Survey evidence tells us that stock prices reflect the risks investors associate with long-run technological change. However, there is a shortage of models that can rationalize long-run risks. Unlike the previous literature assuming a fixed number of products, our model allows for new product varieties that appear in the form of new firms which face entry costs and delay in the entry process. The fixed variety model has a significant limitation in translating macroeconomic volatility into asset return volatility. Our model with growing varieties induces endogenous low-frequency fluctuations in productivity driving large, persistent variations in consumption growth and asset prices. It also changes the valuation of assets through the increase in the volatility of the pricing kernel (with a positive long-run component) and leads to higher excess returns. Our model is motivated by a simple recursively identified VAR model containing quarterly US data 1992Q3-2018Q4 with the following list of variables: total factor productivity, output, a measure of firm entry, and the excess return on stocks.

We develop an N-regime Markov-switching model in which the latent state variable driving the regime switching is endogenously determined with the model disturbance term. The models structure captures a wide variety of patterns of endogeneity and yields a simple test of the null hypothesis of exogenous switching. We derive an iterative filter that generates objects of interest, including the model likelihood function and estimated regime probabilities. Using simulation experiments, we demonstrate that the maximum likelihood estimator performs well in finite samples and that a likelihood ratio test of exogenous switching has good size and power properties. We provide results from two applications of the endogenous switching model: a three-state model of US business cycle dynamics and a three-state volatility model of US equity returns. In both cases, we find statistically significant evidence in favor of endogenous switching.

We explore asset pricing in the context of the one-sector Benhabib-Farmer-Guo (BFG) model with increasing returns to scale in production and compare our results with financial implications of the standard dynamic stochastic general equilibrium (DSGE) model. Our main goal is to determine the effects of local indeterminacy and the presence of sunspot shocks on asset pricing. We find that the BFG model does not adequately represent key stylized facts of U.S. capital markets and does not improve on the asset-pricing results obtained in the standard DSGE model.

We evaluate whether the spirit of capitalism improves the ability of the real business cycle model to explain the main features of both asset return and the business cycle. In our model, the spirit of capitalism is embodied in the assumption that individuals have preferences for financial wealth. Our simulation results suggest that this assumption may improve the model's ability to explain the risk-free rate puzzle but not the equity premium puzzle. This assumption also markedly deteriorates the model's ability to account for the main features of the business cycle.

We derive asset-pricing and portfolio-choice implications of a dynamic incomplete-markets model in which consumers are heterogeneous in several respects: labor income, asset wealth, and preferences. In contrast to earlier papers, we insist on at least roughly matching the model's implications for heterogeneity — notably, the equilibrium distributions of income and wealth — with those in U.S. data. This approach seems natural: Models that rely critically on heterogeneity for explaining asset prices are not convincing unless the heterogeneity is quantitatively reasonable. We find that the class of models we consider here is very far from success in explaining the equity premium when parameters are restricted to produce reasonable equilibrium heterogeneity. We express the equity premium as a product of two factors: the standard deviation of the excess return and the market price of risk. The first factor, as expected, is much too low in the model. The size of the market price of risk depends crucially on the constraints on borrowing. If substantial borrowing is allowed, the market price of risk is about one one-hundredth of what it is in the data (and about 15% higher than in the representative-agent model). However, under the most severe borrowing constraints that we consider, the market price of risk is quite close to the observed value.

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.

We use a log-normal framework to examine the effect of preferences on the market price for risk, that is, the Sharpe ratio. In our framework, the Sharpe ratio can be calculated directly from the elasticity of the stochastic discount factor with respect to consumption innovations as well as the volatility of consumption innovations. This can be understood as an analytical shortcut to the calculation of the Hansen–Jagannathan volatility bounds, and therefore provides a convenient tool for theorists searching for models capable of explaining asset-pricing facts. To illustrate the usefulness of our approach, we examine several popular preference specifications, such as CRRA, various types of habit formation, and the recursive preferences of Epstein–Zin–Weil. Furthermore, we show how the models with idiosyncratic consumption shocks can be studied.

A planner and agent in a permanent-income economy cannot observe part of the state, regard their model as an approximation, and value decision rules that are robust across a set of models. They use robust decision theory to choose allocations. Equilibrium prices reflect the preference for robustness and so embody a “market price of Knightian uncertainty.” We compute market prices of risk and compare them with a model that assumes that the state is fully observed. We use detection error probabilities to constrain a single parameter that governs the taste for robustness.