This is an advance summary of a forthcoming article in the Oxford Research Encyclopedia of Economics and Finance. Please check back later for the full article.
Outcomes from individuals often depend on their age, period, and cohort, where cohort + age = period. An example is consumption, where consumption patterns change with age, but the availability of product changes over time, the period, and this affects individuals of different birth years, the cohort, differently. Age-period-cohort models are linear models allowing different parameter values for each level of age, period, and cohort. Variations of the models are available for data aggregated over age, period, and cohort and for data stemming from repeated cross-sections, where the time effects can be combined with individual covariates. The models could potentially be extended to panel data. It is common to plot the estimated age, period, and cohort effects and analyze them as time series. Further, it is also common to conduct inference on the inclusion of the different time effects, and to use the models for forecasting, which involves extrapolation of the time effects.
The age, period, and cohort time effects are intertwined. Specifically, inclusion of an indicator variable for each level of age, period, and cohort will result in a collinarity, which is referred to as the age-period-cohort identification problem. A first approach to addressing the collinarity is to leave out a suitable number of indicator variables. This gives some difficulties in the interpretation, inference, and forecasting in relation to the time effects. A second approach is the canonical parametrization that is a freely varying parametrization, which is invariant to the identification problem and therefore more amenable to interpretation, inference, and forecasting.
Martin Karlsson, Tor Iversen, and Henning Øien
An open issue in the economics literature is whether health care 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 “Ageing of Population and Health Care 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.
Silvia Miranda-Agrippino and Giovanni Ricco
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.
Silvia Miranda-Agrippino and Giovanni Ricco
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.
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.
The cointegrated VAR approach combines differences of variables with cointegration among them and by doing so allows the user to study both long-run and short-run effects in the same model. The CVAR describes an economic system where variables have been pushed away from long-run equilibria by exogenous shocks (the pushing forces) and where short-run adjustments forces pull them back toward long-run equilibria (the pulling forces). In this model framework, basic assumptions underlying a theory model can be translated into testable hypotheses on the order of integration and cointegration of key variables and their relationships. The set of hypotheses describes the empirical regularities we would expect to see in the data if the long-run properties of a theory model are empirically relevant.
Michael P. Clements and Ana Beatriz Galvão
At a given point in time, a forecaster will have access to data on macroeconomic variables that have been subject to different numbers of rounds of revisions, leading to varying degrees of data maturity. Observations referring to the very recent past will be first-release data, or data which has as yet been revised only a few times. Observations referring to a decade ago will typically have been subject to many rounds of revisions. How should the forecaster use the data to generate forecasts of the future? The conventional approach would be to estimate the forecasting model using the latest vintage of data available at that time, implicitly ignoring the differences in data maturity across observations.
The conventional approach for real-time forecasting treats the data as given, that is, it ignores the fact that it will be revised. In some cases, the costs of this approach are point predictions and assessments of forecasting uncertainty that are less accurate than approaches to forecasting that explicitly allow for data revisions. There are several ways to “allow for data revisions,” including modeling the data revisions explicitly, an agnostic or reduced-form approach, and using only largely unrevised data. The choice of method partly depends on whether the aim is to forecast an earlier release or the fully revised values.
Denzil G. Fiebig and Hong Il Yoo
Stated preference methods are used to collect individual level data on what respondents say they would do when faced with a hypothetical but realistic situation. The hypothetical nature of the data has long been a source of concern among researchers as such data stand in contrast to revealed preference data, which record the choices made by individuals in actual market situations. But there is considerable support for stated preference methods as they are a cost-effective means of generating data that can be specifically tailored to a research question and, in some cases, such as gauging preferences for a new product or non-market good, there may be no practical alternative source of data. While stated preference data come in many forms, the primary focus in this article will be data generated by discrete choice experiments, and thus the econometric methods will be those associated with modeling binary and multinomial choices with panel data.
Hans Olav Melberg
End-of-life spending is commonly defined as all health costs in the 12 months before death. Typically, the costs represent about 10% of all health expenses in many countries, and there is a large debate about the effectiveness of the spending and whether it should be increased or decreased. Assuming that health spending is effective in improving health, and using a wide definition of benefits from end-of-life spending, several economists have argued for increased spending in the last years of life. Others remain skeptical about the effectiveness of such spending based on both experimental evidence and the observation that geographic within-country variations in spending are not correlated with variations in mortality.
