Exactly a week ago, National Australia Bank Ltd (ASX: NAB) stock was making big ASX news.

The ASX 200 bank stock didn't report its latest earnings, like its big four cousin Commonwealth Bank of Australia (ASX: CBA) did earlier this month. Thanks to NAB's funky financial calendar, investors will have to wait until May for that.

However, NAB did give its investors a first-quarter update. And those investors did not like what the bank had to show.

For the three months ended 31 December, the bank stated that its revenues were up 3% against its second-half quarterly average. Saying that, expenses rose by 2%, which pushed the bank's cash earnings down 2%.

The market responded by cutting 8% off the NAB share price at the time. Today, the NAB share price remains down by around 10.1% from where it was before this update became public.

But this share price drop may be a blessing in disguise for anyone wishing to buy NAB shares for dividend income. After all, a share price fall for a dividend-paying stock usually means that the dividend yield available on the shares for new buyers increases.

And most investors who buy NAB shares arguably do so for those fat, fully franked dividends that ASX bank shares are known for.

So let's discuss whether NAB shares are a buy today for dividend income.

Is NAB stock a buy for dividends today?

Well, to start with, NAB shares, at their current pricing, are trading on a trailing dividend yield of 4.76% That comes from December's final dividend worth 85 cents per share, as well as last July's interim dividend of 84 cents per share. As is typical for NAB, both payments came with full franking credits attached.

With NAB's own term deposits not even coming close to that rate of return at present (they currently top out at 4.6%), this is certainly an appealing income investment. Particularly compared to CBA, whose yield is now languishing around the 3% mark.

As an ASX bank, NAB has always been a reasonably reliable dividend payer, with decades of chunky dividends behind it. Sure, investors should expect a dip in their dividends when a recession or other economic shock rolls around. However, history has shown that NAB's payments tend to bounce back fairly quickly.

As such, I think NAB is indeed a buy for income today. But only for investors who invest primarily for dividend income and have the capacity to add NAB stock to a diversified portfolio of reliable dividend shares.

I wouldn't expect NAB to be a market beater at its current pricing in the years ahead. So, investors who prioritise absolute returns might want to keep looking.