Monetary Policy,Expectations and Commitment*

Commitment in monetary policy leads to equilibria that are superior to those from optimal discretionary policies. A number of interest‐rate reaction functions and instrument rules have been proposed to implement or approximate commitment policy. We assess these rules in terms of whether they lead to a rational expectations equilibrium that is both locally determinate and stable under adaptive learning by private agents. A reaction function that appropriately depends explicitly on private sector expectations performs particularly well on both counts.     

Equilibrium Determinacy under Monetary and Fiscal Policies in an Overlapping Generations Model

This paper studies the issue of equilibrium determinacy under monetary and fiscal policy feedback rules in an optimizing general equilibrium model with overlapping generations and flexible prices. It is shown that equilibria may be determinate also when monetary and fiscal policies are both 'passive'. In particular, under passive monetary rules, equilibrium uniqueness is more likely to be verified when fiscal policies are less committed to public debt stabilization.     

Friedman's Money Supply Rule vs. Optimal Interest Rate Policy

Using New Keynesian models, we compare Friedman's k‐percent money supply rule to optimal interest rate setting, with respect to determinacy, stability under learning and optimality. First we review the recent literature: open‐loop interest rate rules are subject to indeterminacy and instability problems, but a properly chosen expectations‐based rule yields determinacy and stability under learning, and implements optimal policy. We show that Friedman's rule also can generate equilibria that are determinate and stable under learning. However, computing the mean quadratic welfare loss, we find for calibrated models that Friedman's rule performs poorly when compared to the optimal interest rate rule.     

Basins of attraction and equilibrium selection under different learning rules

A deterministic learning model applied to a game with multiple equilibria produces distinct basins of attraction for those equilibria. In symmetric two-by-two games, basins of attraction are invariant to a wide range of learning rules including best response dynamics, replicator dynamics, and fictitious play. In this paper, we construct a class of three-by-three symmetric games for which the overlap in the basins of attraction under best response learning and replicator dynamics is arbitrarily small. We then derive necessary and sufficient conditions on payoffs for these two learning rules to create basins of attraction with vanishing overlap. The necessary condition requires that with probability one the initial best response is not an equilibrium to the game. The existence of parasitic or misleading actions allows subtle differences in the learning rules to accumulate.     

Learning by replicator and best-response: the importance of being indifferent

This paper compares two learning processes, namely those generated by replicator and best-response dynamics, from the point of view of the asymptotics of play. We base our study on the intersection of the basins of attraction of locally stable pure Nash equilibria for replicator and best-response dynamics. Local stability implies that the basin of attraction has positive measure but there are examples where the intersection of the basin of attraction for replicator and best-response dynamics is arbitrarily small. We provide conditions, involving the existence of an unstable interior Nash equilibrium, for the basins of attraction of any locally stable pure Nash equilibrium under replicator and best-response dynamics to intersect in a set of positive measure. Hence, for any choice of initial conditions in sets of positive measure, if a pure Nash equilibrium is locally stable, the outcome of learning under either procedure coincides. We provide examples illustrating the above, including some for which the basins of attraction exactly coincide for both learning dynamics. We explore the role that indifference sets play in the coincidence of the basins of attraction of the stable Nash equilibria.     

Unobserved heterogeneity and equilibrium: an experimental study of Bayesian and adaptive learning in normal form games

We describe an experiment based on a simple two-person game designed so that different learning models make different predictions. Econometric analysis of the experimental data reveals clear heterogeneity in the subjects’ learning behavior. But the subjects follow only a few decision rules for basing their play on their information, and these rules have simple cognitive interpretations. There is a unique equilibrium in pure strategies, and many equilibria in mixed strategies. We find that the only equilibrium consistent with the data is one of the mixed strategy equilibria. This equilibrium is shown, surprisingly, to be consistent with Jordan's Bayesian model.     

异质性预期、投资者行为与房价波动：上海和广州的双城记?

