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!