*By* indicates when vaguely something happens. For a future date it means *before*:

>The company vowed to ban all plastic containers **by** 2022.

>Renewables can reduce CO2 emissions by 70% **by** 2050

It's a little weird to use if for a past date but I guess it work to. It would mean *at some time before 2013*.

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I'm not 100% sure about this, but it could also mean *around the year 2013*.

After all, *by* is used in that sense for for spacial indications (the first definition is [*near or next to*](https://en.wiktionary.org/wiki/by#Preposition)), so it could also apply for time indications.

>He liked to sit **by** the tree.

 It makes sense in your example.