## C11 Bayesian Analysis

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#### Document Type

- Working Paper (5)
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#### Keywords

- Bayesian estimation (2)
- business cycles (2)
- competition (2)
- entry (2)
- markups (2)
- Bayes-Lernen (1)
- Bayes-Verfahren (1)
- Bayesian VAR (1)
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- Asset pricing under rational learning about rare disasters : [Version 28 Juli 2011] (2011)
- This paper proposes a new approach for modeling investor fear after rare disasters. The key element is to take into account that investors’ information about fundamentals driving rare downward jumps in the dividend process is not perfect. Bayesian learning implies that beliefs about the likelihood of rare disasters drop to a much more pessimistic level once a disaster has occurred. Such a shift in beliefs can trigger massive declines in price-dividend ratios. Pessimistic beliefs persist for some time. Thus, belief dynamics are a source of apparent excess volatility relative to a rational expectations benchmark. Due to the low frequency of disasters, even an infinitely-lived investor will remain uncertain about the exact probability. Our analysis is conducted in continuous time and offers closed-form solutions for asset prices. We distinguish between rational and adaptive Bayesian learning. Rational learners account for the possibility of future changes in beliefs in determining their demand for risky assets, while adaptive learners take beliefs as given. Thus, risky assets tend to be lower-valued and price-dividend ratios vary less under adaptive versus rational learning for identical priors. Keywords: beliefs, Bayesian learning, controlled diffusions and jump processes, learning about jumps, adaptive learning, rational learning. JEL classification: D83, G11, C11, D91, E21, D81, C61

- The competition effect in business cycles : [Version 21 März 2012] (2012)
- How do changes in market structure affect the US business cycle? We estimate a monetary DSGE model with endogenous rm/product entry and a translog expenditure function by Bayesian methods. The dynamics of net business formation allow us to identify the 'competition effect', by which desired price markups and inflation decrease when entry rises. We find that a 1 percent increase in the number of competitors lowers desired markups by 0.18 percent. Most of the cyclical variability in inflation is driven by markup fluctuations due to sticky prices or exogenous shocks rather than endogenous changes in desired markups.

- Portfolio choice and estimation risk : a comparison of Bayesian approaches to resampled efficiency (2002)
- Estimation risk is known to have a huge impact on mean/variance (MV) optimized portfolios, which is one of the primary reasons to make standard Markowitz optimization unfeasible in practice. Several approaches to incorporate estimation risk into portfolio selection are suggested in the earlier literature. These papers regularly discuss heuristic approaches (e.g., placing restrictions on portfolio weights) and Bayesian estimators. Among the Bayesian class of estimators, we will focus in this paper on the Bayes/Stein estimator developed by Jorion (1985, 1986), which is probably the most popular estimator. We will show that optimal portfolios based on the Bayes/Stein estimator correspond to portfolios on the original mean-variance efficient frontier with a higher risk aversion. We quantify this increase in risk aversion. Furthermore, we review a relatively new approach introduced by Michaud (1998), resampling efficiency. Michaud argues that the limitations of MV efficiency in practice generally derive from a lack of statistical understanding of MV optimization. He advocates a statistical view of MV optimization that leads to new procedures that can reduce estimation risk. Resampling efficiency has been contrasted to standard Markowitz portfolios until now, but not to other approaches which explicitly incorporate estimation risk. This paper attempts to fill this gap. Optimal portfolios based on the Bayes/Stein estimator and resampling efficiency are compared in an empirical out-of-sample study in terms of their Sharpe ratio and in terms of stochastic dominance.

- The competition effect in business cycles : [Version 9 März 2012] (2012)
- How do changes in market structure affect the US business cycle? We estimate a monetary DSGE model with endogenous rm/product entry and a translog expenditure function by Bayesian methods. The dynamics of net business formation allow us to identify the 'competition effect', by which desired price markups and inflation decrease when entry rises. We find that a 1 percent increase in the number of competitors lowers desired markups by 0.18 percent. Most of the cyclical variability in inflation is driven by markup fluctuations due to sticky prices or exogenous shocks rather than endogenous changes in desired markups.

- Marginalized predictive likelihood comparisons of linear Gaussian state-space models with applications to DSGE, DSGE-VAR, and VAR models (2014)
- he predictive likelihood is of particular relevance in a Bayesian setting when the purpose is to rank models in a forecast comparison exercise. This paper discusses how the predictive likelihood can be estimated for any subset of the observable variables in linear Gaussian state-space models with Bayesian methods, and proposes to utilize a missing observations consistent Kalman filter in the process of achieving this objective. As an empirical application, we analyze euro area data and compare the density forecast performance of a DSGE model to DSGE-VARs and reduced-form linear Gaussian models.

- Atypical behavior of credit: evidence from a monetary VAR (2013)
- Credit boom detection methodologies (such as threshold method) lack robustness as they are based on univariate detrending analysis and resort to ratios of credit to real activity. I propose a quantitative indicator to detect atypical behavior of credit from a multivariate system - a monetary VAR. This methodology explicitly accounts for endogenous interactions between credit, asset prices and real activity and detects atypical credit expansions and contractions in the Euro Area, Japan and the U.S. robustly and timely. The analysis also proves useful in real time.