## C52 Model Evaluation and Selection

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Output gap revisions can be large even after many years. Real-time reliability tests might therefore be sensitive to the choice of the final output gap vintage that the real-time estimates are compared to. This is the case for the Federal Reserve’s output gap. When accounting for revisions in response to the global financial crisis in the final output gap, the improvement in real-time reliability since the mid-1990s is much smaller than found by Edge and Rudd (Review of Economics and Statistics, 2016, 98(4), 785-791). The negative bias of real-time estimates from the 1980s has disappeared, but the size of revisions continues to be as large as the output gap itself.
The authors systematically analyse how the realtime reliability assessment is affected through varying the final output gap vintage. They find that the largest changes are caused by output gap revisions after recessions. Economists revise their models in response to such events, leading to economically important revisions not only for the most recent years, but reaching back up to two decades. This might improve the understanding of past business cycle dynamics, but decreases the reliability of real-time output gaps ex post.

A series of recent articles has called into question the validity of VAR models of the global market for crude oil. These studies seek to replace existing oil market models by structural VAR models of their own based on different data, different identifying assumptions, and a different econometric approach. Their main aim has been to revise the consensus in the literature that oil demand shocks are a more important determinant of oil price fluctuations than oil supply shocks. Substantial progress has been made in recent years in sorting out the pros and cons of the underlying econometric methodologies and data in this debate, and in separating claims that are supported by empirical evidence from claims that are not. The purpose of this paper is to take stock of the VAR literature on global oil markets and to synthesize what we have learned. Combining this evidence with new data and analysis, I make the case that the concerns regarding the existing VAR oil market literature have been overstated and that the results from these models are quite robust to changes in the model specification.

Several recent studies have expressed concern that the Haar prior typically imposed in estimating sign-identi.ed VAR models may be unintentionally informative about the implied prior for the structural impulse responses. This question is indeed important, but we show that the tools that have been used in the literature to illustrate this potential problem are invalid. Speci.cally, we show that it does not make sense from a Bayesian point of view to characterize the impulse response prior based on the distribution of the impulse responses conditional on the maximum likelihood estimator of the reduced-form parameters, since the the prior does not, in general, depend on the data. We illustrate that this approach tends to produce highly misleading estimates of the impulse response priors. We formally derive the correct impulse response prior distribution and show that there is no evidence that typical sign-identi.ed VAR models estimated using conventional priors tend to imply unintentionally informative priors for the impulse response vector or that the corre- sponding posterior is dominated by the prior. Our evidence suggests that concerns about the Haar prior for the rotation matrix have been greatly overstated and that alternative estimation methods are not required in typical applications. Finally, we demonstrate that the alternative Bayesian approach to estimating sign-identi.ed VAR models proposed by Baumeister and Hamilton (2015) su¤ers from exactly the same conceptual shortcoming as the conventional approach. We illustrate that this alternative approach may imply highly economically implausible impulse response priors.

We derive the Bayes estimator of vectors of structural VAR impulse responses under a range of alternative loss functions. We also derive joint credible regions for vectors of impulse responses as the lowest posterior risk region under the same loss functions. We show that conventional impulse response estimators such as the posterior median response function or the posterior mean response function are not in general the Bayes estimator of the impulse response vector obtained by stacking the impulse responses of interest. We show that such pointwise estimators may imply response function shapes that are incompatible with any possible parameterization of the underlying model. Moreover, conventional pointwise quantile error bands are not a valid measure of the estimation uncertainty about the impulse response vector because they ignore the mutual dependence of the responses. In practice, they tend to understate substantially the estimation uncertainty about the impulse response vector.

This paper examines the advantages and drawbacks of alternative methods of estimating oil supply and oil demand elasticities and of incorporating this information into structural VAR models. I not only summarize the state of the literature, but also draw attention to a number of econometric problems that have been overlooked in this literature. Once these problems are recognized, seemingly conflicting conclusions in the recent literature can be resolved. My analysis reaffirms the conclusion that the one-month oil supply elasticity is close to zero, which implies that oil demand shocks are the dominant driver of the real price of oil. The focus of this paper is not only on correcting some misunderstandings in the recent literature, but on the substantive and methodological insights generated by this exchange, which are of broader interest to applied researchers.

The authors relax the standard assumption in the dynamic stochastic general equilibrium (DSGE) literature that exogenous processes are governed by AR(1) processes and estimate ARMA (p,q) orders and parameters of exogenous processes. Methodologically, they contribute to the Bayesian DSGE literature by using Reversible Jump Markov Chain Monte Carlo (RJMCMC) to sample from the unknown ARMA orders and their associated parameter spaces of varying dimensions.
In estimating the technology process in the neoclassical growth model using post war US GDP data, they cast considerable doubt on the standard AR(1) assumption in favor of higher order processes. They find that the posterior concentrates density on hump-shaped impulse responses for all endogenous variables, consistent with alternative empirical estimates and the rigidities behind many richer structural models. Sampling from noninvertible MA representations, a negative response of hours to a positive technology shock is contained within the posterior credible set. While the posterior contains significant uncertainty regarding the exact order, the results are insensitive to the choice of data filter; this contrasts with the authors’ ARMA estimates of GDP itself, which vary significantly depending on the choice of HP or first difference filter.

