We consider the well-studied problem of predicting the time-varying covariance matrix of a vector of financial returns. Popular methods range from simple predictors like rolling window or exponentially weighted moving average (EWMA) to more sophisticated predictors such as generalized autoregressive conditional heteroscedastic (GARCH) type methods. Building on a specific covariance estimator suggested by Engle in 2002, we propose a relatively simple extension that requires little or no tuning or fitting, is interpretable, and produces results at least as good as MGARCH, a popular extension of GARCH that handles multiple assets. To evaluate predictors we introduce a novel approach, evaluating the regret of the log-likelihood over a time period such as a quarter. This metric allows us to see not only how well a covariance predictor does overall, but also how quickly it reacts to changes in market conditions. Our simple predictor outperforms MGARCH in terms of regret. We also test covariance predictors on downstream applications such as portfolio optimization methods that depend on the covariance matrix. For these applications our simple covariance predictor and MGARCH perform similarly.

In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference is the norm in several fields of applied econometric work. The purpose of this monograph is to introduce the reader to the world of Bayesian model determination, by surveying modern shrinkage and variable selection algorithms and methodologies. Bayesian inference is a natural probabilistic framework for quantifying uncertainty and learning about model parameters, and this feature is particularly important for inference in modern models of high dimensions and increased complexity. We begin with a linear regression setting in order to introduce various classes of priors that lead to shrinkage/sparse estimators of comparable value to popular penalized likelihood estimators (e.g., ridge, LASSO). We explore various methods of exact and approximate inference, and discuss their pros and cons. Finally, we explore how priors developed for the simple regression setting can be extended in a straightforward way to various classes of interesting econometric models. In particular, the following case-studies are considered, that demonstrate application of Bayesian shrinkage and variable selection strategies to popular econometric contexts: (i) vector autoregressive models; (ii) factor models; (iii) time-varying parameter regressions; (iv) confounder selection in treatment effects models; and (v) quantile regression models. A MATLAB package and an accompanying technical manual1 allow the reader to replicate many of the algorithms described in this monograph.

Climate econometrics is a new sub-discipline that has grown rapidly over the last few years. As greenhouse gas emissions like carbon dioxide (CO2), nitrous oxide (N2O) and methane (CH4) are a major cause of climate change, and are generated by human activity, it is not surprising that the tool set designed to empirically investigate economic outcomes should be applicable to studying many empirical aspects of climate change. Economic and climate time series exhibit many commonalities. Both data are subject to non-stationarities in the form of evolving stochastic trends and sudden distributional shifts. Consequently, the well-developed machinery for modeling economic time series can be fruitfully applied to climate data. In both disciplines, we have imperfect and incomplete knowledge of the processes actually generating the data. As we don’t know that data generating process (DGP), we must search for what we hope is a close approximation to it. The data modeling approach adopted at Climate Econometrics (http://www.climateeconometrics.org/) is based on a model selection methodology that has excellent properties for locating an unknown DGP nested within a large set of possible explanations, including dynamics, outliers, shifts, and non-linearities. The software we use is a variant of machine learning which implements multi-path block searches commencing from very general specifications to discover a well-specified and undominated model of the processes under analysis. To do so requires implementing indicator saturation estimators designed to match the problem faced, such as impulse indicators for outliers, step indicators for location shifts, trend indicators for trend breaks, multiplicative indicators for parameter changes, and indicators specifically designed for more complex phenomena that have a common reaction ‘shape’ like the impacts of volcanic eruptions on temperature reconstructions. We also use combinations of these, inevitably entailing settings with more candidate variables than observations. Having described these econometric tools, we take a brief excursion into climate science to provide the background to the later applications. By noting the Earth’s available atmosphere and water resources, we establish that humanity really can alter the climate, and is doing so in myriad ways. Then we relate past climate changes to the ‘great extinctions’ seen in the geological record. Following the Industrial Revolution in the mid-l8th century, building on earlier advances in scientific, technological and medical knowledge, real income levels per capita have risen dramatically globally, many killer diseases have been tamed, and human longevity has approximately doubled. However, such beneficial developments have led to a global explosion in anthropogenic emissions of greenhouse gases. These are also subject to many relatively sudden shifts from major wars, crises, resource discoveries, technology and policy interventions. Consequently, stochastic trends, large shifts and numerous outliers must all be handled in practice to develop viable empirical models of climate phenomena. Additional advantages of our econometric methods for doing so are detecting the impacts of important policy interventions as well as improved forecasts. The econometric approach we outline can handle all these jointly, which is essential to accurately characterize non-stationary observational data. Few approaches in either climate or economic modeling consider all such effects jointly, but a failure to do so leads to mis-specified models and hence incorrect theory evaluation and policy analyses. We discuss the hazards of modeling wide-sense non-stationary data (namely data not just with stochastic trends but also distributional shifts), which also serves to describe our notation. The application of the methods is illustrated by two detailed modeling exercises. The first investigates the causal role of CO2 in Ice Ages, where a simultaneous-equations system is developed to characterize land ice volume, temperature and atmospheric CO2 levels as non-linear functions of measures of the Earth’s orbital path round the Sun. The second turns to analyze the United Kingdom’s highly non-stationary annual CO2 emissions over the last 150 years, walking through all the key modeling stages. As the first country into the Industrial Revolution, the UK is one of the first countries out, with per capita annual CO2 emissions now below 1860’s levels when our data series begin, a reduction achieved with little aggregate cost. However, very large decreases in all greenhouse gas emissions are still required to meet the UK’s 2050 target set by its Climate Change Act in 2008 of an 80% reduction from 1970 levels, since reduced to a net zero target by that date, as required globally to stabilize temperatures. The rapidly decreasing costs of renewable energy technologies offer hope of further rapid emission reductions in that area, illustrated by a dynamic scenario analysis.

