Econometrics — Open Access Journal

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

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

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

We investigate the marginal predictive content of small versus large jump variation, when forecasting one-week-ahead cross-sectional equity returns, building on Bollerslev et al. (2020). We find that sorting on signed small jump variation leads to greater value-weighted return differentials between stocks in our highest- and lowest-quintile portfolios (i.e., high–low spreads) than when either signed total jump or signed large jump variation is sorted on. It is shown that the benefit of signed small jump variation investing is driven by stock selection within an industry, rather than industry bets. Investors prefer stocks with a high probability of having positive jumps, but they also tend to overweight safer industries. Also, consistent with the findings in Scaillet et al. (2018), upside (downside) jump variation negatively (positively) predicts future returns. However, signed (large/small/total) jump variation has stronger predictive power than both upside and downside jump variation. One reason large and small (signed) jump variation have differing marginal predictive contents is that the predictive content of signed large jump variation is negligible when controlling for either signed total jump variation or realized skewness. By contrast, signed small jump variation has unique information for predicting future returns, even when controlling for these variables. By analyzing earnings announcement surprises, we find that large jumps are closely associated with “big” news. However, while such news-related information is embedded in large jump variation, the information is generally short-lived, and dissipates too quickly to provide marginal predictive content for subsequent weekly returns. Finally, we find that small jumps are more likely to be diversified away than large jumps and tend to be more closely associated with idiosyncratic risks. This indicates that small jumps are more likely to be driven by liquidity conditions and trading activity. Full article

I analyze damage from hurricane strikes on the United States since 1955. Using machine learning methods to select the most important drivers for damage, I show that large errors in a hurricane’s predicted landfall location result in higher damage. This relationship holds across a wide range of model specifications and when controlling for ex-ante uncertainty and potential endogeneity. Using a counterfactual exercise I find that the cumulative reduction in damage from forecast improvements since 1970 is about $82 billion, which exceeds the U.S. government’s spending on the forecasts and private willingness to pay for them. Full article

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

We apply a bootstrap test to determine whether some forecasters are able to make superior probability assessments to others. In contrast to some findings in the literature for point predictions, there is evidence that some individuals really are better than others. The testing procedure controls for the different economic conditions the forecasters may face, given that each individual responds to only a subset of the surveys. One possible explanation for the different findings for point predictions and histograms is explored: that newcomers may make less accurate histogram forecasts than experienced respondents given the greater complexity of the task. Full article

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

In this paper, we propose a hybrid version of Dynamic Stochastic General Equilibrium models with an emphasis on parameter invariance and tracking performance at times of rapid changes (recessions). We interpret hypothetical balanced growth ratios as moving targets for economic agents that rely upon an Error Correction Mechanism to adjust to changes in target ratios driven by an underlying state Vector AutoRegressive process. Our proposal is illustrated by an application to a pilot Real Business Cycle model for the US economy from 1948 to 2019. An extensive recursive validation exercise over the last 35 years, covering 3 recessions, is used to highlight its parameters invariance, tracking and 1- to 3-step ahead forecasting performance, outperforming those of an unconstrained benchmark Vector AutoRegressive model. Full article

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

A two-stage simulation-based framework is proposed to derive Identification Robust confidence sets by applying Indirect Inference, in the context of Autoregressive Moving Average (ARMA) processes for finite samples. Resulting objective functions are treated as test statistics, which are inverted rather than optimized, via the Monte Carlo test method. Simulation studies illustrate accurate size and good power. Projected impulse-response confidence bands are simultaneous by construction and exhibit robustness to parameter identification problems. The persistence of shocks on oil prices and returns is analyzed via impulse-response confidence bands. Our findings support the usefulness of impulse-responses as an empirically relevant transformation of the confidence set. Full article

This work describes a versatile and readily-deployable sensitivity analysis of an ordinary least squares (OLS) inference with respect to possible endogeneity in the explanatory variables of the usual k-variate linear multiple regression model. This sensitivity analysis is based on a derivation of the sampling distribution of the OLS parameter estimator, extended to the setting where some, or all, of the explanatory variables are endogenous. In exchange for restricting attention to possible endogeneity which is solely linear in nature—the most typical case—no additional model assumptions must be made, beyond the usual ones for a model with stochastic regressors. The sensitivity analysis quantifies the sensitivity of hypothesis test rejection p-values and/or estimated confidence intervals to such endogeneity, enabling an informed judgment as to whether any selected inference is “robust” versus “fragile.” The usefulness of this sensitivity analysis—as a “screen” for potential endogeneity issues—is illustrated with an example from the empirical growth literature. This example is extended to an extremely large sample, so as to illustrate how this sensitivity analysis can be applied to parameter confidence intervals in the context of massive datasets, as in “big data”. Full article

A factor model based covariance matrix is used to build a new form of Mahalanobis distance. The distribution and relative properties of the new Mahalanobis distances are derived. A new type of Mahalanobis distance based on the separated part of the factor model is defined. Contamination effects of outliers detected by the new defined Mahalanobis distances are also investigated. An empirical example indicates that the new proposed separated type of Mahalanobis distances predominate the original sample Mahalanobis distance. Full article

The Poisson regression model remains an important tool in the econometric analysis of count data. In a pioneering contribution to the econometric analysis of such models, Lung-Fei Lee presented a specification test for a Poisson model against a broad class of discrete distributions sometimes called the Katz family. Two members of this alternative class are the binomial and negative binomial distributions, which are commonly used with count data to allow for under- and over-dispersion, respectively. In this paper we explore the structure of other distributions within the class and their suitability as alternatives to the Poisson model. Potential difficulties with the Katz likelihood leads us to investigate a class of point optimal tests of the Poisson assumption against the alternative of over-dispersion in both the regression and intercept only cases. In a simulation study, we compare score tests of ‘Poisson-ness’ with various point optimal tests, based on the Katz family, and conclude that it is possible to choose a point optimal test which is better in the intercept only case, although the nuisance parameters arising in the regression case are problematic. One possible cause is poor choice of the point at which to optimize. Consequently, we explore the use of Hellinger distance to aid this choice. Ultimately we conclude that score tests remain the most practical approach to testing for over-dispersion in this context. Full article

We examine the performance of asymptotic inference as well as bootstrap tests for the Alphabeta and Kobus–Miłoś family of inequality indices for ordered response data. We use Monte Carlo experiments to compare the empirical size and statistical power of asymptotic inference and the Studentized bootstrap test. In a broad variety of settings, both tests are found to have similar rejection probabilities of true null hypotheses, and similar power. Nonetheless, the asymptotic test remains correctly sized in the presence of certain types of severe class imbalances exhibiting very low or very high levels of inequality, whereas the bootstrap test becomes somewhat oversized in these extreme settings. Full article

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

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

Although a wide array of stochastic dominance tests exist for poverty measurement and identification, they assume the income distributions have independent poverty lines or a common absolute (fixed) poverty line. We propose a stochastic dominance test for comparing income distributions up to a common relative poverty line (i.e., some fraction of the pooled median). A Monte Carlo study demonstrates its superior performance over existing methods in terms of power. The test is then applied to some Canadian household survey data for illustration. Full article