Retirees may be better off financially than many think.

A recent Center for Retirement Research analysis shows how most retirement income from 401(k) plans and Individual Retirement Accounts is not captured in the Census Bureau’s widely used Current Population Survey — leading to drastic understatements in retirement income, and particularly so among the wealthy.

In “Do Census Data Understate Retirement Income?” authors Alicia H. Munnell and Anqi Chen compare the Census data with the Federal Reserve’s 2013 Survey of Consumer Finances (a nationally representative survey of about 6,100 households that’s considered the “gold standard for data on household wealth”) and the income reported to the Internal Revenue Service.

What they found: the Census’ Current Population Survey reports $18 billion of 401(k)/IRA income in 2012, while the Fed’s Survey of Consumer Finances reports $220 billion and the IRS $229 billion.

Although the CPS appears to under-report income from retirement plans in general, Munnell  and Chen focus on the defined contribution problem because, as they found, under-reporting for defined contribution plans is much larger than that for defined benefit plans.

This poses a serious problem given the shift from defined benefit to defined contribution plans, and the fact that defined contribution plans are likely to eventually be the only source of income from retirement plans for private sector workers.

It should be noted, though, that the Census’ data for low-and middle income households’ retirement income is not actually too far off.

“While the [Current Population Survey] involves significant under-reporting of income from 401(k)s/IRAs, which needs to be fixed, the survey still provides a relatively accurate picture of retirement income for the typical middle-income household, who holds little wealth from retirement plans,” write Munnell and Chen.

Their report analyzes whether the under-reporting of 401(k)/IRA withdrawals affects all parts of the income distribution or just among the higher income. Their analysis sorts households age 65-84 who are not working by total retirement income, including defined benefit income, Social Security benefits, investment income and “potential” 401(k)/IRA income.

Looking at the lowest quintile, the Census reports an average annual 401(k)/IRA income of $18 billion while the Fed’s survey reports $215 billion – a difference of $197 billion. In contrast, within the highest quintile, the Census’ survey and the Fed’s survey show a difference of $14,357 billion in average annual 401(k)/IRA income – with the Census reporting $1,827 billion vs. the Fed’s $16,183 billion.

“A cursory glance shows that dollar discrepancies are small until the two top quintiles,”  write Munnell  and Chen. “This finding is not surprising because the majority of households hold very little 401(k)/IRA assets.”

The government has responded, Munnell and Chen state, with plans to test different question patterns to try to improve responses and better incorporate all sources of retirement income.

Munell and Chen have a couple suggestions for them, though.

“The CPS may want to include a measure of 401(k)/IRA assets both to verify their income estimates and to calculate ‘potential’ defined contribution income in cases when households are not drawing on their retirement wealth,” they write.

Reported income from retirement accounts can fall short of potential for two reasons, Munnell and Chen say.

“First, individuals may not withdraw the money available to them. In fact, studies show that most retirees do not withdraw money until their early 70s when they become subject to the IRS’ required minimum distribution rules,” the pair write. “Second, the income that individuals actually do withdraw is not captured by the survey.”