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.

Your parents' retirement investing plan won't cut it today.

For many years, bonds or other fixed-income assets could produce the yield needed to provide solid income for retirement needs. However, these yields have dwindled over time: 10-year Treasury bond rates in the late 1990s were around 6.50%, but today, that rate is a thing of the past, with a slim likelihood of rates making a comeback in the foreseeable future.

While this yield reduction may not seem drastic, it adds up: for a $1 million investment in 10-year Treasuries, the rate drop means a difference in yield of more than $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

As we see it, dividend-paying stocks from generally low-risk, top notch companies are a brilliant way to create steady and solid income streams to supplant low risk, low yielding Treasury and fixed-income alternatives.

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.

Ameren (AEE) is currently shelling out a dividend of $0.67 per share, with a dividend yield of 3.74%. This compares to the Utility - Electric Power industry's yield of 3.74% and the S&P 500's yield of 1.59%. The company's annualized dividend growth in the past year was 6.78%. Check Ameren (AEE) dividend history here>>>