Monetary policy, indeterminacy and learning

The development of tractable forward looking models of monetary policy has lead to an explosion of research on the implications of adopting Taylor-type interest rate rules. Indeterminacies have been found to arise for some specifications of the interest rate rule, raising the possibility of inefficient fluctuations due to the dependence of expectations on extraneous "sunspots ". Separately, recent work by a number of authors has shown that sunspot equilibria previously thought to be unstable under private agent learning can in some cases be stable when the observed sunspot has a suitable time series structure. In this paper we generalize the "common factor "technique, used in this analysis, to examine standard monetary models that combine forward looking expectations and predetermined variables. We consider a variety of specifications that incorporate both lagged and expected inflation in the Phillips Curve, and both expected inflation and inertial elements in the policy rule. We find that some policy rules can indeed lead to learnable sunspot solutions and we investigate the conditions under which this phenomenon arises

Monetary Policy, Indeterminacy and Learning

The development of tractable forward looking models of monetary policy has lead to an explosion of research on the implications of adopting Taylor-type interest rate rules. Indeterminacies have been found to arise for some specifications of the interest rate rule, raising the possibility of inefficient fluctuations due to the dependence of expectations on extraneous “sunspots ”. Separately, recent work by a number of authors has shown that sunspot equilibria previously thought to be unstable under private agent learning can in some cases be stable when the observed sunspot has a suitable time series structure. In this paper we generalize the “common factor ”technique, used in this analysis, to examine standard monetary models that combine forward looking expectations and predetermined variables. We consider a variety of specifications that incorporate both lagged and expected inflation in the Phillips Curve, and both expected inflation and inertial elements in the policy rule. We find that some policy rules can indeed lead to learnable sunspot solutions and we investigate the conditions under which this phenomenon arises.Monetary Policy, sunspots, expectations, learning, stability

Learning about Education

Limited human capital investment is a common characteristic of low-income countries despite the fact that estimated returns to educational investment in low-income countries are generally higher than in high-income countries. Empirical evidence suggests that income and credit constraints can only account for a small part of this underinvestment. Recent experimental evidence shows that families' misperceptions about the returns to education play a large role in their low investment levels. This paper builds a model of human capital and growth that incorporates an adaptive learning mechanism to capture the way agents form perceptions about returns to education. In an economy where human capital investments have both private and public returns, we find multiple learnable equilibria, including those which are characterized by low investment and low returns. We also find that even when the rational equilibrium corresponds to a high level of human capital investment, the learning mechanism, influenced by the agents' priors and cultural bias, may impart low human capital investment for extended periods. Policies that can speed up the learning process are examined and it is found that faster rates of growth can be achieved through interventions.growth, education, learning

Are Microloans Bad for Growth?

This paper constructs a two-period overlapping generations model of human capital investment decisions where a microloan program designed to finance entrepreneurial activities is active. It is shown that, in the presence of human capital externalities (social returns to education) there exists a range of microloan amounts that are growth depressing and welfare decreasing through their affect on the opportunity cost of schooling. By increasing the opportunity cost of schooling, microloans divert investment away from human capital: by failing to internalize the social returns to education, households’ individually optimal investment decisions in the face of microcredit availability act to depress the growth of the economy and result in sub-optimal welfare outcomes.microloans, growth, human capital

The Dynamic Behavior of Efficient Timber Prices

The problem of when to optimally harvest trees when timber prices evolve according to an exogenous stochastic process has been studied extensively in recent decades. However, little attention has been given to the appropriate form of the stochastic process for timber prices, despite the fact that the choice of a process has important effects on optimal harvesting decisions. We develop a simple theoretical model of a timber market and show that there exists a rational expectations equilibrium in which prices evolve according to a stationary ARMA(1,1) process. Simulations are used to analyze a model with a more general representation of timber stock dynamics and to demonstrate that the unconditional distribution for rational timber prices is asymmetric. Implications for the optimal harvesting literature are: 1) market efficiency provides little justification for random walk prices, 2) unit root tests, used to analyze the informational efficiency of timber markets, do not distinguish between efficient and inefficient markets, and 3) failure to recognize asymmetric disturbances in time-series analyses of historical timber prices can lead to sub-optimal harvesting rules.

Eductive stability in real business cycle models

We re-examine issues of coordination in the standard RBC model. Can the unique rational expectations equilibrium be “educed” by rational agents who contemplate the possibility of small deviations from equilibrium? Surprisingly, we find that coordination along this line cannot be expected. Rational agents anticipating small but possibly persistent deviations have to face the existence of retroactions that necessarily invalidate any initial tentative “common knowledge” of the future. This "impossibility" theorem for eductive learning is not fully overcome when adaptive learning is incorporated into the framework.standard RBC model ; coordination

Interest rate pegs in New Keynesian models

Financial support from National Science Foundation Grant No. SES-1559209 is gratefully acknowledged.The conventional policy perspective is that lowering the interest rate increases output and inflation in the short run, while maintaining inflation at a higher level requires a higher interest rate in the long run. In contrast, it has been argued that a Neo‐Fisherian policy of setting an interest‐rate peg at a fixed higher level will increase the inflation rate. We show that adaptive learning argues against the Neo‐Fisherian approach. Pegging the interest rate at a higher level will induce instability and most likely lead to falling inflation and output over time. Eventually, this would precipitate a change of policy.PostprintPeer reviewe

Stable near-rational sunspot equilibria

Financial support from National Science Foundation Grant No. SES-1559209 is gratefully acknowledged.We introduce a new class of solutions to nonlinear forward-looking models called near-rational sunspot equilibria (NRSE). NRSE are natural nonlinear extensions of the usual sunspot equilibria associated with the linearized version of the economy, and are near-rational in that agents use the optimal linear forecasting model when forming expectations. Generic results for existence and stability under learning are established. NRSE in indeterminate nonlinear models are found to be stable under learning provided that the corresponding linearized model's minimal state variable solution is E-stable. NRSE are readily computable, and our results make it possible to use the standard linear tools to search for stable NRSE. We illustrate our results using a canonical nonlinear New Keynesian model.PostprintPeer reviewe

Equilibrium selection, observability and backward-stable solutions

Financial support from National Science Foundation Grant No. SES-1559209 is gratefully acknowledged.The robustness of stability under learning to observability of exogenous shocks is examined. Regardless of observability assumptions, the minimal state variable solution is robustly stable under learning provided the expectational feedback is not both positive and large, while the nonfundamental solution is never robustly stable. Overlapping generations and New Keynesian models are considered and concerns raised in [Cochrane, J., 2011. Determinacy and identification with Taylor rules. Journal of Political Economy 119, 565-615, Cochrane, J., 2017. The new-Keynesian liquidity trap. Journal of Monetary Economics, forthcoming.] are addressed.PostprintPeer reviewe