Here's an eye-opening statistic: older Americans are more afraid of running out of money than of death itself.

And older Americans have legitimate reasons for this worry, even if they have dutifully saved for their golden years. That\s because the traditional ways people manage retirement may no longer provide enough income to meet expenses- and with people generally living longer, the principal retirement savings is exhausted far too early in the retirement period.

Retirement investing approaches of the past don't work today.

For example, 10-year Treasury bonds in the late 1990s offered a yield of around 6.50%, which translated to an income source you could count on. However, today's yield is much lower and probably not a viable return option to fund typical retirements.

That means if you had $1 million in 10-year Treasuries, the difference in yield between 1999 and today is more than $1 million.

And lower bond yields aren't the only potential problem seniors are facing. Today's retirees aren't feeling as secure as they once did about Social Security, either. Benefit checks will still be coming for the foreseeable future, but based on current estimates, Social Security funds will run out of money in 2035.

So what's a retiree to do? You could cut your expenses to the bone, and take the risk that your Social Security checks don't shrink. Or you could find an alternative investment that provides a steady, higher-rate income stream to replace dwindling bond yields.

Invest in Dividend Stocks

We feel that these dividend-paying equities-as long as they are from high-quality, low-risk issuers-can give retirement investors a smart option to replace low-yielding Treasury bonds (or other bonds).

Look for stocks that have paid steady, increasing dividends for years (or decades), and have not cut their dividends even during recessions.

Going beyond those familiar names, you can find excellent dividend-paying stocks by following a few guidelines. Look for companies that pay a dividend yield of around 3%, with positive annual dividend growth. The growth rate is key to help combat the effects of inflation.

Here are three dividend-paying stocks retirees should consider for their nest egg portfolio.

Amgen (AMGN Quick QuoteAMGN - Free Report) is currently shelling out a dividend of $2.52 per share, with a dividend yield of 3.06%. This compares to the Medical - Biomedical and Genetics industry's yield of 0% and the S&P 500's yield of 1.39%. The company's annualized dividend growth in the past year was 5.78%. Check Amgen dividend history here>>>

Consolidated Edison (ED) is paying out a dividend of $0.89 per share at the moment, with a dividend yield of 3.21% compared to the Utility - Electric Power industry's yield of 2.64% and the S&P 500's yield. The annualized dividend growth of the company was 2.41% over the past year. Check Consolidated Edison dividend history here>>>

Currently paying a dividend of $0.28 per share, Hanmi Financial (HAFC) has a dividend yield of 3.71%. This is compared to the Banks - West industry's yield of 2.59% and the S&P 500's current yield. Annualized dividend growth for the company in the past year was 8%. Check Hanmi Financial dividend history here>>>

But aren't stocks generally more risky than bonds?

Yes, that's true. As a broad category, bonds carry less risk than stocks. However, the stocks we are talking about-dividend-paying stocks from high-quality companies-can generate income over time and also mitigate the overall volatility of your portfolio compared to the stock market as a whole.

Combating the impact of inflation is one advantage of owning these dividend-paying stocks. Here's why: many of these stable, high-quality companies increase their dividends over time, which translates to rising dividend income that offsets the effects of inflation.

Thinking about dividend-focused mutual funds or ETFs? Watch out for fees.

If you're thinking, "I want to invest in a dividend-focused ETF or mutual fund," make sure to do your homework. It's important to know that some mutual funds and specialized ETFs charge high fees, which may diminish your dividend gains or income and thwart the overall objective of this investment strategy. If you do want to invest in fund, research well to identify the best-quality dividend funds with the least charges.

Bottom Line

Whether you select high-quality, low-fee funds or stocks, seeking the steady income of dividend-paying equities can potentially offer you a path to a better and more stress-free retirement.