A jump in welfare, a massive increase in food stamps and young adults moving back in with their parents en masse — that is the popular perception of what has happened in the five years since the financial crisis hit.

It's not totally wrong. But according to a new study, the dramatic expansion in social insurance spending since the start of recession isn't out of line with what's happened in past recessions. Instead, the growth of social insurance programs reflects the severity of the recession more than any changes in the safety net.

That’s what Marianne Bitler of University of California Irvine and Hilary Hoynes of Berkeley find in a new study published by the National Bureau of Economic Research Monday morning.

Bitler and Hoynes write that the growth of the public and private safety nets are what “we would have predicted from the historical patterns,” and, by implication, not the work of President Obama, who took office just as the economy bottomed out.

In fact, Bitler and Hoynes find that cash welfare, a program with capped spending, has shrunk in relative terms.

The study includes data up through 2010, so it does not capture developments in the safety net since then — for instance, almost 4.5 million more households received food stamps in 2013 than in 2010, when 18.6 million claimed benefits.

But in 2010 nearly 2 million households were on cash welfare, 26 million received the earned income tax credit (EITC), and 9 million received unemployment insurance (UI). Another 16 million received disability benefits.

The run-up in the use of those benefits can be seen in this chart from the study:

But by Bitler and Hoynes’ estimation, the increase in social safety expenditures shows that the safety net “fared well in protecting the incomes of our most vulnerable households during the Great Recession.”

The study compares the increase in spending on a few key antipoverty programs with what happened in another severe recession, in 1980, and finds that the response was similar.

This chart shows the share of U.S. households that received income from each of the programs — food stamps, welfare (AFDC/TANF), unemployment insurance, and two kinds of disability insurance — SSI and SSDI:

While food stamp and unemployment use has been relatively high in this recession, cash welfare rolls have fallen.

And the study also finds that the number of young adults “doubling up” with parents did increase during the recession, as would be expected when jobs are scarce for college graduates. But the number of such living arrangements is less than would be expected from past recessions.