State-Observation Sampling and the Econometrics of Learning Models

In nonlinear state-space models, sequential learning about the hidden state can proceed by particle filtering when the density of the observation conditional on the state is available analytically (e.g. Gordon et al., 1993). This condition need not hold in complex environments, such as the incomplete-information equilibrium models considered in financial economics. In this paper, we make two contributions to the learning literature. First, we introduce a new filtering method, the state-observation sampling (SOS) filter, for general state-space models with intractable observation densities. Second, we develop an indirect inference-based estimator for a large class of incomplete-information economies. We demonstrate the good performance of these techniques on an asset pricing model with investor learning applied to over 80 years of daily equity returns

Idiosyncratic Production Risk, Growth and the Business Cycle

We introduce a neoclassical growth economy with idiosyncratic production risk and incomplete markets. The general equilibrium is characterized in closed form. Uninsurable production shocks introduce a risk premium on private equity and typically result in a lower steady-state level of capital than under complete markets. In the presence of such risks, the anticipation of low investment and high interest rates in the future discourages risk-taking and feeds back into low investment in the present. An endogenous macroeconomic complementarity thus arises, which slows down convergence and amplifies the magnitude and persistence of the business cycle. These results — contrasting sharply with those of Aiyagari (1994) and Krusell and Smith (1998) — highlight that idiosyncratic production or capital-income risk can have significant adverse effects on capital accumulation and aggregate volatility. Keywords: Capital income, Entrepreneurial risk, Fluctuations, Growth, Investment, Precautionary savings.

Incomplete Markets, Growth, and the Business Cycle

We introduce a Ramsey growth model with incomplete markets, decentralized production, and idiosyncratic technological risk. The combination of uninsurable shocks with the precautionary motive can slow down capital accumulation or give rise to persistent fluctuations even when agents are very patient and technology is strictly convex. The model generates closed-form expressions for the equilibrium dynamics under a finite or infinite horizon. Multiple steady states and poverty traps can arise from the endogeneity of the interest rate instead of the usual wealth effect. Depending on the economy's parameters, the local dynamics around a steady state are locally unique, totally unstable or locally undetermined, and the equilibrium path can be attracted to a limit cycle. In calibrated examples, financial incompleteness substantially slows down convergence to the steady state and thus increases the persistence of aggregate shocks.

Multifrequency Jump-Diffusions: An Equilibrium Approach

This paper proposes that equilibrium valuation is a powerful method to generate endogenous jumps in asset prices, which provides a structural alternative to traditional reduced-form specifications with exogenous discontinuities. We specify an economy with continuous consumption and dividend paths, in which endogenous price jumps originate from the market impact of regime-switches in the drifts and volatilities of fundamentals. We parsimoniously incorporate shocks of heterogeneous durations in consumption and dividends while keeping constant the number of parameters. Equilibrium valuation creates an endogenous relation between a shock's persistence and the magnitude of the induced price jump. As the number of frequencies driving fundamentals goes to infinity, the price process converges to a novel stochastic process, which we call a multifractal jump-diffusion.

Multifrequency News and Stock Returns

Recent research documents that aggregate stock prices are driven by shocks with persistence levels ranging from daily intervals to several decades. Building on these insights, we introduce a parsimonious equilibrium model in which regime-shifts of heterogeneous durations affect the volatility of dividend news. We estimate tightly parameterized specifications with up to 256 discrete states on daily U.S. equity returns. The multifrequency equilibrium has significantly higher likelihood than the classic Campbell and Hentschel (1992) specification, while generating volatility feedback effects 6 to 12 times larger. We show in an extension that Bayesian learning about stochastic volatility is faster for bad states than good states, providing a novel source of endogenous skewness that complements the "uncertainty" channel considered in previous literature (e.g., Veronesi, 1999). Furthermore, signal precision induces a tradeoff between skewness and kurtosis, and economies with intermediate investor information best match the data.

Down or Out: Assessing the Welfare Costs of Household Investment Mistakes

This paper investigates the efficiency of household investment decisions in a unique dataset containing the disaggregated wealth and income of the entire population of Sweden. The analysis focuses on two main sources of inefficiency in the financial portfolio: underdiversification of risky assets (“down”) and nonparticipation in risky asset markets (“out”). We find that while a few households are very poorly diversified, the cost of diversification mistakes is quite modest for most of the population. For instance, a majority of participating Swedish households are sufficiently diversified internationally to outperform the Sharpe ratio of their domestic stock market. We document that households with greater financial sophistication tend to invest more efficiently but also more aggressively, so the welfare cost of portfolio inefficiency tends to be greater for these households. The welfare cost of nonparticipation is smaller by almost one half when we take account of the fact that nonparticipants would be unlikely to invest efficiently if they participated in risky asset markets.

Down or Out: Assessing the Welfare Costs of Household Investment Mistakes

This paper investigates the efficiency of household investment decisions in a unique dataset containing the disaggregated wealth and income of the entire population of Sweden. The analysis focuses on two main sources of inefficiency in the financial portfolio: underdiversification of risky assets ("down") and nonparticipation in risky asset markets ("out"). We find that while a few households are very poorly diversified, the cost of diversification mistakes is quite modest for most of the population. For instance, a majority of participating Swedish households are sufficiently diversified internationally to outperform the Sharpe ratio of their domestic stock market. We document that households with greater financial sophistication tend to invest more efficiently but also more aggressively, so the welfare cost of portfolio inefficiency tends to be greater for these households. The welfare cost of nonparticipation is smaller by almost one half when we take account of the fact that nonparticipants would be unlikely to invest efficiently if they participated in risky asset markets.

Volatility Comovement: A Multifrequency Approach

We implement a multifrequency volatility decomposition of three exchange rates and show that components with similar durations are strongly correlated across series. This motivates a bivariate extension of the Markov-Switching Multifractal (MSM) introduced in Calvet and Fisher (2001, 2004). Bivariate MSM is a stochastic volatility model with a closed-form likelihood. Estimation can proceed by ML for state spaces of moderate size, and by simulated likelihood via a particle filter in high-dimensional cases. We estimate the model and confirm its main assumptions in likelihood ratio tests. Bivariate MSM compares favorably to a standard multivariate GARCH both in- and out-of-sample. We extend the model to multivariate settings with a potentially large number of assets by proposing a parsimonious multifrequency factor structure.