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Outcomes of interest often depend on the age, period, or cohort of the individual observed, where cohort and age add up to period. An example is consumption: consumption patterns change over the lifecycle (age) but are also affected by the availability of products at different times (period) and by birth-cohort-specific habits and preferences (cohort). Age-period-cohort (APC) models are additive models where the predictor is a sum of three time effects, which are functions of age, period, and cohort, respectively. Variations of these models are available for data aggregated over age, period, and cohort, and for data drawn from repeated cross-sections, where the time effects can be combined with individual covariates.

The age, period, and cohort time effects are intertwined. Inclusion of an indicator variable for each level of age, period, and cohort results in perfect collinearity, which is referred to as “the age-period-cohort identification problem.” Estimation can be done by dropping some indicator variables. However, dropping indicators has adverse consequences such as the time effects are not individually interpretable and inference becomes complicated. These consequences are avoided by instead decomposing the time effects into linear and non-linear components and noting that the identification problem relates to the linear components, whereas the non-linear components are identifiable. Thus, confusion is avoided by keeping the identifiable non-linear components of the time effects and the unidentifiable linear components apart. A variety of hypotheses of practical interest can be expressed in terms of the non-linear components.

An open issue in the economics literature is whether healthcare expenditure (HCE) is so concentrated in the last years before death that the age profiles in spending will change when longevity increases. The seminal article “aging of Population and HealthCare Expenditure: A Red Herring?” by Zweifel and colleagues argued that that age is a distraction in explaining growth in HCE. The argument was based on the observation that age did not predict HCE after controlling for time to death (TTD). The authors were soon criticized for the use of a Heckman selection model in this context. Most of the recent literature makes use of variants of a two-part model and seems to give some role to age as well in the explanation. Age seems to matter more for long-term care expenditures (LTCE) than for acute hospital care. When disability is accounted for, the effects of age and TTD diminish. Not many articles validate their approach by comparing properties of different estimation models. In order to evaluate popular models used in the literature and to gain an understanding of the divergent results of previous studies, an empirical analysis based on a claims data set from Germany is conducted. This analysis generates a number of useful insights. There is a significant age gradient in HCE, most for LTCE, and costs of dying are substantial. These “costs of dying” have, however, a limited impact on the age gradient in HCE. These findings are interpreted as evidence against the red herring hypothesis as initially stated. The results indicate that the choice of estimation method makes little difference and if they differ, ordinary least squares regression tends to perform better than the alternatives. When validating the methods out of sample and out of period, there is no evidence that including TTD leads to better predictions of aggregate future HCE. It appears that the literature might benefit from focusing on the predictive power of the estimators instead of their actual fit to the data within the sample.

“Antitrust” or “competition law,” a set of policies now existing in most market economies, largely consists of two or three specific rules applied in more or less the same way in most nations. It prohibits (1) multilateral agreements, (2) unilateral conduct, and (3) mergers or acquisitions, whenever any of them are judged to interfere unduly with the functioning of healthy markets. Most jurisdictions now apply or purport to apply these rules in the service of some notion of economic “efficiency,” more or less as defined in contemporary microeconomic theory.

The law has ancient roots, however, and over time it has varied a great deal in its details. Moreover, even as to its modern form, the policy and its goals remain controversial. In some sense most modern controversy arises from or is in reaction to the major intellectual reconceptualization of the law and its purposes that began in the 1960s. Specifically, academic critics in the United States urged revision of the law’s goals, such that it should serve only a narrowly defined microeconomic goal of allocational efficiency, whereas it had traditionally also sought to prevent accumulation of political power and to protect small firms, entrepreneurs, and individual liberty. While those critics enjoyed significant success in the United States, and to a somewhat lesser degree in Europe and elsewhere, the results remain contested. Specific disputes continue over the law’s general purpose, whether it poses net benefits, how a series of specific doctrines should be fashioned, how it should be enforced, and whether it really is appropriate for developing and small-market economies.

