Wednesday, January 5, 2011

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.

Tuesday, January 4, 2011

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. 

Holkam Track Results

I've done a time-series regression of amount of track within a 40km radius of Holkham Hall against land rent, controlling for the price of wheat and cattle. I deflated the rent and the commodities to adjust for changes in the cost of living. The result is statistically significant, and I'd love to show you the output but can't work out how to paste it into the blog. Track and cattle have positive signs, but wheat is negative. Why should a drop in the wheat price result in increased rent..I don't know yet! I'll get there. The positive sign for Track is what we had expected to see: more track means increased rent. The savings are being extracted by the landowner. Recall that the equation for locational rent is

where m is the market price of the commodity, c the cost of production, E the yield, f the cost of transportation per unit distance and d the distance. As the distance increases, the right hand side gets smaller, so the rent gets smaller. Eventually the rent would be zero right on the edge of the cultivatable land. By increasing the amount of track, in effect the distance is getting smaller...so the rent goes up.


Encouraged by this, we're going to build a larger dataset. Malcolm is calculating the track for three more estates: Petworth, Thorndon and Dalemain. A graph of their rents is here:



You can see that there is a bump in the rents in the period around 1850----what a coincidence! Once we have the track data in, I'll do the same type of  regression, but this time it will be a panel-data longitudinal regression. This is a very powerful technique, which I'd urge you to learn if you see the chance.

Sunday, January 2, 2011

Track in 40km radius of Holkham Hall

Malcolm has done a wizard job of calculating the amount of track on an annual basis within a 40km radius of Holkham Hall in Norfolk. The graph is here:
Our hypothesis is that the availability of track would reduce the costs of farming to the tenant farmer, but that the landowner would grab the savings in the form of higher land rents---the 'resource extraction' theory.The next step is for me to test this using a time-series regression, controlling for other variables such as the price of wheat and the price of livestock. We need to hold steady the other variables so that we can isolate the effect of the reduced transport cost. Rent is the dependent variable and then the amount of track and the various prices are the independent (or 'explanatory' variables). The equation looks like this:

 
The regression is a time-series, and so we have to remove the effects of auto-correlation over time. I've omitted all the subscripts for time for clarity. We can use ARIMA for the regression. This is exciting and a great way to spend the holiday! Thanks Malcolm for your speedy work. I'll be back with some statistical output shortly.

Saturday, January 1, 2011

New Year's update

So, we have four papers and a book (yes!) to finish off this year. Here is a little run-down job by job:

1. The 'political' paper is under peer review at the moment. Let me know if you want a copy. We showed that there was a strong statitistical relationship between the type of crops grown in a political constituency, the attendance at church of the residents, and how the MP for that constituency voted. The parliament of 1841 was very much about 'church and state' and so these findings make sense. We used some novel statistical techniques to get round the 'missing voter' problem. Many MPs didn't turn up for divisions and so our sample size is small. But we know all we need about the MP except for how he would have voted had he turned up. We want to keep this information, not toss it out. We used Anne Sartori's improvement on the Heckman procedure (he won a Nobel for that). Special kudos to Hugh (Salway) from the University of York in the UK for volunteering a huge amount of time and helping us with hard to get data. Come and visit us, Hugh!

2. The 'Devon rents' paper. Here we are using very old data: from the 1836 Tithe Commission. We find that in the county of Devon, there is an amazingly robust relationship between arable rent, wheat yields, elevation and distance to market town. This fits all the 'locational rent' theories: von Thunen, Ricardo etc. So not content with that, we want to see whether this relationship holds in neighbouring counties. Malcolm has built up a large dataset (n>600) of parishes in six contiguous (look it up!) counties. What is interesting is that some parts of the relationship change as we move east, seeming at first sight to indicate less reliance on local markets as we get closer to London. Makes sense. To test this, we'll be using a relatively new statistical technique called Geographically Weighted Regression. In regular regression, we are trying to estimate some 'global' parameter that fits throughout the statistical population. In GWR, we allow the parameter estimates to vary according to local conditions. I am keen to measure the elasticity between rent and what the tenant farmer could take home to his wife and kids: in other words, were some landlords greedier than others, and if so, why? I am half-hopeful that we'll see the hand of the Anglican Church behind all this, but mustn't get my hopes up.

3. The 'railways and rents' paper. A huge amount of track construction went on in 'our' period, see the graph below. This must have had some impact on farming. James Caird, writing in 1851, makes an intriguing reference to a Norfolk farmer saving four hundred pounds a year ( a lot. You could have bought a Bentley if they had made them then) because his cattle didn't lose weight when they went by rail; when he walked them to market they ended up quite thin. But amazingly there isn't much published on this. And I can see why. Getting the data is like pulling hen's teeth. Malcolm is figuring out the total amount of track in a 40km radius of Holkham Hall, Norfolk for the years 1836 to 1866 on an annual basis. And Mi is scouring the libraries of the world for any sort of references that might help. Here is the graph:.


Growth like this must have had consequences! We hypothesise that the tenant-farmer's savings would have been transferred to the landlord via an increased rent. This is the phenomenon of 'surplus extraction'. Generally you want to be the extractor, not the extracted. But the tenants were in a weak position....so we would expect to see their rents going up in tandem with better transportation. Mi has got us the rents, now we await Malcolm's annual track data. Then I'll use a time-series analysis procedure called ARIMA to test for linkage. If the Norfolk estate gives us a YES, we'll extend the procedure to other estates and use a panel-data approach. Nice cutting edge stuff.

4. The 'supply response' paper. In the 1870s, the price of wheat fell dramatically because those blasted Americans opened up their railroads and shipped in wheat below the domestic price. See the graph of wheat prices below. Quite shocking: halved in price in less than two decades.
Look what has happened: wheat has halved but livestock numbers have shot up. This look like a structural shift in agriculture. But this is at the national level....individual farmers won't all have been able to shift out of wheat and into livestock.  We hypothesise that those estates which were more flexible with what the tenants did with their land probably didn't need to drop their rents as much as those estates which were more rigid. Farmers are not (always) stupid and can adapt pretty well to changing market conditions. Different matter if they can't adapt because of regulations on land use. We will test for a 'breakpoint' in rents, and then use that year as an indicator. Going to borrow from medical statistics, normally for use in working out how long a patient has got to live. Again, nice cutting edge stuff.
5. A book! New idea, inspired by Sarah, one of my two fantastic sisters. This is historical fiction, in other words a story based on real people. The working title is 'Breaking Free From Dr Malthus' and the theme is how the heck did the farmers increase yields enough to allow enough folk to escape from the hard scrabble of agriculture to start off the Industrial Revolution. A new format...left hand side page is fiction, the facing right hand side is economic analysis and commentary on the the fiction. Including the highly exciting new field of neuro