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.

Recent empirical findings suggest that macroeconomic variables are seldom normally distributed. For example, the distributions of aggregate output growth-rate time series of many OECD countries are well approximated by symmetric exponential-power (EP) densities with Laplace fat tails. In this work, we assess whether real business cycle (RBC) and standard medium-scale New Keynesian (NK) models are able to replicate this statistical regularity. We simulate both models, drawing Gaussian- vs Laplace-distributed shocks, and we explore the statistical properties of simulated time series. Our results cast doubts on whether RBC and NK models are able to provide a satisfactory representation of the transmission mechanisms linking exogenous shocks to macroeconomic dynamics.

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.

We study the constant discount rate present value model for stock pricing in a stochastic setting where the exogenous dividend stream is modeled as a random walk with innovations drawn from the family of stable distributions. We derive an exact analytical solution for the fundamental stock price. We evaluate the ability of the model fundamentals and the dividends-driven intrinsic bubbles to explain the observed variation in annual U.S. stock prices. We compare results obtained in this setting with those from the traditional model where all stochastic processes are driven by Gaussian shocks.

For the purpose of Value-at-Risk (VaR) analysis, a model for the return distribution is important because it describes the potential behavior of a financial security in the future. What is primarily, is the behavior in the tail of the distribution since VaR analysis deals with extreme market situations. We analyze the extension of the normal distribution function to allow for fatter tails and for time-varying volatility. Equally important to the distribution function are the associated parameter values. We argue that parameter uncertainty leads to uncertainty in the reported VaR estimates. There is a tradeoff between more complex tail-behavior and this uncertainty. The “best estimate”-VaR should be adjusted to take account of the uncertainty in the VaR. Finally, we consider the VaR forecast for a portfolio of securities. We propose a method to treat the modeling in a univariate, rather than a multivariate, framework. Such a choice allows us to reduce parameter uncertainty and to model directly the relevant variable.