Abstract Recent empirical research finds little or mixed evidence in favour of a negative relationship between central bank independence and inflation. In this paper, we construct a theory where the relationship between inflation and central bank independence depends on the extent of informational asymmetry regarding the government’s efficiency in its provision of public goods and also provide some empirical support for it. In the theoretical part of the paper, we introduce the degree of central bank independence as a fixed cost that is paid when the government (whose objective is to minimize output gap via inflation or costly fiscal expansion) rejects the monetary policy proposal of the central bank (which aims to minimize inflation) and determines both fiscal and monetary policies itself. Government efficiency in providing public goods, i.e. the cost of fiscal expansion, is the private information and the source of informational asymmetry in our model. In this setting, increasing the fixed cost of rejecting the central bank’s offer creates two opposite effects on inflation: delegation effect and seesaw effect (since fiscal and monetary expansion are substitutes for the government, now it relies more on fiscal expansion). We show that while the magnitude of the delegation effect is equal to or higher than the seesaw effect, the magnitude of each effect depends on the current level of the fixed cost. If the current fixed cost is not high enough, then a small improvement in central bank independence creates a relatively smaller delegation effect compared to the case where fixed cost is high enough and both efficient and inefficient government types accept the offer.