The evidence produced by healthcare economic evaluation studies is a key component of any Health Technology Assessment (HTA) process designed to inform resource allocation decisions in a budget-limited context. To improve the quality (and harmonize the generation process) of such evidence, many HTA agencies have established methodological guidelines describing the normative framework inspiring their decision-making process. The information requirements that economic evaluation analyses for HTA must satisfy typically involve the use of complex quantitative syntheses of multiple available datasets, handling mixtures of aggregate and patient-level information, and the use of sophisticated statistical models for the analysis of non-Normal data (e.g., time-to-event, quality of life and costs). Much of the recent methodological research in economic evaluation for healthcare has developed in response to these needs, in terms of sound statistical decision-theoretic foundations, and is increasingly being formulated within a Bayesian paradigm. The rationale for this preference lies in the fact that by taking a probabilistic approach, based on decision rules and available information, a Bayesian economic evaluation study can explicitly account for relevant sources of uncertainty in the decision process and produce information to identify an “optimal” course of actions. Moreover, the Bayesian approach naturally allows the incorporation of an element of judgment or evidence from different sources (e.g., expert opinion or multiple studies) into the analysis. This is particularly important when, as often occurs in economic evaluation for HTA, the evidence base is sparse and requires some inevitable mathematical modeling to bridge the gaps in the available data. The availability of free and open source software in the last two decades has greatly reduced the computational costs and facilitated the application of Bayesian methods and has the potential to improve the work of modelers and regulators alike, thus advancing the fields of economic evaluation of healthcare interventions. This chapter provides an overview of the areas where Bayesian methods have contributed to the address the methodological needs that stem from the normative framework adopted by a number of HTA agencies.

Bayesian vector autoregressions (BVARs) are standard multivariate autoregressive models routinely used in empirical macroeconomics and finance for structural analysis, forecasting, and scenario analysis in an ever-growing number of applications.

A preeminent field of application of BVARs is forecasting. BVARs with informative priors have often proved to be superior tools compared to standard frequentist/flat-prior VARs. In fact, VARs are highly parametrized autoregressive models, whose number of parameters grows with the square of the number of variables times the number of lags included. Prior information, in the form of prior distributions on the model parameters, helps in forming sharper posterior distributions of parameters, conditional on an observed sample. Hence, BVARs can be effective in reducing parameters uncertainty and improving forecast accuracy compared to standard frequentist/flat-prior VARs.

This feature in particular has favored the use of Bayesian techniques to address “big data” problems, in what is arguably one of the most active frontiers in the BVAR literature. Large-information BVARs have in fact proven to be valuable tools to handle empirical analysis in data-rich environments.

BVARs are also routinely employed to produce conditional forecasts and scenario analysis. Of particular interest for policy institutions, these applications permit evaluating “counterfactual” time evolution of the variables of interests conditional on a pre-determined path for some other variables, such as the path of interest rates over a certain horizon.

The “structural interpretation” of estimated VARs as the data generating process of the observed data requires the adoption of strict “identifying restrictions.” From a Bayesian perspective, such restrictions can be seen as dogmatic prior beliefs about some regions of the parameter space that determine the contemporaneous interactions among variables and for which the data are uninformative. More generally, Bayesian techniques offer a framework for structural analysis through priors that incorporate uncertainty about the identifying assumptions themselves.

Vector autoregressions (VARs) are linear multivariate time-series models able to capture the joint dynamics of multiple time series. Bayesian inference treats the VAR parameters as random variables, and it provides a framework to estimate “posterior” probability distribution of the location of the model parameters by combining information provided by a sample of observed data and prior information derived from a variety of sources, such as other macro or micro datasets, theoretical models, other macroeconomic phenomena, or introspection.

In empirical work in economics and finance, informative prior probability distributions are often adopted. These are intended to summarize stylized representations of the data generating process. For example, “Minnesota” priors, one of the most commonly adopted macroeconomic priors for the VAR coefficients, express the belief that an independent random-walk model for each variable in the system is a reasonable “center” for the beliefs about their time-series behavior. Other commonly adopted priors, the “single-unit-root” and the “sum-of-coefficients” priors are used to enforce beliefs about relations among the VAR coefficients, such as for example the existence of co-integrating relationships among variables, or of independent unit-roots.

Priors for macroeconomic variables are often adopted as “conjugate prior distributions”—that is, distributions that yields a posterior distribution in the same family as the prior p.d.f.—in the form of Normal-Inverse-Wishart distributions that are conjugate prior for the likelihood of a VAR with normally distributed disturbances. Conjugate priors allow direct sampling from the posterior distribution and fast estimation. When this is not possible, numerical techniques such as Gibbs and Metropolis-Hastings sampling algorithms are adopted.

Bayesian techniques allow for the estimation of an ever-expanding class of sophisticated autoregressive models that includes conventional fixed-parameters VAR models; Large VARs incorporating hundreds of variables; Panel VARs, that permit analyzing the joint dynamics of multiple time series of heterogeneous and interacting units. And VAR models that relax the assumption of fixed coefficients, such as time-varying parameters, threshold, and Markov-switching VARs.

