While most Americans support policies to encourage the building of more housing in their neighborhoods, less than half of the homeowners surveyed were in favor of building more “affordable” housing nearby, according to a housing survey from Fannie Mae.

Researchers at Fannie Mae surveyed about 1,000 people who were either homeowners or renters, asking them about their attitudes toward housing density and zoning. Homeowners tended to show a distinct “not in my backyard” attitude toward new developments.

The two groups tended to diverge on a variety of issues, including affordable housing. About 82% of those surveyed were in favor of the idea of building new housing in their neighborhood. But when asked about building more affordable housing, 73% of renters were in favor, while only 44% of homeowners approved.

Also, the survey found that while both groups supported building new single-family detached homes in their neighborhood, renters were much more likely to support building other housing types, including apartments, condominiums and townhomes. In addition, just 37% of homeowners were in favor of changing local zoning codes or regulations to allow more housing development, while 63% of renters were in favor.

Economists generally agree that more homes in a neighborhood would tend to slow the rise in housing prices, but a majority of consumers seem to believe the opposite. Nearly 60% of those surveyed said they expected home prices to increase in their neighborhood if more homes were built, and only 13% said home prices would fall. Researchers wrote that one explanation for the discrepancy may be that consumers would assume that the homes being built would not be what they consider affordable.

Nearly 60% of those surveyed also think rent prices would increase if more homes were built, and 61% said that local taxes would increase. Researchers said these results pointed to a perception among consumers that new construction would be expensive for current residents. Researchers concluded that this type of mixed attitude toward new construction might make further developments in neighborhoods challenging.

On the bright side, when researchers asked about the types of homes respondents would likely buy if they were in the market, 31% said they would buy something other than a single-family detached home. However, non-single-family detached homes represent only 18% of the housing stock mix, meaning that there is an unmet demand in the marketplace that builders could fill.