Should central banks lean against the bubble? The monetary policy conundrum under credit frictions and capital accumulation

We develop an OLG model with productive capital accumulation, frictional financial markets, sticky prices and a form of heterogeneity among households which splits them between borrowers and lenders in the credit market. In the spirit of Galí J., 2014. Monetary policy and rational asset price bubbles. Am. Econ. Rev. 104, 721–752, we use this framework to study the consequences of different monetary policy rules, focusing in particular on the so-called “leaning against the wind” policy, according to which the central bank sets the nominal rate so as to prevent the formation of asset price bubbles in the financial markets. Our framework can generate stationary equilibria with rational asset bubbles of different types. In some of these equilibria, the presence of bubbly assets can increase the values of stationary capital and output, whereas in others it reduces them, and we determine three main channels through which the stationary value of the bubble (relative to GDP) can shift the economy in one of the two types of stationary equilibria. We then run numerical simulations to evaluate the dynamic behavior of a bubbly economy in response to different monetary policy rules. Our main conclusion is that, under credit frictions and sticky prices, a “leaning against the wind” policy is desirable only if the reactions of the central bank to inflation and output deviations from their targets are small. If this was not the case, the central bank could run the risk of increasing bubble volatility and rapidly turn the expansionary shock into a recession.