Florence Jusot and Sandy Tubeuf
Recent developments in the analysis of inequality in health and healthcare have turned their interest into an explicit normative understanding of the sources of inequalities that calls upon the concept of equality of opportunity. According to this concept, some sources of inequality are more objectionable than others and could represent priorities for policies aiming to reduce inequality in healthcare use, access, or health status.
Equality of opportunity draws a distinction between “legitimate” and “illegitimate” sources of inequality. While legitimate sources of differences can be attributed to the consequences of individual effort (i.e. determinants within the individual’s control), illegitimate sources of differences are related to circumstances (i.e. determinants beyond the individual’s responsibility).
The study of inequality of opportunity is rooted in social justice research, and the last decade has seen a rapid growth in empirical work using this literature at the core of its approach in both developed and developing countries. Empirical research on inequality of opportunity in health and healthcare is mainly driven by data availability. Most studies in adult populations are based on data from European countries, especially from the UK, while studies analyzing inequalities of opportunity among children are usually based on data from low- or middle-income countries and focus on children under five years old.
Regarding the choice of circumstances, most studies have considered social background to be an illegitimate source of inequality in health and healthcare. Geographical dimensions have also been taken into account, but to a lesser extent, and more frequently in studies focusing on children or those based on data from countries outside Europe. Regarding effort variables or legitimate sources of health inequality, there is wide use of smoking-related variables.
Regardless of the population, health outcome, and circumstances considered, scholars have provided evidence of illegitimate inequality in health and healthcare. Studies on inequality of opportunity in healthcare are mainly found in children population; this emphasizes the need to tackle inequality as early as possible.
Widely used modified least squares estimators for estimation and inference in cointegrating regressions are discussed. The standard case with cointegration in the I(1) setting is examined and some relevant extensions are sketched. These include cointegration analysis with panel data as well as nonlinear cointegrating relationships. Extensions to higher order (co)integration, seasonal (co)integration and fractional (co)integration are very briefly mentioned. Recent developments and some avenues for future research are discussed.
Knut Are Aastveit, James Mitchell, Francesco Ravazzolo, and Herman K. van Dijk
Increasingly, professional forecasters and academic researchers in economics present model-based and subjective or judgment-based forecasts that are accompanied by some measure of uncertainty. In its most complete form this measure is a probability density function for future values of the variable or variables of interest. At the same time, combinations of forecast densities are being used in order to integrate information coming from multiple sources such as experts, models, and large micro-data sets. Given the increased relevance of forecast density combinations, this article explores their genesis and evolution both inside and outside economics. A fundamental density combination equation is specified, which shows that various frequentist as well as Bayesian approaches give different specific contents to this density. In its simplest case, it is a restricted finite mixture, giving fixed equal weights to the various individual densities. The specification of the fundamental density combination equation has been made more flexible in recent literature. It has evolved from using simple average weights to optimized weights to “richer” procedures that allow for time variation, learning features, and model incompleteness. The recent history and evolution of forecast density combination methods, together with their potential and benefits, are illustrated in the policymaking environment of central banks.
Alfred Duncan and Charles Nolan
In recent decades, macroeconomic researchers have looked to incorporate financial intermediaries explicitly into business-cycle models. These modeling developments have helped us to understand the role of the financial sector in the transmission of policy and external shocks into macroeconomic dynamics. They also have helped us to understand better the consequences of financial instability for the macroeconomy. Large gaps remain in our knowledge of the interactions between the financial sector and macroeconomic outcomes. Specifically, the effects of financial stability and macroprudential policies are not well understood.
High-Dimensional Dynamic Factor Models have their origin in macroeconomics, precisely in empirical research on Business Cycles. The central idea, going back to the work of Burns and Mitchell in the years 1940, is that the fluctuations of all the macro and sectoral variables in the economy are driven by a “reference cycle,” that is, a one-dimensional latent cause of variation. After a fairly long process of generalization and formalization, the literature settled at the beginning of the year 2000 on a model in which (1) both the number of variables in the dataset and , the number of observations for each variable, may be large, and (2) all the variables in the dataset depend dynamically on a fixed independent of , a number of “common factors,” plus variable-specific, usually called “idiosyncratic,” components. The structure of the model can be exemplified as follows:
where the observable variables are driven by the white noise , which is common to all the variables, the common factor, and by the idiosyncratic component . The common factor is orthogonal to the idiosyncratic components , the idiosyncratic components are mutually orthogonal (or weakly correlated). Lastly, the variations of the common factor affect the variable dynamically, that is through the lag polynomial . Asymptotic results for High-Dimensional Factor Models, particularly consistency of estimators of the common factors, are obtained for both and tending to infinity.
