Bradley T. Heim (Office of Tax Analysis, Treasury Department) has published The Effect of Tax Rebates on Consumption Expenditures: Evidence from State Tax Rebates, 60 Nat’l Tax J. 685 (2007). Here is the abstract:

This paper uses Consumer Expenditure Survey data to estimate the response to a sequence of state tax rebates implemented during 1995–2001. The results generally suggest that expenditures increased by one–fifth to one–fourth of the rebate amount, with positive effects on nondurable spending, spending on apparel, and among households with single respondents. However, the results vary depending on the sample, regressor, and expenditure component, with several variables entering insignificantly or with the wrong sign. Rebate announcements are estimated to have had a small and insignificant effect on the amount of spending, but may have shifted the composition of spending.