This article examines the new trends in research on capital flows fueled by the 2007–2009 Global Crisis. Previous studies on capital flows focused on current account imbalances and net capital flows. The Global Crisis changed that. The onset of this crisis was preceded by a dramatic increase in gross financial flows while net capital flows remained mostly subdued. The attention in academia zoomed in on gross inflows and outflows with special attention to cross-border banking flows before the crisis erupted and the shift towards corporate bond issuance in its aftermath. The boom and bust in capital flows around the Global Crisis also stimulated a new area of research: capturing the “global factor.” This research adopts two different approaches. The traditional literature on the push–pull factors, which before the crisis was mostly focused on monetary policy in the financial center as the “push factor,” started to explore what other factors contribute to the co-movement of capital flows as well as to amplify the role of monetary policy in the financial center on capital flows. This new research focuses on global banks’ leverage, risk appetite, and global uncertainty. Since the “global factor” is not known, a second branch of the literature has captured this factor indirectly using dynamic common factors extracted from actual capital flows or movements in asset prices.

Unlike traditional first order asymptotic approximations, the bootstrap is a simulation method to solve inferential issues in statistics and econometrics conditional on the available sample information (e.g. constructing confidence intervals, generating critical values for test statistics). Even though econometric theory yet provides sophisticated central limit theory covering various data characteristics, bootstrap approaches are of particular appeal if establishing asymptotic pivotalness of (econometric) diagnostics is infeasible or requires rather complex assessments of estimation uncertainty. Moreover, empirical macroeconomic analysis is typically constrained by short- to medium-sized time windows of sample information, and convergence of macroeconometric model estimates toward their asymptotic limits is often slow. Consistent bootstrap schemes have the potential to improve empirical significance levels in macroeconometric analysis and, moreover, could avoid explicit assessments of estimation uncertainty. In addition, as time-varying (co)variance structures and unmodeled serial correlation patterns are frequently diagnosed in macroeconometric analysis, more advanced bootstrap techniques (e.g., wild bootstrap, moving-block bootstrap) have been developed to account for nonpivotalness as a results of such data characteristics.

This paper reviews selected post–Global Financial Crisis theoretical and empirical contributions on capital controls and identifies three theoretical motives for the use of capital controls: pecuniary externalities in models of financial crises, aggregate demand externalities in New Keynesian models of the business cycle, and terms of trade manipulation in open-economy models with pricing power. Pecuniary and demand externalities offer the most compelling case for the adoption of capital controls, but macroprudential policy can also address the same distortions. So capital controls generally are not the only instrument that can do the job. If evaluated through the lenses of the new theories, the empirical evidence reviewed suggests that capital controls can have the intended effects, even though the extant literature is inconclusive as to whether the effects documented amount to a net gain or loss in welfare terms. Terms of trade manipulation also provides a clear-cut theoretical case for the use of capital controls, but this motive is less compelling because of the spillover and coordination issues inherent in the use of control on capital flows for this purpose. Perhaps not surprisingly, only a handful of countries have used capital controls in a countercyclical manner, while many adopted macroprudential policies. This suggests that capital control policy might entail additional costs other than increased financing costs, such as signaling the bad quality of future policies, leakages, and spillovers.

Since the 1980s policymakers have identified a wide range of policy interventions to improve hospital performance. Some of these have been initiated at the level of government, whereas others have taken the form of decisions made by individual hospitals but have been guided by regulatory or financial incentives. Studies investigating the impact that some of the most important of these interventions have had on hospital performance can be grouped into four different research streams. Among the research streams, the strongest evidence exists for the effects of privatization. Studies on this topic use longitudinal designs with control groups and have found robust increases in efficiency and financial performance. Evidence on the entry of hospitals into health systems and the effects of this on efficiency is similarly strong. Although the other three streams of research also contain well-conducted studies with valuable findings, they are predominantly cross-sectional in design and therefore cannot establish causation. While the effects of introducing DRG-based hospital payments and of specialization are largely unclear, vertical and horizontal cooperation probably have a positive effect on efficiency and financial performance. Lastly, the drivers of improved efficiency or financial performance are very different depending on the reform or intervention being investigated; however, reductions in the number of staff and improved bargaining power in purchasing stand out as being of particular importance.

Several promising avenues for future investigation are identified. One of these is situated within a new area of research examining the link between changes in the prices of treatments and hospitals’ responses. As there is evidence of unintended effects, future studies should attempt to distinguish between changes in hospitals’ responses at the intensive margin (e.g., upcoding) versus the extensive margin (e.g., increase in admissions). When looking at the effects of entering into a health system and of privatizations, there is still considerable need for research. With privatizations, in particular, the underlying processes are not yet fully understood, and the potential trade-offs between increases in performance and changes in the quality of care have not been sufficiently examined. Lastly, there is substantial need for further papers in the areas of multi-institutional arrangements and cooperation, as well as specialization. In both research streams, natural experiments carried out using program evaluation design are lacking. One of the main challenges here, however, is that cooperation and specialization cannot be directly observed but rather must be constructed based on survey or administrative data.

