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

And retirees have good reason to be worried about making their assets last. People are living longer, so that money has to cover a longer period. Making matters worse, income generated using tried-and-true retirement planning approaches may not cover expenses these days. That means seniors must dip into principal to meet living expenses.

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.

The effect of this drop in rates is substantial: over 20 years, the change in yield for a $1 million investment in 10-year Treasuries is over $1 million.

In addition to the considerable drop in bond yields, today's retirees are nervous about their future Social Security benefits. Because of certain demographic factors, it's been estimated that the funds that pay the Social Security benefits 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.

A rule of thumb for finding solid income-producing stocks is to seek those that average 3% dividend yield, and positive yearly dividend growth. These stocks can help combat inflation by boosting dividends over time.

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 $2.25 per share, with a dividend yield of 3.23%. This compares to the Medical - Biomedical and Genetics industry's yield of 0% and the S&P 500's yield of 1.5%. The company's annualized dividend growth in the past year was 5.63%. Check Amgen dividend history here>>>

First American Financial (FAF Quick QuoteFAF - Free Report)

is paying out a dividend of $0.54 per share at the moment, with a dividend yield of 3.3% compared to the Insurance - Property and Casualty industry's yield of 0.13% and the S&P 500's yield. The annualized dividend growth of the company was 1.89% over the past year. Check First American Financial dividend history here>>>

Currently paying a dividend of $0.5 per share,

Portland General Electric (POR Quick QuotePOR - Free Report)

has a dividend yield of 4.28%. This is compared to the Utility - Electric Power industry's yield of 3.3% and the S&P 500's current yield. Annualized dividend growth for the company in the past year was 5.26%. Check Portland General Electric dividend history here>>>

But aren't stocks generally more risky than bonds?

The fact is that stocks, as an asset class, carry more risk than bonds. To counterbalance this, invest in superior quality dividend stocks that not only can grow over time but more significantly, can also decrease your overall portfolio volatility with respect to the broader stock market.

An upside to adding dividend stocks to your retirement portfolio: they can help lessen the effects of inflation, since many dividend-paying companies (especially blue chip stocks) generally increase their dividends over time.

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

If you're interested in investing in dividends, but are thinking about mutual funds or ETFs rather than stocks, beware of fees. Mutual funds and specialized ETFs may carry high fees, which could lower the overall gains you earn from dividends, undercutting your dividend income strategy. Be sure to look for funds with low fees if you decide on this approach.

Bottom Line

Regardless of whether you select high-quality, low-fee funds or stocks, looking for a steady stream of income from dividend-paying equities can potentially lead you to a solid and more peaceful retirement.