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.

In the past, investors going into retirement could invest in bonds and count on attractive yields to produce steady, reliable income streams to fund a predictable retirement. 10-year Treasury bond rates in the late 1990s hovered around 6.50%, whereas the current rate is much lower.

The impact of this rate decline is sizable: over 20 years, the difference in yield for a $1 million investment in 10-year Treasuries 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 can retirees do? You could dramatically reduce your expenses, and go out on a limb hoping your Social Security benefits don't diminish. On the other hand, you could opt for an alternative investment that gives a steady, higher-rate income stream to supplant lessening bond yields.

Invest in Dividend Stocks

Dividend-paying stocks from low-risk, high-quality companies are a smart way to generate steady and reliable attractive income streams to replace low risk, low yielding Treasury and bond options.

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.

Grupo Aeroportuario del Sureste (ASR Quick QuoteASR - Free Report)

is currently shelling out a dividend of $22.13 per share, with a dividend yield of 6.8%. This compares to the Transportation - Services industry's yield of 0% and the S&P 500's yield of 1.54%. The company's annualized dividend growth in the past year was 110.53%. Check Grupo Aeroportuario del Sureste dividend history here>>>

New Jersey Resources (NJR Quick QuoteNJR - Free Report)

is paying out a dividend of $0.45 per share at the moment, with a dividend yield of 3.91% compared to the Utility - Gas Distribution industry's yield of 3.25% and the S&P 500's yield. The annualized dividend growth of the company was 7.14% over the past year. Check New Jersey Resources dividend history here>>>

Currently paying a dividend of $0.29 per share,

Old Republic International (ORI Quick QuoteORI - Free Report)

has a dividend yield of 3.04%. This is compared to the Insurance - Multi line industry's yield of 1.58% and the S&P 500's current yield. Annualized dividend growth for the company in the past year was 9.43%. Check Old Republic International 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.

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

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.