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

Also, retirees who have constructed a nest egg have valid justifications to be concerned, since the traditional ways to plan for retirement may mean income can no longer cover expenses. Some retirees are now tapping their principal to make a decent living, pressed for time between decreasing investment balances and longer life expectancies.

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

Years ago, investors at or close to retirement could put money into fixed-income assets and depend on appealing yields to generate consistent, solid pay streams to fund a comfortable retirement. 10-year Treasury bond rates in the late 1990s floated around 6.50%, but unfortunately, those days of being able to exclusively rely on Treasury yields to fund retirement income are over.

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.

Today's retirees are getting hit hard by reduced bond yields - and the Social Security picture isn't too rosy either. Right now and for the near future, Social Security benefits are still being paid, but it has been estimated that the Social Security funds will be depleted as soon as 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 current low risk, low yielding Treasury and fixed-income alternatives.

For example, AT&T and Coca-Cola are income stocks with attractive dividend yields of 3% or better. Look for stocks like this that have paid steady, increasing dividends for years (or decades), and have not cut their dividends even during recessions.

One approach to recognizing appropriate stocks is to look for companies with an average dividend yield of 3% and positive average annual dividend growth. Numerous stocks hike dividends over time, counterbalancing inflation risks.

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

Donegal Group (DGICA - Free Report) is currently shelling out a dividend of $0.15 per share, with a dividend yield of 4.26%. This compares to the Insurance - Property and Casualty industry's yield of 1.55% and the S&P 500's yield of 1.97%. In terms of dividend growth, the company's current annualized dividend of $0.6 is up 1.75% from last year.

Highwoods Properties (HIW - Free Report) is paying out a dividend of 0.48 per share at the moment, with a dividend yield of 4.89% compared to the REIT and Equity Trust - Other industry's yield of 4.63% and the S&P 500's yield. Taking a look at the company's dividend growth, its current annualized dividend of $1.92 is up 1.05% from last year.

Currently paying a dividend of 1.07 per share, Kimberly-Clark (KMB - Free Report) has a dividend yield of 3.03%. This is compared to the Consumer Products - Staples industry's yield of 0% and the S&P 500's current yield. Looking at dividend growth, the company's current annualized dividend of $4.28 is up 3.88% from last year.