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28 pages, 3560 KiB

Open AccessFeature PaperArticle

Confidence Distributions for FIC Scores

by Céline Cunen and Nils Lid Hjort

Econometrics 2020, 8(3), 27; https://doi.org/10.3390/econometrics8030027 - 01 Jul 2020

Viewed by 3163

Abstract

When using the Focused Information Criterion (FIC) for assessing and ranking candidate models with respect to how well they do for a given estimation task, it is customary to produce a so-called FIC plot. This plot has the different point estimates along the [...] Read more.

When using the Focused Information Criterion (FIC) for assessing and ranking candidate models with respect to how well they do for a given estimation task, it is customary to produce a so-called FIC plot. This plot has the different point estimates along the y-axis and the root-FIC scores on the x-axis, these being the estimated root-mean-square scores. In this paper we address the estimation uncertainty involved in each of the points of such a FIC plot. This needs careful assessment of each of the estimators from the candidate models, taking also modelling bias into account, along with the relative precision of the associated estimated mean squared error quantities. We use confidence distributions for these tasks. This leads to fruitful CD–FIC plots, helping the statistician to judge to what extent the seemingly best models really are better than other models, etc. These efforts also lead to two further developments. The first is a new tool for model selection, which we call the quantile-FIC, which helps overcome certain difficulties associated with the usual FIC procedures, related to somewhat arbitrary schemes for handling estimated squared biases. A particular case is the median-FIC. The second development is to form model averaged estimators with weights determined by the relative sizes of the median- and quantile-FIC scores. Full article

(This article belongs to the Special Issue Bayesian and Frequentist Model Averaging)

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15 pages, 1659 KiB

Open AccessArticle

Bayesian Model Averaging with the Integrated Nested Laplace Approximation

by Virgilio Gómez-Rubio, Roger S. Bivand and Håvard Rue

Econometrics 2020, 8(2), 23; https://doi.org/10.3390/econometrics8020023 - 01 Jun 2020

Cited by 15 | Viewed by 4760

Abstract

The integrated nested Laplace approximation (INLA) for Bayesian inference is an efficient approach to estimate the posterior marginal distributions of the parameters and latent effects of Bayesian hierarchical models that can be expressed as latent Gaussian Markov random fields (GMRF). The representation as [...] Read more.

The integrated nested Laplace approximation (INLA) for Bayesian inference is an efficient approach to estimate the posterior marginal distributions of the parameters and latent effects of Bayesian hierarchical models that can be expressed as latent Gaussian Markov random fields (GMRF). The representation as a GMRF allows the associated software R-INLA to estimate the posterior marginals in a fraction of the time as typical Markov chain Monte Carlo algorithms. INLA can be extended by means of Bayesian model averaging (BMA) to increase the number of models that it can fit to conditional latent GMRF. In this paper, we review the use of BMA with INLA and propose a new example on spatial econometrics models. Full article

(This article belongs to the Special Issue Bayesian and Frequentist Model Averaging)

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24 pages, 333 KiB

Open AccessArticle

Sovereign Risk Indices and Bayesian Theory Averaging

by Alex Lenkoski and Fredrik L. Aanes

Econometrics 2020, 8(2), 22; https://doi.org/10.3390/econometrics8020022 - 29 May 2020

Cited by 1 | Viewed by 3137

Abstract

In economic applications, model averaging has found principal use in examining the validity of various theories related to observed heterogeneity in outcomes such as growth, development, and trade. Though often easy to articulate, these theories are imperfectly captured quantitatively. A number of different [...] Read more.

In economic applications, model averaging has found principal use in examining the validity of various theories related to observed heterogeneity in outcomes such as growth, development, and trade. Though often easy to articulate, these theories are imperfectly captured quantitatively. A number of different proxies are often collected for a given theory and the uneven nature of this collection requires care when employing model averaging. Furthermore, if valid, these theories ought to be relevant outside of any single narrowly focused outcome equation. We propose a methodology which treats theories as represented by latent indices, these latent processes controlled by model averaging on the proxy level. To achieve generalizability of the theory index our framework assumes a collection of outcome equations. We accommodate a flexible set of generalized additive models, enabling non-Gaussian outcomes to be included. Furthermore, selection of relevant theories also occurs on the outcome level, allowing for theories to be differentially valid. Our focus is on creating a set of theory-based indices directed at understanding a country’s potential risk of macroeconomic collapse. These Sovereign Risk Indices are calibrated across a set of different “collapse” criteria, including default on sovereign debt, heightened potential for high unemployment or inflation and dramatic swings in foreign exchange values. The goal of this exercise is to render a portable set of country/year theory indices which can find more general use in the research community. Full article