We theoretically and empirically study large-scale portfolio allocation problems when transaction costs are taken into account in the optimization problem. We show that transaction costs act on the one hand as a turnover penalization and on the other hand as a regularization, which shrinks the covariance matrix. As an empirical framework, we propose a flexible econometric setting for portfolio optimization under transaction costs, which incorporates parameter uncertainty and combines predictive distributions of individual models using optimal prediction pooling. We consider predictive distributions resulting from highfrequency based covariance matrix estimates, daily stochastic volatility factor models and regularized rolling window covariance estimates, among others. Using data capturing several hundred Nasdaq stocks over more than 10 years, we illustrate that transaction cost regularization (even to small extent) is crucial in order to produce allocations with positive Sharpe ratios. We moreover show that performance differences between individual models decline when transaction costs are considered. Nevertheless, it turns out that adaptive mixtures based on high-frequency and low-frequency information yield the highest performance. Portfolio bootstrap reveals that naive 1=N-allocations and global minimum variance allocations (with and without short sales constraints) are significantly outperformed in terms of Sharpe ratios and utility gains.

This paper addresses whether and to what extent econometric methods used in experimental studies can be adapted and applied to financial data to detect the best-fitting preference model. To address the research question, we implement a frequently used nonlinear probit model in the style of Hey and Orme (1994) and base our analysis on a simulation stud. In detail, we simulate trading sequences for a set of utility models and try to identify the underlying utility model and its parameterization used to generate these sequences by maximum likelihood. We find that for a very broad classification of utility models, this method provides acceptable outcomes. Yet, a closer look at the preference parameters reveals several caveats that come along with typical issues attached to financial data, and that some of these issues seems to drive our results. In particular, deviations are attributable to effects stemming from multicollinearity and coherent under-identification problems, where some of these detrimental effects can be captured up to a certain degree by adjusting the error term specification. Furthermore, additional uncertainty stemming from changing market parameter estimates affects the precision of our estimates for risk preferences and cannot be simply remedied by using a higher standard deviation of the error term or a different assumption regarding its stochastic process. Particularly, if the variance of the error term becomes large, we detect a tendency to identify SPT as utility model providing the best fit to simulated trading sequences. We also find that a frequent issue, namely serial correlation of the residuals, does not seem to be significant. However, we detected a tendency to prefer nesting models over nested utility models, which is particularly prevalent if RDU and EXPO utility models are estimated along with EUT and CRRA utility models.

Microeconomic modeling of investors behavior in financial markets and its results crucially depends on assumptions about the mathematical shape of the underlying preference functions as well as their parameterizations. With the purpose to shed some light on the question, which preferences towards risky financial outcomes prevail in stock markets, we adopted and applied a maximum likelihood approach from the field of experimental economics on a randomly selected dataset of 656 private investors of a large German discount brokerage firm. According to our analysis we find evidence that the majority of these clients follow trading pattern in accordance with Prospect Theory (Kahneman and Tversky (1979)). We also find that observable sociodemographic and personal characteristics such as gender or age don't seem to correlate with specific preference types. With respect to the overall impact of preferences on trading behavior, we find a moderate impact of preferences on trading decisions of individual investors. A classification of investors according to various utility types reveals that the strength of the impact of preferences on an investors' rading behavior is not connected to most personal characteristics, but seems to be related to round-trip length.

Shortcomings revealed by experimental and theoretical researchers such as Allais (1953), Rabin (2000) and Rabin and Thaler (2001) that put the classical expected utility paradigm von Neumann and Morgenstern (1947) into question, led to the proposition of alternative and generalized utility functions, that intend to improve descriptive accuracy. The perhaps best known among those alternative preference theories, that has attracted much popularity among economists, is the so called Prospect Theory by Kahneman and Tversky (1979) and Tversky and Kahneman (1992). Its distinctive features, governed by its set of risk parameters such as risk sensitivity, loss aversion and decision weights, stimulated a series of economic and financial models that build on the previously estimated parameter values by Tversky and Kahneman (1992) to analyze and explain various empirical phenomena for which expected utility doesn't seem to offer a satisfying rationale. In this paper, after providing a brief overview of the relevant literature, we take a closer look at one of those papers, the trading model of Vlcek and Hens (2011) and analyze its implications on Prospect Theory parameters using an adopted maximum likelihood approach for a dataset of 656 individual investors from a large German discount brokerage firm. We find evidence that investors in our dataset are moderately averse to large losses and display high risk sensitivity, supporting the main assumptions of Prospect Theory.