Track, rent and causality

I have been working on the mathematical model for the relationship between the laying of railway track and changes in rent. A bit of a problem is showing that there is 'causality' between the two. How can we prove that track caused change in rent? The answer is we can't, and the whole area of causality is frankly speaking a philosophical minefield. It is extraordinarily difficult to show that one thing 'causes' another. For our purposes, the only tool we can use is Granger causality which tests the relationship using time. What we want to see is that rent changes AFTER a change in track, not simultaneously or even worse, before. Malcolm has just given me the track for our eighth estate and I have done the Granger test on all of the them. I'm pleased to say that they all scraped through, some only just. I limited the range of years from 1832-1882 which gives us a half-century. We don't have thorough track measurements for the period after 1872, and wheat and cattle prices were highly volatile in the 1880s. That's OK...we've made the point.

I've been using an interesting form of regression, called Vector Auto-Regression or VAR to get out the stats.  It is simply beautiful! Life doesn't get better than this!