In many countries of the world, consumers choose their health insurance coverage from a large menu of often complex options supplied by private insurance companies. Economic benefits of the wide choice of health insurance options depend on the extent to which the consumers are active, well informed, and sophisticated decision makers capable of choosing plans that are well-suited to their individual circumstances.

There are many possible ways how consumers’ actual decision making in the health insurance domain can depart from the standard model of health insurance demand of a rational risk-averse consumer. For example, consumers can have inaccurate subjective beliefs about characteristics of alternative plans in their choice set or about the distribution of health expenditure risk because of cognitive or informational constraints; or they can prefer to rely on heuristics when the plan choice problem features a large number of options with complex cost-sharing design.

The second decade of the 21st century has seen a burgeoning number of studies assessing the quality of consumer choices of health insurance, both in the lab and in the field, and financial and welfare consequences of poor choices in this context. These studies demonstrate that consumers often find it difficult to make efficient choices of private health insurance due to reasons such as inertia, misinformation, and the lack of basic insurance literacy. These findings challenge the conventional rationality assumptions of the standard economic model of insurance choice and call for policies that can enhance the quality of consumer choices in the health insurance domain.

In the wake of the 2008 financial collapse, clearinghouses have emerged as critical players in the implementation of the post-crisis regulatory reform agenda. Recognizing serious shortcomings in the design of the over-the-counter derivatives market for swaps, regulators are now relying on clearinghouses to cure these deficiencies by taking on a central role in mitigating the risks of these instruments. Rather than leave trading firms to manage the risks of transacting in swaps privately, as was largely the case prior to 2008, post-crisis regulation requires that clearinghouses assume responsibility for ensuring that trades are properly settled, reported to authorities, and supported by strong cushions of protective collateral. With clearinghouses effectively guaranteeing that the terms of a trade will be honored—even if one of the trading parties cannot perform—the market can operate with reduced levels of counterparty risk, opacity, and the threat of systemic collapse brought on by recklessness and over-complexity.

But despite their obvious benefit for regulators, clearinghouses also pose risks of their own. First, given their deepening significance for market stability, ensuring that clearinghouses themselves operate safely represents a matter of the highest policy priority. Yet overseeing clearinghouses is far from easy and understanding what works best to undergird their safe operation can be a contentious and uncertain matter. U.S. and EU authorities, for example, have diverged in important ways on what rules should apply to the workings of international clearinghouses. Secondly, clearinghouse oversight is critical because these institutions now warehouse enormous levels of counterparty risk. By promising counterparties across the market that their trades will settle as agreed, even if one or the other firm goes bust, clearinghouses assume almost inconceivably large and complicated risks within their institutions. For swaps in particular—whose obligations can last for months, or even years—the scale of these risks can be far more extensive than that entailed in a one-off sale or a stock or bond. In this way, commentators note that by becoming the go-to bulwark against risk-taking and its spread in the financial system, clearinghouses have themselves become the too-big-to-fail institution par excellence.

Quality competition between alternative providers is an increasingly important topic in the health economics literature. This literature includes theoretical and empirical studies that have been developed in parallel to 21st-century policies to increase competition between doctors or hospitals. Theoretical studies have clarified how competitive markets can give healthcare providers the incentive to improve quality. Broadly speaking, if providers have an incentive to attract more patients and patients value quality, providers will raise quality until the costs of raising quality are equal to the additional revenue from patients attracted by the rise in quality. The theoretical literature has also investigated how institutional and policy parameters determine quality levels in equilibrium. Important parameters in models of quality competition include the degree of horizontal differentiation, the level of information about provider quality, the costs of switching between providers, and the time-horizon of quality investment decisions.

Empirical studies have focused on the prerequisites of quality competition (e.g., do patients choose higher quality providers?) and the impact of pro-competition policies on quality levels. The most influential studies have used modern econometric approaches, including difference-in differences and instrumental variables, to identify plausibly causal effects. The evidence suggests that in most contexts, quality is a determinant of patient choice of provider, especially after greater patient choice is made available or information is published about provider quality.

The evidence that increases in competition improve quality in healthcare is less clear cut. Perhaps reflecting the economic theory of quality competition, showing that different parameter combinations or assumptions can produce different outcomes, empirical results are also mixed. While a series of high-quality studies in the United Kingdom appear to show strong improvements in quality in more competitive areas following pro-competition reforms introducing more choice and competition, other studies showed that these quality improvements do not extend to all types of healthcare or alternative measures of quality.

The most promising areas for future research include investigating the “black box” of quality improvement under competition, and behavioral studies investigating financial and nonfinancial motivations for quality improvements in competitive markets.