I am writing a novel on Microsoft Word 2016. Does it give a correct word count that I can tell to my publisher?
Different tools use different algorithms to count words in a document.
For example, Apple's Pages counts
2-7 mg/v as four words while Microsoft Word counts the same string as two words. Or if for some reason you have a space between a word and the punctuation that ends a sentence:
Bla bla !, Word will count the punctuation mark as a word. And then there are the settings that will include headers, tables, and footnotes into the word count, or not. And so on.
But the truth is that unless you are paid by the word (in which case you need to ask the publisher how you should count words and what tool to use), the usually minor differences in word count do not matter when you submit a manuscript to an agent or publisher.
The publisher, when he considers your manuscript for publication, isn't worried wether he will have to print 563 or 564 pages. What he wants to know is wether your novel is in the range of 60,000 to 80,000 words for a newcomer young adult novel (or whatever you write and whatever the publisher's range is for that).
And publishers understand word counting with Word. If you send them a Word document or say (in your letter) that you counted your words with Word, they will know from experience what to expect.
Different versions of Word count words slightly differently. For files that are just text, this isn't generally a problem, it's things like text in graphics and footnotes that throw this off. There's more information in this related question on SuperUser: What is MS Word counting or ignoring when it counts words in an open vs. closed file?
It's worth noting that in publishing, wordcount is often estimated by counting pages in standard manuscript format, generally double-spaced 12-point Courier with 1" margins. Pages formatted like this are assumed to be about 250 words, so a 200-page manuscript would be about 50,000 words.