(This article belongs to the Special Issue Bayesian and Frequentist Model Averaging)

29 pages, 540 KiB

Open AccessArticle

BACE and BMA Variable Selection and Forecasting for UK Money Demand and Inflation with Gretl

by Marcin Błażejowski, Jacek Kwiatkowski and Paweł Kufel

Econometrics 2020, 8(2), 21; https://doi.org/10.3390/econometrics8020021 - 22 May 2020

Cited by 2 | Viewed by 4507

Abstract

In this paper, we apply Bayesian averaging of classical estimates (BACE) and Bayesian model averaging (BMA) as an automatic modeling procedures for two well-known macroeconometric models: UK demand for narrow money and long-term inflation. Empirical results verify the correctness of BACE and BMA [...] Read more.

In this paper, we apply Bayesian averaging of classical estimates (BACE) and Bayesian model averaging (BMA) as an automatic modeling procedures for two well-known macroeconometric models: UK demand for narrow money and long-term inflation. Empirical results verify the correctness of BACE and BMA selection and exhibit similar or better forecasting performance compared with a non-pooling approach. As a benchmark, we use Autometrics—an algorithm for automatic model selection. Our study is implemented in the easy-to-use gretl packages, which support parallel processing, automates numerical calculations, and allows for efficient computations. Full article

(This article belongs to the Special Issue Bayesian and Frequentist Model Averaging)

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36 pages, 1528 KiB

Open AccessFeature PaperArticle

Triple the Gamma—A Unifying Shrinkage Prior for Variance and Variable Selection in Sparse State Space and TVP Models

by Annalisa Cadonna, Sylvia Frühwirth-Schnatter and Peter Knaus

Econometrics 2020, 8(2), 20; https://doi.org/10.3390/econometrics8020020 - 20 May 2020

Cited by 26 | Viewed by 6468

Abstract

Time-varying parameter (TVP) models are very flexible in capturing gradual changes in the effect of explanatory variables on the outcome variable. However, in particular when the number of explanatory variables is large, there is a known risk of overfitting and poor predictive performance, [...] Read more.

Time-varying parameter (TVP) models are very flexible in capturing gradual changes in the effect of explanatory variables on the outcome variable. However, in particular when the number of explanatory variables is large, there is a known risk of overfitting and poor predictive performance, since the effect of some explanatory variables is constant over time. We propose a new prior for variance shrinkage in TVP models, called triple gamma. The triple gamma prior encompasses a number of priors that have been suggested previously, such as the Bayesian Lasso, the double gamma prior and the Horseshoe prior. We present the desirable properties of such a prior and its relationship to Bayesian Model Averaging for variance selection. The features of the triple gamma prior are then illustrated in the context of time varying parameter vector autoregressive models, both for simulated dataset and for a series of macroeconomics variables in the Euro Area. Full article

(This article belongs to the Special Issue Bayesian and Frequentist Model Averaging)

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15 pages, 418 KiB

Open AccessFeature PaperArticle

Bayesian Model Averaging Using Power-Expected-Posterior Priors

by Dimitris Fouskakis and Ioannis Ntzoufras

Econometrics 2020, 8(2), 17; https://doi.org/10.3390/econometrics8020017 - 11 May 2020

Cited by 1 | Viewed by 3895

Abstract

This paper focuses on the Bayesian model average (BMA) using the power–expected– posterior prior in objective Bayesian variable selection under normal linear models. We derive a BMA point estimate of a predicted value, and present computation and evaluation strategies of the prediction accuracy. [...] Read more.

This paper focuses on the Bayesian model average (BMA) using the power–expected– posterior prior in objective Bayesian variable selection under normal linear models. We derive a BMA point estimate of a predicted value, and present computation and evaluation strategies of the prediction accuracy. We compare the performance of our method with that of similar approaches in a simulated and a real data example from economics. Full article

(This article belongs to the Special Issue Bayesian and Frequentist Model Averaging)

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22 pages, 496 KiB

Open AccessArticle

Improved Average Estimation in Seemingly Unrelated Regressions

by Ali Mehrabani and Aman Ullah

Econometrics 2020, 8(2), 15; https://doi.org/10.3390/econometrics8020015 - 27 Apr 2020

Cited by 4 | Viewed by 4555

Abstract

In this paper, we propose an efficient weighted average estimator in Seemingly Unrelated Regressions. This average estimator shrinks a generalized least squares (GLS) estimator towards a restricted GLS estimator, where the restrictions represent possible parameter homogeneity specifications. The shrinkage weight is inversely proportional [...] Read more.

