WASHINGTON — After the drama of electing a new speaker of the House and the changing of control in the Senate, the House on Tuesday approved an obscure but significant rule change requiring the economic effects of legislation to be included in a bill’s official cost to the Treasury.

The change on “dynamic scoring” — ardently sought since the 1990s by Republicans — could ease passage of major tax cuts by showing that their impact on economic growth would substantially reduce their cost to the Treasury. The move is widely seen as a way for Republican leaders to set ground rules for an ambitious overhaul of the entire United States tax code.

“We’re saying, ‘If you think a piece of legislation is going to have a big effect on the economy, then include that effect in the official cost estimate,’ ” said Representative Tom Price, Republican of Georgia, the new chairman of the House Budget Committee. “So if you think a bill is going to help or hurt the economy, then tell us how much.”

Democrats blasted the change as “voodoo economics,” a “gamble” and “tax fraud.” Opponents said the rule change would invite politicized scorekeeping, further tilt policy to benefit the rich, and expand the budget deficit. Shaun Donovan, the White House budget director, implored the House not to “upend the level playing field that has existed for decades” and “call into question the accuracy, consistency and fairness” of congressional budget estimates.