the omission. Mi's remark made me think about the variation in wheat prices on a locality basis. If the wheat price varies from point to point, then Dunn's equation gets more complicated. I've found a remarkable set of wheat prices by county which last from 1770 1820. I have been looking at these to see what regional difference there might be. On the graph I've plotted the yearly mean price for our four counties of interest. Interesting things: the wheat prices converge when the variation is small. But when there are peaks (for example a huge jump in 1800) then there is considerable divergence. And it is always Somerset that is most expensive. Cornwall is always cheapest, with the two counties between them geographically, also between them with regard to price. I'd guess that this effect is caused by proximity to London. London was a major market, with about 14% of the population living there. This is really interesting (isn't it?).

Sunshine and wheat yields

Malcolm has been plugging away at data from the UK Meteorological Office, calculating mean hours of sunshine in August for our 715 parishes. Now, the data comes from earlier last century and not from 1836, when the wheat yields were recorded, but that’s the best we can do.

August sunshine is a critical factor in wheat yields: best is hot of course, allowing the ear to ripen fully before harvest. I’ve done a regression of wheat yields against hours of sunshine in August, as well as the other data we have: elevation, amounts of rainfall in different groupings. There is a map of sunshine to the right and the regression output is below. The map is interesting, because you can see the parishes in bright yellow, indicating the most sunshine. Along the coasts, and down to the tip of Cornwall. And of course this matches up with where people like to go on holiday. The best wheat yields come from Somerset, inland and with plenty of August sunshine.

Here is the regression output. Elevation has a negative sign, meaning less yield with height. Sunshine is positive...as expected. Rainfall is negative above a certain amount. More than 1000 mm in a year waterlogs the wheat plant. This is not a bad result at all, and it will improve once I get data for soil types and amounts of available water into the regression.

Statement of the theory!

We are trying to apply a combination of von Thunen’s rent and distance theory [1] and Ricardo’s rent and land fertility theories, using Dunn’s equation[2] from 1954:

where R is the rent for crop j at location i. E is the yield of crop i, and a is the production cost. k is the cost per unit distance of transporting crop j and d is the distance from the farm to the next commercial transit point (let’s call it CTP). P is the price of the crop at the market. This might be the mill, or a dealer’s yard---wherever the production next changes hands and where its value needs to be calculated.

The rent right next to the CTP will be highest because the distance is shortest. In the same way there will eventually be a ‘margin of cultivation’ where the cost of transport exactly equals the revenue from production. So at this point the rent will be zero. Farmers will bid for the use of the land at any point along a bid curve we construct just by joining up rent at the CTP and rent at the margin of cultivation:

Farmers won’t bid for land if the rent is set at any point to the right of the red line: it is too expensive. Likewise, landowners won’t accept any offer to the left of the red line, because they think they can get a better offer.

In the empirical testing we have been doing, we found that Dunn’s equation worked very well for Cornwall, Devon and Dorset. So far so good. But when I tried to include counties to the east, such as Somerset, the results were no longer statistically significant. In particular, the regression results gave a POSITIVE sign for Ekd, on the right hand side whereas it should (the theory goes) be negative.

In the literature I found several theoretical reasons for why this might happen. First:  worker wages are less further out from the CTP. So this would mean a reduction in ‘a’ in the equation, making the net revenue greater the further away from the CTP. (We see this happening in contemporary business: that’s why firms ‘outsource’ to China and India). Second: the perception of the farmer as to future harvests might differ from place to place. If he/she thinks that the weather will make yields highly variable, then he/she probably won’t bid as much for the land [3]. This second reason is why I have been getting you working on meteorological data these last few weeks.

But actually----I think the solution is simpler (they usually are). I have been mis-specifying the model. Instead of just distance to nearest market town (which worked well enough for Devon), I should have been thinking about the ‘connectivity’ of the towns and villages. The network density of the county/area in which the farm was. If it was highly interconnected with several different routes to the next town, then we would expect the rent to be higher, because the flow of goods in any direction would be less. Just have to figure out how to do that. Less reliance on distance to market town and more on how the towns were all connected together.

[1] von Thunen, J.H. Von Thunen's' Isolated State': An English Edition Pergamon, 1966.

[2] Dunn, E.S. The location of agricultural production University of Florida Press, Gainesville, FL, 1954.
[3] Cromley, R.G. "The von Thünen model and environmental uncertainty." Annals of the Association of American Geographers 72 (1982):404-10.

Malcolm's comment on Cornish railways

Old Cornish tin-mine pumping station (Wikipedia, Tim Corsler)

Malcolm made a perceptive comment about why distance to market seemed to matter much more down in the 'toe' of Cornwall than in the lusher pastures of Somerset, well to the east. He thought this might have something to do with railways. This is interesting, because railways did develop early on in Cornwall, but mostly for the freighting of minerals, especially tin. The steam engine started off in Cornwall to pump water out of mines. The Cornish railway system was purely local though, and didn't get connected up with the rest of the system until the 1850s. What is interesting about Cornwall, and which Malcolm's comment made me think about, was the amount of food rioting that went on among the tin-miners. As the linked text notes, the rioters were isolated groups of non-local non-farmers who suffered when food prices went up. This isn't just history: we're seeing the same thing these last few weeks in Tunisia and Eqypt. Underlying the protests are concerns about high food prices, caused by stock-piling, poor harvests (possibly climate-change driven though this is risky speculation) and the large amount of food production being converted into ethanol (primarily in the US). There is an article here from the British Daily Telegraph about the world being one poor harvest away from chaos. History does repeat itself, and only fools don't learn from the past.

Market distance signs: a clear break

I used geographically-weighted regression to get location specific coefficients for market distance in the regression: Rent = wheat yield + market-town population + distance to market-town. As I have gone on and on about before, the theory is that there should be a negative sign for distance, because the further you are from your market, the more it costs you to truck your produce in on market day. The fact that this sign changes has been perplexing me...and there is something interesting going on here. Look at the map below.  Can you see that the locations to the west of that thick red line have a negative sign, those to the right a positive sign? I did put a marking on the map but it is a little faint. Wow! Such a clear boundary. But why is it there and not a few kilometres to the west or east for that matter? What are factors that decide the location of this line? Interesting!

Mountains and food security

Just been reading a really interesting article about food supply chains in mountainous areas. The ideas behind the article...in mountainous areas you rely more on your neighbours etc, could apply to any time period. The article is a bit light on theory and math, but it gave me the idea that perhaps Devon was unusually reliant on local food markets. That is why the sign for distance to market is so resolutely negative. So it is not Somerset that is the odd county out for having a positive sign for distance to market....it is Devon because Devon was a bit cut off (in more ways than one) and relied on its local food markets. Here is a map of population density and slopes. The population density I got by looking at the 1831 census and then dividing the number of inhabitants by the area of the county. Having less than one person per square kilometre seems unimaginably empty to us now.

You can see how fewer people and big slopes go together. So in Devon they would have felt pretty isolated, and so relied on their local market towns. I think I'll work on this theory for a bit. I've circled Devon in the map of southwest England below.

Density (in green) and slope (red for small, blue for big)

Water and wheat yield

I've been mapping topsoil water availability throughout the year and wheat yield. The relationship is clear: more water gives more yield. A more reliable indicator than rainfall. Here is a map with high water availability matched by high wheat yield.