Family #12 in the 1767 Grimm census.
Family #94 in the 1775 Grimm census.
Family #35 in the 1798 Grimm census.
Father unlinked: Christoph Rau
Mother unlinked: Unknown Unknown
1767 Grimm Census 
The first bit of confusion is in the 1767 census, when it refers to his daughter as Anna Margaretha, age 12, so born about 1755. More on this daughter later.
The AHSGR Origins project says:
The Immigration of German Colonists to Denmark and Their Subsequent Emigration to Russia in the Years 1759-1766 lists four Rau families, but none is a match for Balthasar Rau of this profile.  I checked for misspellings or alternate spellings of the name, also with no luck.
There is a Balzer Rau listed in the Kulberg Reports, and it appears to be a match with the 1767 census entry. 
The family arrived in Russia on 22 July 1766 via the pink "Lev."  No ages are listed for Balzer and his wife Maria. There is no mention of the family in the Volga German Transportation List.  The one possible misspelling of the name as Rausch is not a match.
The reference above from the Kulberg Reports mentions a two-month old daughter named Susanna, but she is missing from the 1767 Grimm census. She most likely did not survive the winter in St. Petersburg or the journey to the Volga River region.
By 1775, he is listed in the Grimm census as Balthasar. No doubt Balzer was a nickname used by some people. At the time of the census, he was 45. He has a different wife, presumably wife number two: Elisabeth with no last name given, age 46. The only children from the Kulberg Reports who are still listed with the family are (Heinrich) Johann Philipp, age 8, and Juliana, age 16. Eldest son Heinrich and daughter Anna are missing...unless Anna Margaretha was the wife of David Lutz, misidentified in this census as his Balthasar's sister and brother-in-law, in which case she is still identified as living with the family.
1775 Grimm Census 
Now, back to Anna Margaretha Lutz. The 1775 census says that also living with Balthasar was his brother-in-law, David Lutz, and David's wife Anna Margaretha, who is the same age as Balthasar's daughter Anna Margaretha. Was this an error by the census taker, referring to David Lutz as his brother-in-law instead of his son-in-law? Or does Balthasar really have a sister or half-sister who was the same name and age as his own daughter? Or is David Lutz Balthasar's brother-in-law from some other relationship? Maybe the brother of his own first wife who is identified in the Kulberg Reports as Maria. Was Balthasar's wife's name at birth Maria Lutz?
A census-taker error seems the most likely reason for the confusion. For the purpose of this single family tree, I am listing Anna Margaretha, Balthasar's daughter born in 1755-1757, as the wife of David Lutz. If I learn otherwise, I will update Anna Margaretha's parents as needed.
Balthasar's first wife Maria may have died due to complications from the birth of her youngest child, Johann Georg Philipp, who by 1775 was going by simply Johann Philipp. She also may not have survived those early years in Grimm, which were subject to hostile interaction by the native Cossacks. Whatever the case, Balthasar probably remarried quickly because of his infant son. Because second wife Elisabeth was 46 years old, she had probably been married before and lost her husband on the journey to the Volga. She may have had children from her first marriage also living in Grimm or another Volga village.
By 1798, Balthasar was 67 and once again a widower. His son Philip and his wife Anna Katharina Stoll lived with him, along with five grandchildren
1798 Grimm Census 
By 1834, Balthasar is no longer listed with his family in the census. His son Johann Philipp Rau had been named the new head of the household, and when he died in 1831, Philipp's son Johann Wilhelm took on that role. Had Balthasar survived, he would have been 104 years old.
1834 Grimm Census 
Since Balthasar's name was not included in the 1834 census, even if simply to announce his death, it suggests that Balthasar died before the 1816 male-only census was taken. Once a male's name was listed as deceased, it was not repeated in the next census. A copy of his death record from the Lutheran Church in Grimm would reveal his death details, but those records have not yet been transcribed and are not available to the public.
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