Stated preference elicitation methods collect data on consumers by “just asking” about tastes, perceptions, valuations, attitudes, motivations, life satisfactions, and/or intended choices. Choice-Based Conjoint (CBC) analysis asks subjects to make choices from hypothetical menus in experiments that are designed to mimic market experiences. Stated preference methods are controversial in economics, particularly for valuation of non-market goods, but CBC analysis is accepted and used widely in marketing and policy analysis. The promise of stated preference experiments is that they can provide deeper and broader data on the structure of consumer preferences than is obtainable from revealed market observations, with experimental control of the choice environment that circumvents the feedback found in real market equilibria. The risk is that they give pictures of consumers that do not predict real market behavior. It is important for both economists and non-economists to learn about the performance of stated preference elicitations and the conditions under which they can contribute to understanding consumer behavior and forecasting market demand. This monograph re-examines the discrete choice methods and stated preference elicitation procedures that are commonly used in CBC, and provides a guide to techniques for CBC data collection, model specification, estimation, and policy analysis. The aim is to clarify the domain of applicability and delineate the circumstances under which stated preference elicitations can provide reliable information on preferences.

Spatial econometrics can be defined in a narrow and in a broader sense. In a narrow sense it refers to methods and techniques for the analysis of regression models using data observed within discrete portions of space such as countries or regions. In a broader sense it is inclusive of the models and theoretical instruments of spatial statistics and spatial data analysis to analyze various economic effects such as externalities, interactions, spatial concentration and many others. Indeed, the reference methodology for spatial econometrics lies on the advances in spatial statistics where it is customary to distinguish between different typologies of data that can be encountered in empirical cases and that require different modelling strategies. A first distinction is between continuous spatial data and data observed on a discrete space. Continuous spatial data are very common in many scientific disciplines (such as physics and environmental sciences), but are still not currently considered in the spatial econometrics literature. Discrete spatial data can take the form of points, lines and polygons. Point data refer to the position of the single economic agent observed at an individual level. Lines in space take the form of interactions between two spatial locations such as flows of goods, individuals and information. Finally data observed within polygons can take the form of predefined irregular portions of space, usually administrative partitions such as countries, regions or counties within one country. In this monograph we will adopt a broader view of spatial econometrics and we will introduce some of the basic concepts and the fundamental distinctions needed to properly analyze economic datasets observed as points, regions or lines over space. It cannot be overlooked the fact that the mainstream spatial econometric literature was recently the subject for harsh and radical criticisms by a number of papers. The purpose of this monograph is to show that much of these criticisms are in fact well grounded, but that they lose relevance if we abandon the narrow paradigm of a discipline centered on the regression analysis of regional data, and we embrace the wider acceptation adopted here. In Section 2 we will introduce methods for the spatial econometric analysis of regional data that, so far, have been the workhorse of most theoretical and empirical work in the literature. We will consider modelling strategies falling within the general structure of the SARAR paradigm and its particularizations by presenting the various estimation and hypothesis testing procedures based on Maximum Likelihood (ML), Generalized Method of Moments (GMM) and Two-Stage Least Squares (2SLS), that were proposed in the literature to remove the ineffieciencies and inconsistencies arising from the presence of various forms of spatial dependence. Section 3 is devoted to the new emerging field of spatial econometric analysis of individual granular spatial data sometimes referred to as spatial microeconometrics. We present modelling strategies that use information about the actual position of each economic agent to explain both individuals’ location decisions and the economic actions observed in the chosen locations. We will discuss the peculiarities of general spatial autoregressive model in this setting and the use of models where distances are used as predictors in a regression framework. We will also present some point pattern methods to model individuals’ locational choices, as well as phenomena of co-localization and joint-localization. Finally in Section 4 the general SARAR paradigm is applied to the case of spatial interaction models estimated using data in the form of origin–destination variables and specified following models based on the analogy with the Newtonian law of universal gravitation. The discussion in this monograph is intentionally limited to the analysis of spatial data observed in a single moment of time leaving out of presentation the case of dynamic spatial data such as those observed in spatial panel data.

This monograph reviews the econometric literature on the estimation of stochastic frontiers and technical efficiency. Special attention is devoted to current research.

The overall objectives of this review and synthesis are to study the basics of information-theoretic methods in econometrics, to examine the connecting theme among these methods, and to provide a more detailed summary and synthesis of the sub-class of methods that treat the observed sample moments as stochastic. Within the above objectives, this review focuses on studying the inter-connection between information theory, estimation, and inference. To achieve these objectives, it provides a detailed survey of information-theoretic concepts and quantities used within econometrics. It also illustrates the use of these concepts and quantities within the subfield of information and entropy econometrics while paying special attention to the interpretation of these quantities. The relationships between information-theoretic estimators and traditional estimators are discussed throughout the survey. This synthesis shows that in many cases information-theoretic concepts can be incorporated within the traditional likelihood approach and provide additional insights into the data processing and the resulting inference.