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.

In answer to the question “Will borrowing constraints necessarily intensify aggregate fluctuations and aggregate cyclical variability?” it has been found that complete markets equilibrium displays aggregate fluctuations that may be dampened when borrowing constraints are introduced. Like others, I find that variability in the distribution of labor productivity shocks amplifies aggregate fluctuations. I also find that allowing agents to have different permanent incomes amplifies aggregate fluctuations, enriching the asset-pricing implications of the complete contingent claims model when demand aggregation is not possible. Although agents are able to equalize their intertemporal marginal rates of substitution (IMRS) of consumption state-by-state, the IMRS of labor is not equalized across agents, creating gains from specialization. To determine how frictions affect aggregate variability, two types of borrowing constraints are studied. In the first model, dividend payments are restricted and, in the second, nonhuman wealth is restricted to be positive. Either type of borrowing constraint can dampen aggregate fluctuations.

The credibility criterion commonly used in the strategic macroeconomic policy literature, subgame perfection or its variants, ignores a critical problem concerning intertemporal consistency of policy announcements. To capture this additional credibility constraint, this note applies two distinct notions of Renegotiation-Proof, originally proposed in the context of two-person repeated games. Macroeconomic policy games, where the benevolent government interacts with atomistic private agents, offers a new testing ground for these criteria to be evaluated. This note discusses the relative strengths and weaknesses of these criteria.

The market economy is modeled as a decentralized joint production system. Markets in such an economy require the use of money or credit instruments to facilitate exchange. As a result, market economies are at risk for monetary instability induced by real-side production coordination failure. In particular, economies decentralized via centralized wholesaling markets are subject to precipitous collapses. The most stable monetary system is trade in specie. However, there very likely is a scarcity of specie, which generates inefficiency and discourages production. There is, then, a need for an elastic currency. Bank-issued bills of exchange are a perfectly elastic medium and eliminate the scarcity of specie and its attendant inefficiency, but are a less stable monetary system than is trade in specie. In the trade-off between elasticity and stability, fiduciary currency (or fiduciary deposits) lies between specie and bank-issued bills of exchange.

We consider an economy with an incomplete securities market and heterogeneously informed investors. Each investor trades in the market to hedge the risk to his endowment and to speculate on future security payoffs using his private information. We examine the efficiency of the securities market in allocating risk and transmitting information under different market structures, as defined by the set of securities traded in the market. We show that the introduction of derivative securities can decrease the market's efficiency in revealing information on security payoffs, and increase the equity premium and price volatility in the market.

The failure of consumption-based asset pricing models to match the stochastic properties of the equity premium and the risk-free rate has been attributed by some authors to frictions, transaction costs, or durability. However, such frictions primarily would affect the higher-frequency data components: Consumption-based pricing models that concentrate on long-horizon returns should be more successful. We consider two consumption-based models: time-separable utility, and the habit model of Constantinides. We estimate a vector ARCH model that includes the pricing kernel and the equity return, and use the fitted model to assess the model's implications for the equity premium and for the risk-free rate. Neither model performs well at a quarterly horizon, but at longer horizons the Constantinides model can match the mean and the variance of the observed equity premium, captures time variation of the equity premium, and can better match the observed risk-free rate. We conclude that the equity-premium and risk-free-rate puzzles are primarily problems for shorter-horizon returns.

Barnett originated the Divisia monetary aggregates, which in continuous time exactly track any monetary aggregator function under perfect certainty. With user costs measuring the prices of the services of components, Barnett's aggregates are based on Francois Divisia's derivation of the Divisia line integral from the first-order conditions for optimizing behavior by economic agents under perfect certainty. We derive an extended Divisia index from the first-order conditions (Euler equations) that apply under risk. Our extended Divisia index is the first extension of index number theory into the domain of decision making under risk and thereby produces a route for the extension of all index number theory to permit non-risk-neutrality. We generate simulated data from a modeled rational consumer and investigate the tracking accuracy of the extended Divisia index to the consumer's exact aggregator function.

The behavior of the real interest rate in a general equilibrium multisector model with irreversible investment is examined. It is shown that in such a model purely sectoral shocks can lead to substantial variation in the real interest rate and other aggregate time series. A source of variation in aggregate time series that is not found in one-sector models is thus examined, and the implications of this source of variation for the behavior of the interest rate are highlighted. Such a model seems to better capture the relationship among the real interest and output or investment than the standard one-sector stochastic growth model. It is also shown that, because of a desire to smooth consumption, with irreversible investment a rise in uncertainty concerning the future return to capital tends to lead to more current investment and a lower real interest rate.

The Divisia monetary index weights each monetary asset by its expenditure share, evaluated at its user cost.See Barnett et al. [1997, equations (5) and (6)]. In a world of perfect certainty, the user costs can be computed directly from asset return data, and so, the index is model-free. In the presence of uncertainty, however, the true user cost of a monetary asset depends on the covariance of the asset's return with the marginal utility of wealth. Intuitively, an asset's value depends both on its expected payoff and on the asset's ability to hedge wealth fluctuations. As a result, the true user cost cannot be computed without an explicit model of preferences. It follows that the exact Divisia monetary index in a stochastic economy is not model-free, but depends on the underlying preference assumptions.

This study examines the effect of short-sale constraints on a stock market, in particular, on stock prices, trading volume, and the relationship between stock price movements and output cycles. The economic model features incomplete markets and heterogeneous agents. The short-sale constraint is endogenously determined in the economy and is a function of agents' risk aversion, time preference, and exogenous driving forces. The dynamic model is solved using a policy function iteration algorithm. We find that, for an array of reasonable time-preference parameters and risk-aversion coefficients, the short sale limits range from 27 to 45% of total outstanding shares. Imposing short-sale constraints causes stock prices to move upward. Trading volume is high when some agents have a large amount of stock holdings but incur a negative shock on their nonfinancial income and is low when some agents have few stock holdings and also incur a negative shock to their nonfinancial income. Stock prices are found to be countercyclical and the expected stock returns are procyclical. These countercyclical stock-price movements are shown to be related to the imposition of a short-sale constraint.

Economic theory indicates the need for nonlinear structural models to study medium-term and long-run dynamic behavior of an economy. This paper argues that economic systems can be better specified and estimated using differential-equation rather than difference-equation systems and briefly reviews the estimators of continuous models. This approach of specifying structural models on the basis of economic theory and institutional structure explicitly and then testing the underlying hypothesis to verify the structural form is contrasted with a general-to-specific approach of successively more restricted VARMAX processes. Previous analyses of stability about the steady state or fixed point in phase space are extended to more general attractors to allow an investigation of complexity in economic systems. The critical dependence of some attractors, and particularly strange attractors, on parameter values emphasizes the need for consistent, efficient estimation. A structural approach provides a rigorous alternative to using single time series to determine whether economic systems exhibit aperiodic or chaotic dynamical behavior.

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.