Learning to forecast and cyclical behavior of output and inflation

This paper considers a sticky price model with a cash-in-advance constraint where agents forecast inflation rates with the help of econometric models. Agents use least squares learning to estimate two competing models of which one is consistent with rational expectations once learning is complete. When past performance governs the choice of forecast model, agents may prefer to use the inconsistent forecast model, which generates an equilibrium where forecasts are inefficient. While average output and inflation result the same as under rational expectations, higher moments differ substantially: output and inflation show persistence, inflation responds sluggishly to nominal disturbances, and the dynamic correlations of output and inflation match U.S. data surprisingly well

Learning and equilibrium selection in a monetary overlapping generations model with sticky prices

We study adaptive learning in a monetary overlapping generations model with sticky prices and monopolistic competition for the case where learning agents observe current endogenous variables. Observability of current variables is essential for informational consistency of the learning setup with the model set up but generates multiple temporary equilibria when prices are flexible and prevents a straightforward construction of the learning dynamics. Sticky prices overcome this problem by avoiding simultaneity between prices and price expectations. Adaptive learning then robustly selects the determinate (monetary) steady state independent from the degree of imperfect competition. The indeterminate (non-monetary) steady state and non-stationary equilibria are never stable. Stability in a deterministic version of the model may differ because perfect foresight equilibria can be the limit of restricted perceptions equilibria of the stochastic economy with vanishing noise and thereby inherit different stability properties. This discontinuity at the zero variance of shocks suggests to analyze learning in stochastic models

On the relation between robust and Bayesian decision making

This paper compares Bayesian decision theory with robust decision theory where the decision maker optimizes with respect to the worst state realization. For a class of robust decision problems there exists a sequence of Bayesian decision problems whose solution converges towards the robust solution. It is shown that the limiting Bayesian problem displays infinite risk aversion and that decisions are insensitive (robust) to the precise assignment of prior probabilities. This holds independent from whether the preference for robustness is global or restricted to local perturbations around some reference model

Optimal monetary policy with imperfect common knowledge

We study optimal nominal demand policy in an economy with monopolistic competition and flexible prices when firms have imperfect common knowledge about the shocks hitting the economy. Parametrizing firms´ information imperfections by a (Shannon) capacity parameter that constrains the amount of information flowing to each firm, we study how policy that minimizes a quadratic objective in output and prices depends on this parameter. When price setting decisions of firms are strategic complements, for a large range of capacity values optimal policy nominally accommodates mark-up shocks in the short-run. This finding is robust to the policy maker observing shocks imperfectly or being uncertain about firms´ capacity parameter. With persistent mark-up shocks accommodation may increase in the medium term, but decreases in the long-run thereby generating a hump-shaped price response and a slow reduction in output. Instead, when prices are strategic substitutes, policy tends to react restrictively to mark-up shocks. However, rational expectations equilibria may then not exist with small amounts of imperfect common knowledge

Should macroeconomists consider restricted perception equilibria? Evidence from the experimental laboratory

Abstract: This paper studies a simple model of output and inflation in the experimental laboratory. While the Rational Expectations Equilibrium (REE)predicts output and inflation to be white noise processes, output and inflation in experimental sessions display stable cyclical patterns. For about 50 model periods agents' expectations, which are the sole source of these patterns, are described extremely well by a Restricted Perceptions Equilibrium (RPE). In this equilibrium agents use the univariate forecast function which generates the lowest mean squared forecast error at the 1-step forecast horizon and iterate these forecasts to derive multi-step predictions. After about 50 model periods agents seem to learn that their simple univariate forecast function is misspecified and start to employ different forecast models for different prediction horizons. The data suggests that the new models are again optimal univariate forecast functions and evidence in favor of convergence towards the REE remains weak, even after more than 100 model periods. However, for model parameterizations where an RPE does not exist, agents' expectations are captured relatively well by the REE.Experiments, Equilibrium Selection, Restricted Perceptions Equilibrium, Univariate Forecast Functions

Optimal Stabilization Policy When the Private Sector Has Information Processing Constraints

This paper considers a linear-quadratic control problem and determines how optimal policy is affected when the private sector has finite (Shannon) capacity to process information. Such capacity constraints prevent private agents from perfectly observing the state variables and the policy choices. The first result is that the control problem when including these constraints remains to be of a linear-quadratic form, which makes the problem technically tractable. The main difference to a standard problem are the costs associated with the use of the policy instrument, which are now endogenous. Depending on parameters these costs might be either higher or lower and lead to less or more aggressive optimal policies, respectively. If shocks show persistence and are heteroskedastic then the costs of using the policy instrument are non-constant and generate either sluggish or overshooting optimal policy reactions.optimal policy, Shannon capacity, communication theory, sluggish and overshooting policy, measurement errors

On the Relation between Robust and Bayesian Decision Making

This paper compares Bayesian decision theory with robust decision theory where the decision maker optimizes with respect to the worst state realization. For a class of robust decision problems there exists a sequence of Bayesian decision problems whose solution converges towards the robust solution. It is shown that the limiting Bayesian problem displays infinite risk aversion and that decisions are insensitive (robust) to the precise assignment of prior probabilities. This holds independent from whether the preference for robustness is global or restricted to local perturbations around some reference model.robust decision theory, uncertainty aversion, risk aversion

Competitive Prices in Markets with Search and Information Frictions

This paper introduces directed search into the sequential search model of Diamond (1971) by allowing buyers to observe the distribution of prices charged by two (or more) distinct subgroups of firms in the market. This enables buyers to direct their searches towards the most desirable group of firms. Search within groups remains random since price information about each of the groups is imperfect, as in a standard setup. I find that competitive pricing is then the unique equilibrium outcome. This holds even when different buyers observe very different groups of firms and face different and strictly positive levels of search costs. Considering an explicit learning scheme the paper shows that convergence of prices to competitive equilibrium depends crucially on the level of search costs and the number of groups observed by buyers. Lower search costs and a higher number of observed groups generate a higher price elasticity of demand and thereby favor the emergence of competitive prices.Diamond paradox, competitive pricing, random and directed sequential search, equilibrium search model, learning

Learning and Equilibrium Selection in a Monetary Overlapping Generations Model with Sticky Prices

We study adaptive learning in a monetary overlapping generations model with sticky prices and monopolistic competition for the case where learning agents observe current endogenous variables. Observability of current variables is essential for informational consistency of the learning setup with the model set up but generates multiple temporary equilibria when prices are flexible and prevents a straightforward construction of the learning dynamics. Sticky prices overcome this problem by avoiding simultaneity between prices and price expectations. Adaptive learning then robustly selects the determinate (monetary) steady state independent from the degree of imperfect competition. The indeterminate (non-monetary) steady state and non-stationary equilibria are never stable. Stability in a deterministic version of the model may differ because perfect foresight equilibria can be the limit of restricted perceptions equilibria of the stochastic economy with vanishing noise and thereby inherit different stability properties. This discontinuity at the zero variance of shocks suggests to analyze learning in stochastic models.adaptive learning, sticky prices, temporary equilibrium