Monetary Policy and Asset Prices with In nite-Horizon Learning

We study the stabilizing properties of interest rate rules that grant an explicit response to stock prices in a New Keynesian framework where imperfect knowledge and incomplete markets generate wealth e¤ects from equity holdings. Boundedly-rational agents need to form in nitehorizon forecast about pay-o¤ relevant variable in order to solve their intertemporal optimization problems, as in Preston (2005, 2006). In this context, we nd that, when the central bank adopts a forecast-based Taylor rule, granting an explicit response to stock prices can facilitate the attainment of a determinate rational expectations equilibrium which is also stable under learning dynamics. Keywords: Interest Rate Rules; Multiple Equilibria; Determinacy; Multiple Sectors; Learning; Expectational Stability; JEL Classi cations: C62, D83, E32, E52. 1 Introduction Since burst of the dot.com bubble in early 2000  and even more after the 2007-8 global nancial crisis  policy-makers and academic economists have lively debated whether central banks should move the policy rate in response to asset price uctuations. Advocates of such policy argue that, Corresponding Author. School of Economics, LeBow College of Business, Drexel University, Gerri C. LeBow Hall, 3220 Market Street, Philadelphia, PA 19104. Email: marco.airaudo@drexel.edu because of frictions in credit and/or nancial markets, asset prices exert distortionary e¤ects on individual decisions.1 By raising interest rates during a nancial booms (and cutting them during a downturn), a learning-against-the-wind policy could smooth those uctuations and therefore tame their undesired consequences on the macroeconomy. Opponents of it claim instead that the costs might outweigh the gains as i) part of those uctuations might be e¢ cient reactions to market conditions, and ii) a policy strictly targeting price stability might be su¢ cient to stabilize also asset prices. 2 In this paper, we assess the desirability of interest rate rules granting an explicit response to stock prices for what concerns the determinacy of an equilibrium under rational expectations, and its stability under learning dynamics. We consider a small-scale New Keynesian DSGE model where boundedly-rational agents trade risky equity shares issues by monopolistically competitive pro t-maximizing rms and form expectations about future variables using simple adaptive rules. In this respect, we adopt the in nite horizon learning approach proposed by Preston (2005, 2006): agents and rms are internally rational, in the sense that they take optimal decision subject to known individual objectives and constraints, understanding the mapping betweeen own actions and expected pay-o¤s, given subjective beliefs about aggregate variables beyond their control. However, they do not have any knowledge about other agentsobjectives, constraints and beliefs. As in Prestons work, for arbitrary beliefs satisfying standard probability laws, the solutions to intertemporal optimization problems requires agents to make in nite horizon forecasts about their pay-o¤ relevant variables. We show that in nite-horizon-learning (henceforth, IHL) induces wealth e¤ects of equity shares holdings on consumption via householdsEuler equation. We therefore study the determinacy and expectational stability properties of forward-looking Taylor rules granting an explicit response to stock prices. Our main ndings are the followings. First, we nd that, in the context of our model, forward-looking rules which exclusively respond to ination and output perform better than in Preston (2006). The latter shows that i) no determinate equilibrium is learnable, and ii) learnability of the fundamental REE requires an implausibly large response coe¢ cient to ination (larger than 100! ). A key di¤erence with respect to ours, is that in Prestons set-up there is no Case, Quigley and Shiller (2005) and Carrol, Otsuka and Slacalek (2011) provide statistical evidence for housing and nancial wealth e¤ects on consumption. The debate between Bernanke and Gertler (1999, 2001) and Cecchetti et al. (2000, 2002) is the most prominent. Dupor (2005) discusses optimal monetary policy in a New-Keynesian model subject to exuberance shocks.