Throughout the entire industry, however, the national average bank interest rate for savings accounts is only .21 percent
So why might be it rational to overpay your taxes by a small amount? Consider this comment from Megan McArdle:
A tax refund is not free money you get from the government. It’s free money you gave to the government—by overpaying your taxes all year. You think the interest rate on your savings account is paltry? At least it's not zero, which is the amount Uncle Sam pays you for your yearlong interest free loan. (If you underpay the government, on the other hand, they charge you not only interest, but also penalties.)
On one hand her advice is completely sensible. It makes a lot of sense to reduce a very large tax refund. On the other hand, you need to save a lot of money for the 0.21% interest in that savings account to outweigh the interest and penalties. Since even interest is 3% (15 times the savings rate), I think it makes sense to aim for a small refund rather than to make errors on both sides of the distribution (since underpaying is much more expensive than the lost revenue from overpaying). This logic may not hold if interest rates and/or inflation pick up in the future.