This article introduces a model with high time-varying volatility in consumption. The model explains a series of puzzles in macrofinance, including the (i) equity premium puzzle, (ii) the risk-free rate puzzle, (iii) the bond premium puzzle, and (iv) the predictability of aggregate stock market returns with price-dividend ratios. Furthermore, it is argued that stochastic volatility of the kind introduced in this article is a necessary ingredient for explaining these puzzles within a broad class of models.
I illustrate a novel method for pricing assets within recursive utility models in continuous time, that has first been used in Melissinos (2023). My method builds on the analytic solution of Tsai and Wachter (2018). While their solution is valid for a value of the intertemporal elasticity of substitution equal to 1, I provide the full perturbation series in terms of the IES, which gives rise to a global perturbation approximation in terms of the state variable. This allows the pricing of assets for a much larger range of values for the IES, which are economically meaningful. I comment on the convergence properties of the perturbation series, and I show that the method provides a straightforward and reliable approach to asset pricing. I employ my method to derive prices of long-term bonds, the price consumption ratio and the instantaneous return of the consumption perpetuity.
I introduce a package in the Julia programming language to perform asset pricing based on a stochastic discount factor in continuous time. Prices are computed through Monte Carlo simulations according to a pricing partial differential equation and the corresponding Feynman-Kac formula. At this stage it is possible to compute a) prices of zero-coupon fixed income securities and b) price-dividend ratios, which also allow the calculation of prices and returns of these securities. The package is focused on ease of use and is meant to be used in research and teaching. I illustrate the functionality of the package with examples and an application. In particular, I show how asset prices react after shifts in economic variables within a consumption-based model, and I discuss to what extent these shifts can be classified as monetary policy shocks or information shocks in connection to monetary policy announcements.
In this paper, we introduce a framework with multidimensional skills, in which we estimate how fast skills accumulate due to on-the-job experience. We model an individual’s wage as a weighted sum of her productivities in different skills. We call this skill-specific productivity expertise. Since expertise is not directly observable, we proxy this variable with skill-specific experience, which depends on the years of labor market experience across different occupations and the importance of the corresponding skill in those occupations. We compute skill-specific experience using the data on occupational skill requirements from O*NET. We then estimate the wage equation using skill-specific experience to evaluate the speed of expertise accumulation (learning rate) in different skills. We find that expertise in different skills grows with skill-specific experience and that different skills exhibit different learning rates.