In various agent-based models, the stylized facts of financial markets (unit roots, fat tails, and volatility clustering) have been shown to emerge from the interactions of agents. However, the complexity of these models often limits their analytical accessibility. In this paper we show that even a very simple model of a financial market with heterogeneous interacting agents is capable of reproducing these ubiquitous statistical properties. The simplicity of our approach permits us to derive some analytical insights using concepts from statistical mechanics. In our model, traders are divided into two groups, fundamentalists and chartists, and their interactions are based on a variant of the herding mechanism introduced by A. Kirman (Ants, rationality, and recruitment, Quarterly Journal of Economics 108, 137–156, 1993). The statistical analysis of simulated data points toward long-term dependence in the autocorrelations of squared and absolute returns and hyperbolic decay in the tail of the distribution of raw returns, both with estimated decay parameters in the same range as those of empirical data. Theoretical analysis, however, excludes the possibility of “true” scaling behavior because of the Markovian nature of the underlying process and the boundedness of returns. The model, therefore, only mimics power law behavior. Similarly to the phenomenological volatility models analyzed by LeBaron (Stochastic volatility as a simple generator of apparent financial power laws and long memory, Quantitative Finance 1, 621–631, 2001), the usual statistical tests are not able to distinguish between true and pseudo-scaling laws in the dynamics of our artificial market.

The standard approach to modeling consumption/saving problems is to assume that the decisionmaker is solving a dynamic stochastic optimization problem. However, under realistic descriptions of utility and uncertainty, the optimal consumption/saving decision is so difficult that only recently have economists managed to find solutions, using numerical methods that require previously infeasible amounts of computation. Yet, empirical evidence suggests that household behavior conforms fairly well with the prescriptions of the optimal solution, raising the question of how average households can solve problems that economists, until recently, could not. This paper examines whether consumers might be able to find a reasonably good rule-of-thumb approximation to optimal behavior by trial-and-error methods, as Milton Friedman proposed long ago. We find that such individual learning methods can reliably identify reasonably good rules of thumb only if the consumer is able to spend absurdly large amounts of time searching for a good rule.

Inflation and the monetary financing of deficits are analyzed in a model in which the deficit is constrained to be less than a given fraction of a measure of aggregate market activity. Depending on parameter values, the model can have multiple steady states. Under adaptive learning with heterogeneous learning rules, there is convergence to a subset of these steady states. In some cases, a high-inflation constrained steady state will emerge. However, with a sufficiently tight fiscal constraint, the low-inflation steady state is globally stable. We provide experimental evidence in support of our theoretical results.

We review the properties of algorithms that characterize the solution of the Bellman equation of a stochastic dynamic program, as the solution to a linear program. The variables in this problem are the ordinates of the value function; hence, the number of variables grows with the state space. For situations in which this size becomes computationally burdensome, we suggest the use of low-dimensional cubic-spline approximations to the value function. We show that fitting this approximation through linear programming provides upper and lower bounds on the solution to the original large problem. The information contained in these bounds leads to inexpensive improvements in the accuracy of approximate solutions.

We study the dynamics of the distribution of wealth in an economy with infinitely lived agents, intergenerational transmission of wealth, and redistributive fiscal policy. We show that wealth accumulation with idiosyncratic investment risk and uncertain lifetimes can generate a double Pareto wealth distribution.

This paper uses a New Keynesian model with banks and deposits to study the macroeconomic effects of policies that pay interest on reserves. Although their effects on output and inflation are small, these policies require major adjustments in the way that the monetary authority manages the supply of reserves, as liquidity effects vanish in the short run. In the long run, however, the additional freedom the monetary authority acquires by paying interest on reserves is best described as affecting the real quantity of reserves: policy actions that change prices must still change the nominal quantity of reserves proportionally.