In this paper, we propose an efficient weighted average estimator in Seemingly Unrelated Regressions. This average estimator shrinks a generalized least squares (GLS) estimator towards a restricted GLS estimator, where the restrictions represent possible parameter homogeneity specifications. The shrinkage weight is inversely proportional to a weighted quadratic loss function. The approximate bias and second moment matrix of the average estimator using the large-sample approximations are provided. We give the conditions under which the average estimator dominates the GLS estimator on the basis of their mean squared errors. We illustrate our estimator by applying it to a cost system for United States (U.S.) Commercial banks, over the period from 2000 to 2018. Our results indicate that on average most of the banks have been operating under increasing returns to scale. We find that over the recent years, scale economies are a plausible reason for the growth in average size of banks and the tendency toward increasing scale is likely to continue Full article

(This article belongs to the Special Issue Bayesian and Frequentist Model Averaging)

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22 pages, 2908 KiB

Open AccessArticle

Bayesian Model Averaging and Prior Sensitivity in Stochastic Frontier Analysis

by Kamil Makieła and Błażej Mazur

Econometrics 2020, 8(2), 13; https://doi.org/10.3390/econometrics8020013 - 20 Apr 2020

Cited by 3 | Viewed by 4447

Abstract

This paper discusses Bayesian model averaging (BMA) in Stochastic Frontier Analysis and investigates inference sensitivity to prior assumptions made about the scale parameter of (in)efficiency. We turn our attention to the “standard” prior specifications for the popular normal-half-normal and normal-exponential models. To facilitate [...] Read more.

This paper discusses Bayesian model averaging (BMA) in Stochastic Frontier Analysis and investigates inference sensitivity to prior assumptions made about the scale parameter of (in)efficiency. We turn our attention to the “standard” prior specifications for the popular normal-half-normal and normal-exponential models. To facilitate formal model comparison, we propose a model that nests both sampling models and generalizes the symmetric term of the compound error. Within this setup it is possible to develop coherent priors for model parameters in an explicit way. We analyze sensitivity of different prior specifications on the aforementioned scale parameter with respect to posterior characteristics of technology, stochastic parameters, latent variables and—especially—the models’ posterior probabilities, which are crucial for adequate inference pooling. We find that using incoherent priors on the scale parameter of inefficiency has (i) virtually no impact on the technology parameters; (ii) some impact on inference about the stochastic parameters and latent variables and (iii) substantial impact on marginal data densities, which are crucial in BMA. Full article

(This article belongs to the Special Issue Bayesian and Frequentist Model Averaging)

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35 pages, 996 KiB

Open AccessFeature PaperArticle

Cross-Validation Model Averaging for Generalized Functional Linear Model

by Haili Zhang and Guohua Zou

Econometrics 2020, 8(1), 7; https://doi.org/10.3390/econometrics8010007 - 24 Feb 2020

Cited by 5 | Viewed by 4553

Abstract

Functional data is a common and important type in econometrics and has been easier and easier to collect in the big data era. To improve estimation accuracy and reduce forecast risks with functional data, in this paper, we propose a novel cross-validation model [...] Read more.

Functional data is a common and important type in econometrics and has been easier and easier to collect in the big data era. To improve estimation accuracy and reduce forecast risks with functional data, in this paper, we propose a novel cross-validation model averaging method for generalized functional linear model where the scalar response variable is related to a random function predictor by a link function. We establish asymptotic theoretical result on the optimality of the weights selected by our method when the true model is not in the candidate model set. Our simulations show that the proposed method often performs better than the commonly used model selection and averaging methods. We also apply the proposed method to Beijing second-hand house price data. Full article

(This article belongs to the Special Issue Bayesian and Frequentist Model Averaging)

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20 pages, 352 KiB

Open AccessArticle

Forecast Bitcoin Volatility with Least Squares Model Averaging

by Tian Xie

Econometrics 2019, 7(3), 40; https://doi.org/10.3390/econometrics7030040 - 14 Sep 2019

Cited by 6 | Viewed by 6497

Abstract

In this paper, we study forecasting problems of Bitcoin-realized volatility computed on data from the largest crypto exchange—Binance. Given the unique features of the crypto asset market, we find that conventional regression models exhibit strong model specification uncertainty. To circumvent this issue, we [...] Read more.

