Financial crisis, effective policy rules and bounded rationality in a New Keynesian framework

Abstract

This paper extends a standard open-economy New Keynesian model to include a third-generation “balance sheet effect” which is made operational through an endogenous risk premium impacting on investment. Using rational expectations and adaptive learning solutions, the efficiency of alternative monetary policy rules is examined during a period of financial crisis. We find that the Taylor rule is the welfare superior policy, questioning the idea of an “information encompassing” inflation-forecast based rule. Under adaptive learning we find additional policy traction and less instrument variability in rules augmented with the exchange rate. All rules, however, advocate a sharp initial interest rate response to the crisis.

Appendix

Adaptive Learning is an alternative specification for expectations and represents a complete dynamic system enabling agents to learn adaptively using a least squares algorithm based on the Kalman filter (see Hall et al. (2000) and Garrat and Hall (1995)).

Under adaptive learning, agents are unaware of the true structure of the economy as it would exist under rational expectations and must learn about it over time using a ‘reasonable rule of thumb’. Therefore, agents employ their own ‘forecast rule’ (or perceived law of motion; PLM) to obtain estimates of the unobserved state variables, or the actual law of motion (ALM) of the economy. Using their PLM, agents optimally update their expectations of future endogenous variables each period subject to observed data. It is in this spirit that agents are boundedly rational. The system, therefore, is self-referential and we draw on the properties inherent in the E-stability principle where, under standard conditions, small forecasting errors made relative to the rational solution (ALM) are corrected over time.²²

Garrat and Hall (1995) and Evans and Honkapohja (2001), among others, note that there is no theoretical basis for modeling the PLM of agents, so we are left to form a guess as to how agents learn over time. As is common in the endogenous learning literature, we adopt simple forecast rules based on past values of relevant variables.²³ In this study, for any expected variable X, its PLM in time t follows

$$ \hat{E}_{t} X_{t + 1} = \rho_{0,t} + \rho_{1,t} X_{t - 1} . $$

(20)

This PLM forms the one period ahead expectation of X based on information held at time t where $\rho_{0t}$ and $\rho_{1,t}$ are a set of time-varying parameters each evolving over time according to the following stationary AR(1) process

$$ \rho_{i,t} = \alpha_{i} \rho_{i,t - 1} + \omega_{i,t} , $$

(21)

where $i = \begin{array}{*{20}c} {0,} & 1 \\ \end{array}$ for each respective case, $\omega_{i,t}$ is an iid error term, and $\alpha_{i} < 1$.

Given that (21) is a stationary process, over time $\rho_{0} \to \bar{\rho }_{0}$ and $\rho_{1} \to \bar{\rho }_{1}$ thus representing a stable mapping from the PLM to the ALM and satisfying the E-stability principle for convergence (see Evans and Honkapohja 2001 for a full proof).