One bill, filed by state Sen. Bruce Tarr, R-Gloucester, allows tax credits for up to 50 percent of a new worker’s salary following one year of employment. The program would be capped at 50 new employees per company and available for three consecutive years.

Another measure, sponsored by Sen. Eileen Donoghue, D-Lowell, provides businesses tax credits up to $600 for each college graduate given a job, provided the worker is employed at least 185 days of the year.

“One of the most prevalent issues facing young people is finding a well-paying job after graduating,” Donoghue told the Legislature’s Joint Committee on Revenue, which heard testimony on more than a dozen corporate tax break bills last week. “This would give employers an incentive to hire grads.”

The push for more business tax breaks comes as the state wrestles chronic budget shortfalls that have led to cuts in spending and sparked a debate over the effectiveness of the incentives.

Massachusetts faces a $1.8 billion deficit for this budget year, which began July 1. Gov. Charlie Baker and legislative leaders have warned they may need to make additional budget cuts this fiscal year to offset revenue shortfalls.

It’s not clear how much Tarr’s or Donoghue’s proposals would cost the state.

A recent report by the nonprofit Massachusetts Budget and Policy Center found that the value of the state’s business tax credits has more than doubled in two decades, from $342 million in 1996 to more than $770 million in 2012.

And the Tax Expenditure Commission, a state committee that reviews tax breaks, concluded in a report two years ago that Massachusetts has too many deductions, credits and exclusions on the books.

Click here for more information about new Massachusetts tax breaks.