Considering that the wealthiest one-tenth of households own more than 80 percent of stocks, it's easy to see why market movements might not have a noticeable effect on retirement patterns of the average American, but with the rise of 401(k)  and IRA plans and the few hangers-on among defined benefit plans—all of which hold equities—the average American is becoming more dependent on market movements than he perhaps realizes.

And when it comes to that average American, while he might not be responsible for poor investments held in a traditional DB plan and thus does not bear the responsibility for providing his own retirement benefit—his employer is obligated in that regard—he is on the hook for his own retirement benefit resulting from investments in 401(k)s and IRAs.

Therefore, according to the report, "When the stock market tanks, 401(k) and IRA savers who invest in equities face the prospect of a less prosperous retirement."

And while that may not be much of a worry for workers in their 30s or 40s with a relatively long time horizon till retirement, "it ought to be a major concern for workers near retirement or already retired. Many of these workers have large retirement account balances, and a big share of their balances is invested in equities."

Another worry factor to keep in mind is the rise of the private retirement system—pensions, 401(k)s, IRAs—over the public retirement system, which now provides a far smaller share of retirement income than it used to.

Says the report, "Back in 1990, the private system made annual distributions to beneficiaries that were about 8 percent less than the payouts from the public retirement system–Social Security and Supplemental Security Income. By 2015, the annual distributions from the private retirement system were 57 greater than the payouts from the public retirement system."

And of course the private system is largely dependent on equities investments.

Erosion of Social Security and Supplemental Security benefits thanks to inflation and cost-of-living adjustments that don't keep up means that the average American is now far more reliant on his own efforts to save for retirement.

That, coupled with the growth of the private system, results in "an obvious channel through which stock market gyrations can affect behavior," the report explains, adding, "When equity prices soar, workers in 401(k) plans become richer and may be able to retire at a younger age. When the stock market slumps, people in these plans are poorer. They have to work longer to enjoy a comfortable retirement."

And while economists have tried to measure the effects of stock market movements on retirement trends, it can be tough "to distinguish the impact of stock market fluctuations separately from the effects of other economic factors that help determine stock prices."

Considering that major changes in stock prices often come just before or in tandem with recessions, with investors fearing that company profits are tanking, there are also the effects of increasing layoffs and slowdowns in hiring.

So it's difficult to attribute retirement trends specifically to stock market movement, particularly since even if workers want to keep working lest they run out of money in retirement, they may not be able to hold or keep a job as recession-plagued employers shed employees rather than add them.

However, the report concludes, even if the effect on retirement patterns of drops in the market isn't readily attributable, the shift of retirees' dependence from public pensions to private plans dependent on stock prices "may mean that retirement patterns become more sensitive to stock prices."