We demonstrate that multiple stationary rational-expectations equilibria exist in a version of Lucas's island economy. The existence of these equilibria follows from the fact that there is an indeterminate set of monetary equilibria in the two-period overlapping-generations model. We show how to construct stationary rational-expectations equilibria by randomizing over the set of nonstationary monetary equilibria. In some of our equilibria, a positively sloped Phillips curve exists even though our economy contains no signal-extraction problem as in the original Lucas paper. Our equilibria are indexed by beliefs and are examples of the existence of sunspot equilibria in which allocations may differ across states of nature for which preferences, technology, and endowments are identical. Our technique for constructing stationary sunspot equilibria should prove useful in a wide class of models in which an indeterminate stationary equilibrium exists.

Brazil's Gini coefficient rose from 0.57 in 1981 to 0.63 in 1989, before falling back to 0.56 in 2004. Poverty incidence rose from 0.30 in 1981 to 0.33 in 1993, before falling to 0.22 in 2004. This paper presents a preliminary investigation of the determinants of Brazil's distributional reversal over this period. The rise in inequality in the 1980s appears to have been driven by increases in educational attainment in a context of convex returns, and by high and accelerating inflation. Although the secular decline in inequality, which began in 1993, is associated with declining inflation, it also appears to have been driven by four structural and policy changes, namely, declining returns to education; pronounced rural-urban convergence; increases in social assistance transfers targeted to the poor; and a possible decline in racial inequality. Falling inequality has made a substantial contribution to poverty reduction.

This paper studies the long- and short-run relationships between inflation and financial development. Applying the Pooled Mean Group estimator of Pesaran, Shin, and Smith (1999, Journal of the American Statistical Association 94, 621–634) to unbalanced panel data for 87 countries over the period 1960–2005, we find that a negative long-run relationship between inflation and financial development coexists with a positive short-run relationship. However, when the data are split into different income or inflation groups, these results can be observed only in low-income or low-inflation economies.

Price fluctuations under adaptive learning in renewable resource markets such as fisheries are examined. Optimal fishery management with logistic fish population growth implies a backward-bending, discounted supply curve for bioeconomic equilibrium sustained yield. Higher discount rates bend supply backward more to generate multiple steady-state rational expectations equilibria. Under bounded rationality, adaptive learning of a linear forecasting rule generates steady-state, two-cycle as well as chaotic consistent expectations equilibria, which are self-fulfilling in sample average and autocorrelations. The possibility of “learning to believe in chaos” is robust and even enhanced by dynamic noise.

We study the effects of model uncertainty in a simple New Keynesian model using robust control techniques. Due to the simple model structure, we are able to find closed-form solutions for the robust control problem, analyzing both instrument rules and targeting rules under different timing assumptions. In all cases but one, an increased preference for robustness makes monetary policy respond more aggressively to cost shocks but leaves the response to demand shocks unchanged. As a consequence, inflation is less volatile and output is more volatile than under the nonrobust policy. Under one particular timing assumption, however, increasing the preference for robustness has no effect on the optimal targeting rule (nor on the economy).

I develop an algorithm for solving dynamic models in which individual decision rules and the cross-sectional distribution of agents' characteristics influence each other. To illustrate the algorithm, I solve an endowment economy with incomplete markets, a continuum of heterogeneous agents, and aggregate shocks. The key innovation of the algorithm is to parameterize the (cross-sectional) density with a flexible functional form, which makes it possible to avoid simulation techniques. The paper shows how to check for accuracy and establishes links between the properties of the incomplete-markets economy and the aspects involved in obtaining a numerical solution.

This paper seeks to answer the following questions: Do oil price shocks affect firms' investment decisions? Do oil price shocks affect investment decisions differentially depending on firm-specific uncertainty? Over what time horizon do oil price shocks affect high-uncertainty firms? Is the intensity of the oil price shock important, or just its existence? It is found that oil price shocks depress firms' investment decisions, and do so differentially by depressing investment more for more uncertain firms. Oil shocks affect investment for at least the first and second year after the shock. In the short term, the mere existence of a shock drives most of the effect. In the long term, the intensity of the oil shock is also important. Bloom, Bond, and Van Reenan's result [Review of Economic Studies 74, 391–415 (2007)] regarding responsiveness to demand shocks being eroded at more uncertain firms for data on U.K. firms is replicated using data on U.S. firms and persists after oil shocks are considered.

