We investigate implications of search and matching frictions in the labor market for inflation targeting interest rate policy in terms of equilibrium stability. When the interest rate is set in response to past or present inflation, determinacy of equilibrium is ensured similarly to comparable previous studies with frictionless labor markets. In stark contrast to these studies, indeterminacy is very likely if the interest rate is adjusted in response solely to expected future inflation. This is due to a vacancy channel of monetary policy that stems from the labor market frictions and renders inflation expectations self-fulfilling. The indeterminacy can be overcome once the interest rate is adjusted in response also to output or the unemployment rate or if the policy contains interest rate smoothing. When E-stability is adopted as an equilibrium selection criterion, a unique E-stable fundamental rational expectations equilibrium is generated under active, but not too strong, policy responses only to expected future inflation. This suggests that the problem is not critical from the perspective of learnability of the fundamental equilibrium.