The basic method by which receipts from tithes sold for cash are turned into estimates of grain output is described in chapters 1 and 2. This appendix deals with the technical aspects of estimating aggregate arable output in the Durham Priory parishes. The historiography of the method of deflating cash tithe receipt data has been described elsewhere and therefore the discussion here is confined to the method itself. The first section deals with problems associated with indexing and the second examines the impact of a number of unknown factors on the series.

Indexing

The Durham monks collected tithes from around sixty different townships, combined in a variety of ways, but data do not survive from all these units for every single year. As a result, there are many separate series of cash tithe receipts from townships, or groups of townships, all with lots of gaps. This means aggregate income from tithes sold for cash calculated by summing all individual cash receipts for each year would be unrelated to fluctuations in the sale price of tithe corn because some townships would be included one year and excluded the next. The only solution to this problem is indexing, that is expressing each tithe receipt as a percentage of some earlier level. If the tithe receipt from each township for each year is expressed as an index then all the indices can be averaged annually and a series of comparable indices running from one year to the next is created. In order for the indices to be representative of cash tithe receipts throughout the Durham Priory parishes, only years for which ten or more individual receipts survive have been used in the series. The annual average number of cash tithe receipts used to calculate the indices is over forty.

Indices require a base year. It is not possible to use just one fixed base year for the whole series since the combinations of townships from which tithe was collected change across this long period.