In England, local churches were required to keep registers of all baptisms, marriages and burials. Are there any studies that show how complete these records generally were, in particular in relation to the 1700s.
This is a certainly tricky question, however their have being many studies of the baptisms,marriages,deaths for one The east lake church history: http://www.eastleake-history.org.uk/church-records.html
This may help, as bill one of the priests donated 20 years discovering the truths of the church he has discovered before the 1700 and all the way to the year 1901.
I don't know about a full-fledged academic study, but there is a very detailed book about the parish records, published in 1910, The Parish Registers of England by J. Charles Cox. The entire book is in the public domain and may be found online at archive.org. It discusses some of the circumstances that may have led to gaps in the records.
In 1694 taxes were imposed on marriages, births, burials, bachelors, and widowers. Tax collectors read the registers to find out about these events, and there was a £100 penalty on ministers for neglect to register. So this would have been an incentive to get it right!
In 1695 there was a fine of 40s. on parents who neglected giving notice to the minister after a birth, and ministers were to be fined the same if they did not keep a reference of those born and not christened. But Cox says that this particular registration was "for the most part neglected," and an Act of Immunity was passed in 1706 to avoid impoverishing the clergy.
The Stamp Act of 1783 required a 3d. duty for every register entry, and Cox says it "was a direct inducement to defective registration."
Cox also writes,
I don't feel qualified to estimate how complete the records were in any authoritative sense, but I think Cox's book does give some insight into the completeness or lack thereof. In addition, it includes a lot of interesting entries from the registers. Perhaps this will help somewhat until someone shows up with further information.