Oil prices are among the most important variables for inflation. A sustained rise in crude prices can push headline inflation higher directly, but its impact can extend beyond energy prices by influencing inflation expectations. One useful market-based measure of those expectations is the breakeven inflation rate.What are breakeven inflation rates?A breakeven inflation rate is the difference between the yield on a conventional Treasury bond and the yield on an inflation-protected Treasury of the same maturity.For example, taking the 10-year breakeven, which is generally used as benchmark: 10-year breakeven = 10-year Treasury yield − 10-year TIPS yieldThe result represents the average annual inflation rate that would make an investor indifferent between holding the two securities until maturity, although it is important to remember that breakevens also contain inflation-risk and liquidity premia and are therefore not a pure measure of expected inflation. Nonetheless, breakevens are particularly useful for monitoring how financial markets are pricing the inflation outlook. Historically, there has been a meaningful positive relationship between oil prices and inflation breakevens. Chart: WTI crude oil (blue) vs 10-year breakeven (red)Why do oil prices matter for inflation?The most obvious channel is direct energy inflation. When crude oil rises, other energy products generally become more expensive. Since energy is part of consumer price indexes, higher oil prices can lift headline CPI directly.Oil is also an important input into transportation, manufacturing, chemicals and other parts of the economy. Higher energy costs can therefore increase businesses' costs, which may eventually be passed on to consumers through higher prices and impact core CPI.There is also an expectations channel. If consumers and businesses believe that higher oil prices will persist, they may begin to expect higher overall inflation. Workers may demand higher wages, while companies may become more willing to raise prices. These second-round effects can make an initially energy-driven inflation shock more persistent.Chart: WTI crude oil (blue) vs US headline CPI (red)Monetary policy impactThe relationship between oil prices and inflation is especially important for central banks, as they have a mandate to keep inflation stable over the medium term, generally around a target of 2% per year. Central banks usually ignore supply-driven shocks because most of the time they are temporary. They push up headline inflation, but don't have much impact on core inflation. What central banks care more about is whether inflation expectations remain anchored.A sustained increase in oil prices that pushes up inflation expectations is much more significant for a central bank because it raises the risk of second-round inflation effects. That can complicate the central bank's job of keeping inflation stable and require a monetary policy action. Policymakers must consider whether an energy shock is temporary or whether it risks becoming embedded in broader inflation.When a central bank adopts a hawkish bias to combat energy-driven inflation, inflation expectations are generally kept in check and don't rise too much as markets expect rate hikes to eventually lower inflation. Conversely, if a central bank keeps a neutral or even dovish bias despite persistently higher energy prices, inflation expectations generally rise faster and the risk of second-round effects rises substantially. ConclusionCentral banks cannot directly control oil prices, but they can influence how an oil shock affects the broader economy. Higher energy prices initially push inflation higher from the supply side, but monetary policy can respond by weakening demand through tighter financial conditions, helping prevent the shock from becoming embedded in underlying inflation and inflation expectations.This creates an important interaction between oil and monetary policy. Oil prices can push inflation higher, while the central bank can counteract the resulting inflationary pressure by cooling demand. The more persistent the oil shock and the stronger its impact on inflation expectations, the greater the pressure on the central bank to keep policy restrictive. This article was written by Giuseppe Dellamotta at investinglive.com.