In this paper, we study forecasting problems of Bitcoin-realized volatility computed on data from the largest crypto exchange—Binance. Given the unique features of the crypto asset market, we find that conventional regression models exhibit strong model specification uncertainty. To circumvent this issue, we suggest using least squares model-averaging methods to model and forecast Bitcoin volatility. The empirical results demonstrate that least squares model-averaging methods in general outperform many other conventional regression models that ignore specification uncertainty. Full article

(This article belongs to the Special Issue Bayesian and Frequentist Model Averaging)

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26 pages, 1804 KiB

Open AccessArticle

On the Forecast Combination Puzzle

by Wei Qian, Craig A. Rolling, Gang Cheng and Yuhong Yang

Econometrics 2019, 7(3), 39; https://doi.org/10.3390/econometrics7030039 - 10 Sep 2019

Cited by 6 | Viewed by 6651

Abstract

It is often reported in the forecast combination literature that a simple average of candidate forecasts is more robust than sophisticated combining methods. This phenomenon is usually referred to as the “forecast combination puzzle”. Motivated by this puzzle, we explore its possible explanations, [...] Read more.

It is often reported in the forecast combination literature that a simple average of candidate forecasts is more robust than sophisticated combining methods. This phenomenon is usually referred to as the “forecast combination puzzle”. Motivated by this puzzle, we explore its possible explanations, including high variance in estimating the target optimal weights (estimation error), invalid weighting formulas, and model/candidate screening before combination. We show that the existing understanding of the puzzle should be complemented by the distinction of different forecast combination scenarios known as combining for adaptation and combining for improvement. Applying combining methods without considering the underlying scenario can itself cause the puzzle. Based on our new understandings, both simulations and real data evaluations are conducted to illustrate the causes of the puzzle. We further propose a multi-level AFTER strategy that can integrate the strengths of different combining methods and adapt intelligently to the underlying scenario. In particular, by treating the simple average as a candidate forecast, the proposed strategy is shown to reduce the heavy cost of estimation error and, to a large extent, mitigate the puzzle. Full article

(This article belongs to the Special Issue Bayesian and Frequentist Model Averaging)

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12 pages, 320 KiB

Open AccessArticle

A Combination Method for Averaging OLS and GLS Estimators

by Qingfeng Liu and Andrey L. Vasnev

Econometrics 2019, 7(3), 38; https://doi.org/10.3390/econometrics7030038 - 09 Sep 2019

Cited by 1 | Viewed by 4884

Abstract

To avoid the risk of misspecification between homoscedastic and heteroscedastic models, we propose a combination method based on ordinary least-squares (OLS) and generalized least-squares (GLS) model-averaging estimators. To select optimal weights for the combination, we suggest two information criteria and propose feasible versions [...] Read more.

To avoid the risk of misspecification between homoscedastic and heteroscedastic models, we propose a combination method based on ordinary least-squares (OLS) and generalized least-squares (GLS) model-averaging estimators. To select optimal weights for the combination, we suggest two information criteria and propose feasible versions that work even when the variance-covariance matrix is unknown. The optimality of the method is proven under some regularity conditions. The results of a Monte Carlo simulation demonstrate that the method is adaptive in the sense that it achieves almost the same estimation accuracy as if the homoscedasticity or heteroscedasticity of the error term were known. Full article

(This article belongs to the Special Issue Bayesian and Frequentist Model Averaging)

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21 pages, 437 KiB

Open AccessTutorial

A Review of the ‘BMS’ Package for R with Focus on Jointness

by Shahram Amini and Christopher F. Parmeter

Econometrics 2020, 8(1), 6; https://doi.org/10.3390/econometrics8010006 - 24 Feb 2020

Cited by 5 | Viewed by 5590

Abstract

We provide a general overview of Bayesian model averaging (BMA) along with the concept of jointness. We then describe the relative merits and attractiveness of the newest BMA software package, BMS, available in the statistical language R to implement a BMA exercise. BMS [...] Read more.

We provide a general overview of Bayesian model averaging (BMA) along with the concept of jointness. We then describe the relative merits and attractiveness of the newest BMA software package, BMS, available in the statistical language R to implement a BMA exercise. BMS provides the user a wide range of customizable priors for conducting a BMA exercise, provides ample graphs to visualize results, and offers several alternative model search mechanisms. We also provide an application of the BMS package to equity premia and describe a simple function that can easily ascertain jointness measures of covariates and integrates with the BMS package. Full article

(This article belongs to the Special Issue Bayesian and Frequentist Model Averaging)

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