What is the short-run effect of an unexpected and temporary monetary policy tightening on inflation? The conventional view suggests that inflation should have a negative reaction to such a monetary policy move (see e.g. Woodford (2003a)). However, empirical investigations based on the VAR-methodology cast doubts on this prediction. Figure 1 makes this point. In a trivariate VAR for the U.S. that considers inflation, output gap, and the federal funds rate, an unexpected one-shot increase in the policy rate leads to a positive and significant reaction of inflation. As said, this result hardly squares with the predictions offered by standard models of the business cycle. This is the reason why Eichenbaum (1992) labeled as the "price puzzle" this empirical conditional correlation.
A growing body of the empirical literature has supported the relevance of the "cost channel" in determining inflation. The idea is simple. Cash-constrained firms must borrow money from financial intermediaries to pay the wage-bills to the workers employed in the production process. Consequently, the interest rate paid on borrowings is one of the elements of the firms’ marginal costs. This creates a direct and positive link between oscillations in the marginal costs and movements in the prices charged by monopolistically competitive firms. In aggregate terms, this translates into movements in the inflation rate.
Therefore, in a simple AD/AS model, monetary policy affects inflation throughout two channels: The standard "demand channel", which is featured by a transmission going from the policy rate to demand and finally to the price level, and the "supply channel" (or "cost channel"), based on the influence that the policy rate exerts on inflation via firms’ marginal costs. If the latter is stronger than the former, the model can produce a conditional correlation between inflation and the policy rate in line with the one in Figure 1.
Of course, the assessment of the relative strength of the supply vs. demand channel must be based on a fully specified model. Along this line, Chowdhury et al (2006) add to an estimated Phillips curve with the cost-channel a purely forward looking IS curve along with a Taylor rule without interest rate smoothing motive. Their findings point towards a positive reaction of the inflation rate to a monetary policy shock for Italy, the U.K., and possibly the United States. Christiano et al (2005) estimate a model allowing for several nominal and real rigidities by matching the impulse response functions of the endogenous variables of the model to a monetary policy shock. In so doing, they automatically build into their model a positive reaction of the inflation rate to a monetary policy tightening. By contrast, Rabanal (2007) estimates the Christiano et al (2005) model with Bayesian techniques and show that, even in presence of a significant cost channel, a monetary policy tightening is actually associated to a negative on-impact inflation reaction.
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Cost Channel and the Price Puzzle: The Role of Interest Rate Smoothing