US labor share has been falling since the 1970s. I show that it has not fallen as much once items that do not add to capital, depreciation and production taxes, are netted out. Recent net labor share is within its historical range, whereas gross share is at its lowest level. This effect holds for other high-income economies. The overall picture is no longer one of unprecedented, globally declining labor share. Using gross share as a proxy for net share can give misleading results. US gross share and inequality are correlated, whereas net share, the correct measure, is not.

We study the quantitative properties of a dynamic general equilibrium model. Agents face both idiosyncratic and aggregate income risk, state-dependent borrowing constraints that bind occasionally, and markets that are incomplete. Equilibrium consumption-savings plans and asset prices are computed under various assumptions about income uncertainty. Then, we investigate whether the model replicates two empirical observations: the high correlation between individual consumption and individual income, and the equity premium puzzle. We find that, when the driving processes are calibrated according to the data from wage income in different sectors of the U.S. economy, the results move in the direction of explaining these observations, but we fall short of explaining the observations quantitatively. If the incomes of agents are assumed to be independent of each other, the observations can be explained quantitatively.

This paper develops methods to solve for optimal discretionary policies and optimal commitment policies in rational expectations models. These algorithms, which allow the optimization constraints to be conveniently expressed in second-order structural form, are more general than existing methods and are simple to apply. We use several New Keynesian business cycle models to illustrate their application. Simulations show that the procedures developed in this paper can quickly solve small-scale models and that they can be usefully and effectively applied to medium- and large-scale models.

We develop a framework for measuring and analyzing medium-run departures from balanced growth, and apply it to developments in the euro area. A time-varying factor-augmenting production function (mimicking directed technical change) with below-unitary substitution elasticity is shown to account for the observed dynamics of factor incomes shares, TFP growth, and its components. Based on careful data accounting, we also identify a rising markup and the importance of financial-market regulations in the 1970s. The balanced growth path emerges as a special (and testable) case of our framework, as do existing strands of medium-run debates.

This paper provides a survey of the applications of evolutionary algorithms in macroeconomic models. Discussion is organized around the issues related to stability of equilibria, equilibrium selection, transitional dynamics, and the long-run evolutionary dynamics different from rational-expectations equilibrium outcomes. The survey also discusses criteria that can be used to evaluate the performance and usefulness of evolutionary algorithms in the macroeconomic context.

This paper explores the influence of inflation on economic growth both theoretically and empirically. We propose to merge an endogenous growth model of learning by doing with a New Keynesian one with sticky wages. We show that the intertemporal elasticity of substitution of working time is a key parameter for the shape of the inflation–growth nexus. When it is set equal to zero, the inflation–growth nexus is weak and hump-shaped. When it is greater than zero, inflation has a sizable and negative effect on growth. Endogenizing the length of wage contracts does not lead to inflation superneutrality in the presence of a fixed cost of wage resetting. Adopting various semiparametric and instrumental-variable estimation approaches on a cross-country/time-series data set, we show that increasing inflation reduces real economic growth, consistent with our theoretical model with a positive intertemporal elasticity of substitution of working time.

Efficient Method of Moments is used to estimate and test continuous-time diffusion models for stock returns and interest rates. For stock returns, a four-state, two-factor diffusion with one state observed can account for the dynamics of the daily return on the S&P Composite Index, 1927–1987. This contrasts with results indicating that discrete-time, stochastic volatility models cannot explain these dynamics. For interest rates, a trivariate Yield-Factor Model is estimated from weekly, 1962–1995, Treasury rates. The Yield-Factor Model is sharply rejected, although extensions permitting convexities in the local variance come closer to fitting the data.