First-time home buyers aren’t playing as big a role in the housing market as they did a few years ago, when lower prices and a big tax credit lured them to the market.

But when it comes to homes financed by conventional or government-backed loans, first-time buyers still account for a historically high share of purchases, according to a new paper from researchers at the Federal Housing Finance Agency.

The FHFA, which regulates mortgage-finance giants Fannie Mae and Freddie Mac, examined loans that were either sold to those companies or insured by the Federal Housing Administration, a government agency that has traditionally played a large role serving first-time buyers. These entities have backed more than 80% of all loans made since 2009. Before the housing bubble swelled in 2003, they guaranteed around two-thirds of all loans, but during the bubble their market share fell to around half of the market.

Here’s what they found: The first-time buyer share of purchase-mortgage lending rose to a high of 63% in 2009, when Congress enacted an $8,000 tax credit for first-time buyers. That was from a nadir of 37% in 2003.

First-time buyers accounted for a lower share of purchases from 2004 to 2006, when home prices were rising rapidly and credit was available on much easier terms from lenders that were selling those loans to Wall Street firms, bypassing Fannie, Freddie, and the FHA.

First-time buyers’ share of loans began to increase steadily in 2007, until reaching that 2009 peak. Since 2009, the share of mortgages to first-time buyers has declined, dropping to 56% last year. That is still higher than at any time between 1993 and 2008.

An updated version of the paper that was released last month breaks out the first-time buyer share by state. As you might expect, it finds that the first-time buyer share tends to decline in states as home prices rise.  Declining home prices, by contrast, “tend to induce relatively robust home purchasing volume by first-time home buyers,” the paper said.

States with the highest first-time buyer shares include California, Nevada, Maryland, New York and Washington, D.C. “These are areas that have metropolitan areas and there are more opportunities for younger folks,” says Nayantara Hensel, one of the study’s authors. First-time buyer shares were lowest in rural states: Montana, Wyoming, Iowa, Kansas and Wisconsin.

One third of states have seen an increase in their first-time buyer shares by more than 10 percentage points between 1996 and 2013, with the largest gains in Nevada, Rhode Island, Washington, Ohio and Arizona. Over the same period, North Dakota, South Dakota and Washington, D.C., reported declines in the share of first-time buyers.

So what should we make about other reports that say first-time buyers are accounting for a woefully small share of the market?

First, the FHFA data doesn’t take into account the fact that the share of all-cash sales is much higher today than a few years ago. The data only look at the share of homes being financed with conventional loans or FHA-backed mortgages. Because most of the all-cash purchases probably aren’t first-time buyers, the total share of homes being purchased by first-time buyers is lower given the increased role of first-time buyers.

Second, the reported share of first-time buyers also could be higher in more expensive states due to the conforming loan limits. Fannie and Freddie, for example, can’t buy loans that exceed $417,000, though the limit was increased for certain high-cost areas in 2008. It currently runs as high as $625,500 in the more expensive markets. This means a significant share of more expensive home sales—which are less likely to include first time buyers—aren’t captured in the data.

The fact that a larger portion of loans would be excluded from the analysis in more expensive states could make state-by-state comparisons less revealing. But the data still provide an interesting view of how the first-time borrower component has changed over time within a particular state. They show that first-time buyers continue to make up a higher-than-average share of borrowers, even if they are off of their 2009 highs.