房地产市场中存在大量的投资者,其市场行为会使房价出现大幅的波动,从而引起市场不稳定。文章在引入投资者异质性预期假设的基础上,构建了包含房地产消费者、投资者、供给者在内的房地产市场均衡模型,分析了房地产市场中基本面型投资者和趋势型投资者的异质性行为对房价变动的影响,并利用上海和广州两个一线城市的实际数据进行了对比分析。研究结果表明：在房地产市场中,两类投资者对于未来房价不同的预期以及投资行为会引起房价的变动;上海投资者的行为整体上会使上海的房价始终处于不断上涨的趋势中,而广州投资者的行为会随着投资策略的转变而使静态下的“整体上推动房价趋势型变化”转变为“整体上将房价‘拉回’基本面价格”;房地产市场中的投资者占比会显著影响房价的变动趋势,当基本面型投资者占比上升时,房价偏离度和房价变动率降低,而当这类投资者占比达到峰值时,房价会出现拐点;投资者之间的策略转换速度也会通过引起基本面型投资者占比的变化,引起房价的频繁波动,而且策略转换速度越快,房价波动越频繁。     

Heterogeneous learning

There is by now a large literature characterising conditions under which learning schemes converge to rational expectations equilibria (REEs). It has been claimed that these results depend on the assumption of homogeneous agents and homogeneous learning. This paper analyses the stability of REEs under heterogeneous adaptive learning, for the class of self-referential linear stochastic models. Agents may differ in their initial perceptions about the evolution of the economy, the degrees of inertia in revising their expectations, or the learning rules they use. General conditions are provided for local stability of an REE. In general, it is not possible to show that stability under homogeneous learning implies stability under heterogeneous learning. To illustrate how to apply the results, several examples are provided.     

Delays and equilibria with large and small information in social learning

The general model of social learning with irreversible investment and endogenous timing is analyzed for any distribution of private informations. Strategic complementarities and multiple equilibria appear which are generated solely by information externalities. Different equilibria generate strikingly different amounts of information. The impacts of various assumptions (bounded beliefs, large number of agents, discrete time and short periods) are examined carefully. The properties are robust to the introduction of observation noise with a continuum of agents.     

RE‐EXAMINATION OF THE GROWTH‐ENHANCING BUBBLE

We investigate the growth and welfare effects of the bubble that arise on equities on newly created firms by R&D activities. Considering an economy where the input to the R&D sector is the final goods financed by the savings of the household sector, we show that such a bubble has a growth‐enhancing effect under the condition opposite to the previous literature. We also explore the characteristics of the steady state equilibrium with the bubble and demonstrate that there can be dual bubbly equilibria, one of which is unstable and the other stable, and that the growth and welfare effects of an unexpected permanent change in the initial bubble are very different depending on which equilibrium the economy stays in.     

Saddlepath learning

Saddlepath learning occurs when agents learn adaptively using a perceived law of motion that has the same form as the saddlepath relationship in rational expectations equilibrium. Under saddlepath learning, we obtain a completely general relationship between determinacy and e-stability, and generalise minimum state variable results previously derived only under full information. When the system is determinate, we show that a learning process based on the saddlepath is always e-stable. When the system is indeterminate, we find there is a unique MSV solution that is iteratively e-stable. However, in this case there is a sunspot solution that is learnable as well. We conclude by demonstrating that our results hold for any information set.     

The Design and Performance of Sharing Rules for a Partnership in Continuous Time

We study repeated partnerships with imperfect monitoring and risk neutrality. The interval between the partners' decisions, the delay, is given but can be arbitrarily small. Each stage-game's output is Gaussian, with mean and variance depending on the partners' actions, making the sequence of outcomes a discretization of a diffusion. A sharing rule is efficient if there is an equilibrium of the corresponding game whose outcomes are Pareto efficient; it is stable if these equilibria approach a limit as the delay approaches zero. We characterize partnerships for which there exist stable, efficient sharing rules, and describe the corresponding equilibria.Journal of Economic LiteratureClassification Numbers: C73, D2, D82.     

