Our short answer to this question is no. The long answer is it depends.
In any case, we highly recommend you to keep your deductible amount as low as possible if you don't have $2,000 or $5,000 lying around to cover a sudden expense out-of-pocket such a car accident. While you see increasing your deducible could help you save some buck on your premium, it could highly impact your financials if you don't have enough in your savings.
On the other hand, if paying $2,000 or $5,000 out-of-pocket would not impact your finances tremendously, you can consider increasing to save on your premium.
Alternatively, you could subscribe to our Allegory Deductible Waiver product to get an additional peace of mind.