Convergence of Least Squares Learning in Self-Referential Discontinuous Stochastic Models

We examine the stability of rational expectations equilibria in the class of models in which the decision of the individual agent is discontinuous with respect to the state variables. Instead of rational expectations, each agent learns the unknown parameters through a recursive stochastic algorithm. If the agents the estimated value function ``rapidly'' enough, then each agent learns the true value function associated with the optimal action with probability, and almost always takes the optimal action asymptotically.

Escapist policy rules

We study a simple, microfounded macroeconomic system in which the monetary authority employs a Taylor-type policy rule. We analyze situations in which the self-confirming equilibrium is unique and learnable according to Bullard and Mitra (2002). We explore the prospects for the use of 'large deviation' theory in this context, as employed by Sargent (1999) and Cho, Williams, and Sargent (2002). We show that our system can sometimes depart from the self-confirming equilibrium towards a non-equilibrium outcome characterized by persistently low nominal interest rates and persistently low inflation. Thus we generate events that have some of the properties of "liquidity traps" observed in the data, even though the policymaker remains committed to a Taylor-type policy rule which otherwise has desirable stabilization properties

Escapist Policy Rules

We study a simple, microfounded macroeconomic system in which the monetary authority employs a Taylor-type policy rule. We analyze situations in which the self-confirming equilibrium is unique and learnable according to Bullard and Mitra (2002). We explore the prospects for the use of ‘large deviation’ theory in this context, as employed by Sargent (1999) and Cho, Williams, and Sargent (2002). We show that our system can sometimes depart from the self-confirming equilibrium towards a non-equilibrium outcome characterized by persistently low nominal interest rates and persistently low inflation. Thus we generate events that have some of the properties of “liquidity traps” observed in the data, even though the policymaker remains committed to a Taylor-type policy rule which otherwise has desirable stabilization properties.Learning, monetary policy rules, escape dynamics

Escapist policy rules

We study a simple, microfounded macroeconomic system in which the monetary authority employs a Taylor-type policy rule. We analyze situations in which the self-confirming equilibrium is unique and learnable according to Bullard and Mitra (2002). We explore the prospects for the use of ‘large deviation’ theory in this context, as employed by Sargent (1999) and Cho, Williams, and Sargent (2002). We show that our system can sometimes depart from the self-confirming equilibrium towards a non-equilibrium outcome characterized by persistently low nominal interest rates and persistently low in- flation. Thus we generate events that have some of the properties of “liquidity traps” observed in the data, even though the policymaker remains committed to a Taylor-type policy rule which otherwise has desirable stabilization properties.Monetary policy ; Inflation (Finance) ; Interest rates

Learning and Model Validation

This paper studies the following problem. An agent takes actions based on a possibly misspecified model. The agent is 'large', in the sense that his actions influence the model he is trying to learn about. The agent is aware of potential model misspecification and tries to detect it, in real-time, using an econometric specification test. If his model fails the test, he formulates a new better-fitting model. If his model passes the test, he uses it to formulate and implement a policy based on the provisional assumption that the current model is correctly specified, and will not change in the future. We claim that this testing and model validation process is an accurate description of most macroeconomic policy problems. Unfortunately, the dynamics produced by this process are not well understood. We make progress on this problem by relating it to a problem that is well understood. In particular, we relate it to the dynamics of constant-gain stochastic approximation algorithms. This enables us to appeal to well known results from the large deviations literature to help us understand the dynamics of testing and model revision. We show that as the agent applies an increasingly stringent specification test, the large deviation properties of the discrete model validation dynamics converge to those of the continuous learning dynamics. This sheds new light on the recent constant-gain learning literature.Learning, Validation, Relative Entropy, Large Deviation

Escaping Nash inflation

Mean dynamics govern convergence to rational expectations equilibria of self-referential systems under least squares learning. We highlight escape dynamics that propel away from a rational expectations equilibrium under fixed-gain recursive learning schemes. These learning schemes discount past observations. In a model with a unique self-confirming equilibrium, we show that the destination of the escape dynamics is an outcome associated with government discovery of too strong a version of the natural rate hypothesis. That destination is not sustainable as a self-confirming equilibrium but is visited recurrently. The escape route dynamics cause recurrent outcomes close to the Ramsey (commitment) inflation rate in a model with an adaptive government. JEL Classification: E3, E52, E58

Efficiency and marginal cost pricing in dynamic competitive markets with friction

This paper examines a dynamic general equilibrium model with supply friction. With or without friction, the competitive equilibrium is efficient. Without friction, the market price is completely determined by the marginal production cost. If friction is present, no matter how small, then the market price fluctuates between zero and the "choke-up" price, without any tendency to converge to the marginal production cost, exhibiting considerable volatility. The distribution of the gains from trading in an efficient allocation may be skewed in favor of the supplier, although every player in the market is a price taker.Dynamic general equilibrium model with supply friction, choke-up price, marginal production cost, welfare theorems