The Pareto-like tail of the size distribution of firms can arise from random growth of productivity or stochastic accumulation of capital. If the shocks that give rise to firm growth are perfectly correlated within a firm, then the growth rates of small and large firms are equally volatile, contrary to what is found in the data. If firm growth is the result of many independent shocks within a firm, it can take hundreds of years for a few large firms to emerge. This paper describes an economy with both types of shocks that can account for the thick-tailed firm size distribution, high entry and exit rates, and the relatively young age of large firms. The economy is one in which aggregate growth is driven by the creation of new products by both new and incumbent firms. Some new firms have better ideas than others and choose to implement those ideas at a more rapid pace. Eventually, such firms slow down when the quality of their ideas reverts to the mean. As in the data, average growth rates in a cross section of firms will appear to be independent of firm size, for all but the smallest firms.

This paper examines how proportional transaction costs, short-sale constraints, and margin requirements affect inferences based on asset return data about intertemporal marganil rates of substitution (IMRSs). Small transaction costs greatly reduce the required variability of IMRSs, suggesting that the low variability of many parametric, aggregate consumption based IMRSs need not be inconsistent with asset return data. Euler inequalities for a transaction cost economy with power utility are tested using aggregate consumption data and returns on stocks and U.S. Treasury bills. In the majority of cases, there is little evidence against power utility specifications with a low risk-aversion parameter.

This paper proposes a lower bound on the level of fixed transaction costs that is required for observations on consumption choices to be consistent with data on asset returns and a given set of preferences. The bound is derived from necessary conditions for the optimality of consumption choices in the presence of fixed transaction costs. These conditions reduce to standard Euler equations when transaction costs are zero. Conservative point estimates suggest that a consumer with log utility who consumes U. S. per capita consumption and who can trade in U. S. Treasury bills and an index of New York Stock Exchange stocks must face a fixed transaction cost of at least 3 percent of monthly per capita consumption. This lower bound declines rapidly with increases in risk aversion or when certain restrictions on short selling are included.

[In this article we provide econometric tools for the evaluation of intertemporal asset pricing models using specification-error and volatility bounds. We formulate analog estimators of these bounds, give conditions for consistency, and derive the limiting distribution of these estimators. The analysis incorporates market frictions such as short-sale constraints and proportional transactions costs. Among several applications we show how to use the methods to assess specific asset pricing models and to provide nonparametric characterizations of asset pricing anomalies.]

This paper describes the equilibrium of a discrete‐time exchange economy in which consumers with arbitrary subjective discount factors and homothetic period utility functions follow linear Markov consumption and portfolio strategies. Explicit expressions are given for state prices and consumption‐wealth ratios. We provide an analytically convenient continuous‐time approximation and show how subjective rates of time preference affect risk‐free rates but not instantaneous risk‐return trade‐offs. Hyperbolic discount factors can be a source of return volatility, but they cannot be used to address asset pricing puzzles related to high‐frequency Sharpe ratios.

In this article we characterize and estimate the process for short-term interest rates using federal funds interest rate data. We presume that we are observing a discrete-time sample of a stationary scalar diffusion. We concentrate on a class of models in which the local volatility elasticity is constant and the drift has a flexible specification. To accommodate missing observations and to break the link between "economic time" and calendar time, we model the sampling scheme as an increasing process that is not directly observed. We propose and implement two new methods for estimation. We find evidence for a volatility elasticity between one and one-half and two. When interest rates are high, local mean reversion is small and the mechanism for inducing stationarity is the increased volatility of the diffusion process.

In this article we provide econometric tools for the evaluation of intertemporal asset pricing models using specification-error and volatility bounds. We formulate analog estimators of these bounds, give conditions for consistency, and derive the limiting distribution of these estimators. The analysis incorporates market frictions such as short-sale constraints and proportional transactions costs. Among several applications we show how to use the methods to assess specific asset pricing models and to provide non-parametric characterizations of asset pricing anomalies.

In this article we characterize and estimate the process for short-term interest rates using federal funds interest rate data. We presume that we are observing a discrete-time sample of a stationary scalar diffusion. We concentrate on a class of models in which the local volatility elasticity is constant and the drift has a flexible specification. To accommodate missing observations and to break the link between “economic time” and calendar time, we model the sampling scheme as an increasing process that is not directly observed. We propose and implement two new methods for estimation. We find evidence for a volatility elasticity between one and one-half and two. When interest rates are high, local mean reversion is small and the mechanism for inducing stationarity is the increased volatility of the diffusion process.