This paper investigates the stabilization bias that arises in a model of monetary and fiscal policy stabilization of the economy, when assuming that the monetary authority put higher weight on inflation stabilization than society. We demonstrate that inflation-conservatism unambiguously leads to social welfare losses if the fiscal authority acts strategically. Although the precise form of monetary-fiscal interactions depends on the choice of fiscal instrument and on the level of steady state debt, the assessment of gains is robust to these assumptions. We also study how the outcome of stabilization depends on the leadership structure. We develop an algorithm that computes leadership equilibria in much wider spectrum of problems with strategic agents in LQ RE models.