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.

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

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.

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

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.

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 $2.38 per share, with a dividend yield of 3.02%. This compares to the Medical - Biomedical and Genetics industry's yield of 0% and the S&P 500's yield of 1.56%. The company's annualized dividend growth in the past year was 5.63%. Check Amgen dividend history here>>>

Fulton Financial (FULT Quick QuoteFULT - Free Report)

is paying out a dividend of $0.18 per share at the moment, with a dividend yield of 3.94% compared to the Banks - Northeast industry's yield of 2.57% and the S&P 500's yield. The annualized dividend growth of the company was 5.88% over the past year. Check Fulton Financial dividend history here>>>

Currently paying a dividend of $0.72 per share,

Shell (SHEL Quick QuoteSHEL - Free Report)

has a dividend yield of 4%. This is compared to the Oil and Gas - Integrated - International industry's yield of 0% and the S&P 500's current yield. Annualized dividend growth for the company in the past year was 3.93%. Check Shell 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.

An advantage of owning dividend stocks for your retirement nest egg is that numerous companies, particularly blue chip stocks, raise their dividends over time, helping alleviate the impact of inflation on your potential retirement income.

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

If you prefer investing in funds or ETFs compared to individual stocks, you can still pursue a dividend income strategy. However, it's important to know the fees charged by each fund or ETF, which can ultimately reduce your dividend income, working against your strategy. Do your homework and make sure you know the fees charged by any fund before you invest.

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.