On Endogenously Staggered Prices

Taylor's model of staggered contracts is an influential explanation for nominal inertia and the persistent real effects of nominal shocks. However, in standard imperfect competition models, if agents are allowed to choose the timing of pricing decisions, they will typically choose to synchronize. This paper provides a simple model of imperfect competition which produces stable staggering. Our argument relies on strategic interaction at two levels—between firms within an industries, and across industries—and produces a continuum of staggered price equilibria. These equilibria are strict, and hence stable under a simple adaptive learning process.     

Constitutional Rules of Exclusion in Jurisdiction Formation

The rules under which jurisdictions (nations, provinces) can deny immigration or expel residents are generally governed by a constitution, but there do not exist either positive or normative analyses to suggest what types of exclusion rules are best. We stylize this problem by suggesting four constitutional rules of admission: free mobility, admission by majority vote, admission by unanimous consent, admission by a demand threshold for public goods. In a simple model we characterize the equilibria that result from these rules, and provide a positive theory for which constitutional rules will be chosen.     

The design of monetary and fiscal policy: A global perspective

We study the emergence of multiple equilibria in models with capital and bonds under various monetary and fiscal policies. We show that the presence of capital is indeed another independent source of local and global multiplicities, even under active policies that yield local determinacy. We also show how a very similar mechanism generates multiplicities in models with bonds and distortionary taxation. We then explore the design of monetary policies that avoid multiple equilibria. We show that interest rate policies that respond to the output gap, while potentially a source of significant inefficiencies, may be effective in preventing multiple equilibria and costly oscillatory equilibrium dynamics.     

Cycling in a stochastic learning algorithm for normal form games

In this paper we study a stochastic learning model for 2×2 normal form games that are played repeatedly. The main emphasis is put on the emergence of cycles. We assume that the players have neither information about the payoff matrix of their opponent nor about their own. At every round each player can only observe his or her action and the payoff he or she receives. We prove that the learning algorithm, which is modeled by an urn scheme proposed by Arthur (1993), leads with positive probability to a cycling of strategy profiles if the game has a mixed Nash equilibrium. In case there are strict Nash equilibria, the learning process converges a.s. to the set of Nash equilibria.     

Learning in Elections and Voter Turnout

Voter turnout in game theoretic models of voting has typically been difficult to predict because of the problem of multiple Nash equilibria ( Palfrey and Rosenthal 1983, 1985 ). Many of these equilibria require an extreme precision of beliefs among voters that is unlikely to be reached in real elections. At the same time, mechanisms like pre‐election polls exist to shape the beliefs of voters about expected turnout. We combine these two features in a model of voter learning in elections and characterize the asymptotically stable equilibria of both complete and incomplete information games in a simple symmetric setting with two candidates. We also show how the model can be used to qualitatively explain several phenomena observed in reality: increases in costs of voting affect turnout adversely but there may be persistence of turnout levels between elections even though costs and other parameters change. Increase in uncertainty increases turnout while increases in the size of the electorate decrease it, in line with intuition.     

WHEN DOES DETERMINACY IMPLY EXPECTATIONAL STABILITY?

Since the introduction of rational expectations, there have been issues with multiple equilibria and equilibrium selection. We study the connections between determinacy of rational expectations equilibrium and learnability of that equilibrium in a general class of purely forward‐looking models. Our framework is sufficiently flexible to encompass lags in agents' information and either finite horizon or infinite horizon approaches to learning. We are able to isolate conditions under which determinacy does and does not imply learnability and also conditions under which long‐horizon forecasts make a clear difference for learnability. Finally, we apply our result to a relatively general New Keynesian model.     

Increasing Returns, Learning, and Beneficial Tax Competition

We analyze the welfare impact of entrepreneur mobility in a two‐country overlapping generations model. Increasing returns in production yield multiple equilibria that are stable under adaptive learning. Governments compete for the mobile resource by setting income taxes. We show that large welfare gains can arise from noncooperative taxation. If expectational barriers prevent the realization of high output equilibria, tax competition can sufficiently perturb expectations so that high steady states become attainable. Once in a high production regime, governments may institute cooperative tax increases or reductions so as to bring the economy to the global joint optimum without disturbing the regime.