Jonathan Brogaard & Kevin Roshak (both of Northwestern University, Kellogg School of Management) have posted The Effectiveness of the Financial Crisis Housing Tax Credit Programs on SSRN. Here is the abstract:

Fiscal stimulus has been suggested as a tool to prevent excessive price declines by creating incentives to increase current demand. In 2008 and 2009 the U.S. Congress passed several housing tax incentive programs to encourage activity in the residential real estate market. This paper examines the impact of the different housing tax incentive programs on the demand for housing during the financial crisis. Using city level data we implement a differences-in-differences-in-differences methodology to isolate the impact of the tax credits on the quantity of housing transactions and their prices. We find that quantity was unaffected and that prices rose only temporarily. The results showed no statistically significant difference in quantity. However, prices in affected housing markets rose on average $6,509 more than unaffected markets during the program. This price differential more than reverses, falling $7,721 after the expiration of the final tax credit program. The speed of these price movements is quick. The price increase takes place largely within a month of the first large tax credit, and the price drop occurs predominately in the two months following the credit expiration.

The paper concludes:

This paper finds that (1) the home buyer tax credits had an insignificant effect on the number of homes sold, (2) sellers in markets with low and stable prices captured most of the credit, and (3) The effects of the credits sharply reversed after expiration. … Rather than igniting ‘animal spirits’ or pulling housing demand forward from the distant future, the tax incentives were a simple redistribution of wealth.