Model , generalized to allow for more than one common factor and a rich dynamic loading of the factors, has been studied in a fairly vast literature, with many applications based on macroeconomic datasets: (a) forecasting of inflation, industrial production, and unemployment; (b) structural macroeconomic analysis; and (c) construction of indicators of the Business Cycle. This literature can be broadly classified as belonging to the time- or the frequency-domain approach. The works based on the second are the subject of the present chapter.
We start with a brief description of early work on Dynamic Factor Models. Formal definitions and the main Representation Theorem follow. The latter determines the number of common factors in the model by means of the spectral density matrix of the vector . Dynamic principal components, based on the spectral density of the ’s, are then used to construct estimators of the common factors.
These results, obtained in early 2000, are compared to the literature based on the time-domain approach, in which the covariance matrix of the ’s and its (static) principal components are used instead of the spectral density and dynamic principal components. Dynamic principal components produce two-sided estimators, which are good within the sample but unfit for forecasting. The estimators based on the time-domain approach are simple and one-sided. However, they require the restriction of finite dimension for the space spanned by the factors.
Recent papers have constructed one-sided estimators based on the frequency-domain method for the unrestricted model. These results exploit results on stochastic processes of dimension that are driven by a -dimensional white noise, with , that is, singular vector stochastic processes. The main features of this literature are described with some detail.
Lastly, we report and comment the results of an empirical paper, the last in a long list, comparing predictions obtained with time- and frequency-domain methods. The paper uses a large monthly U.S. dataset including the Great Moderation and the Great Recession.
Economists have long regarded health care as a unique and challenging area of economic activity on account of the specialized knowledge of health care professionals (HCPs) and the relatively weak market mechanisms that operate. This places a consideration of how motivation and incentives might influence performance at the center of research. As in other domains economists have tended to focus on financial mechanisms and when considering HCPs have therefore examined how existing payment systems and potential alternatives might impact on behavior. There has long been a concern that simple arrangements such as fee-for-service, capitation, and salary payments might induce poor performance, and that has led to extensive investigation, both theoretical and empirical, on the linkage between payment and performance. An extensive and rapidly expanded field in economics, contract theory and mechanism design, had been applied to study these issues. The theory has highlighted both the potential benefits and the risks of incentive schemes to deal with the information asymmetries that abound in health care. There has been some expansion of such schemes in practice but these are often limited in application and the evidence for their effectiveness is mixed. Understanding why there is this relatively large gap between concept and application gives a guide to where future research can most productively be focused.
Long memory models are statistical models that describe strong correlation or dependence across time series data. This kind of phenomenon is often referred to as “long memory” or “long-range dependence.” It refers to persisting correlation between distant observations in a time series. For scalar time series observed at equal intervals of time that are covariance stationary, so that the mean, variance, and autocovariances (between observations separated by a lag j) do not vary over time, it typically implies that the autocovariances decay so slowly, as j increases, as not to be absolutely summable. However, it can also refer to certain nonstationary time series, including ones with an autoregressive unit root, that exhibit even stronger correlation at long lags. Evidence of long memory has often been been found in economic and financial time series, where the noted extension to possible nonstationarity can cover many macroeconomic time series, as well as in such fields as astronomy, agriculture, geophysics, and chemistry.
As long memory is now a technically well developed topic, formal definitions are needed. But by way of partial motivation, long memory models can be thought of as complementary to the very well known and widely applied stationary and invertible autoregressive and moving average (ARMA) models, whose autocovariances are not only summable but decay exponentially fast as a function of lag j. Such models are often referred to as “short memory” models, becuse there is negligible correlation across distant time intervals. These models are often combined with the most basic long memory ones, however, because together they offer the ability to describe both short and long memory feartures in many time series.
The majority of econometric models ignore the fact that many economic time series are sampled at different frequencies. A burgeoning literature pertains to econometric methods explicitly designed to handle data sampled at different frequencies. Broadly speaking these methods fall into two categories: (a) parameter driven, typically involving a state space representation, and (b) data driven, usually based on a mixed-data sampling (MIDAS)-type regression setting or related methods. The realm of applications of the class of mixed frequency models includes nowcasting—which is defined as the prediction of the present—as well as forecasting—typically the very near future—taking advantage of mixed frequency data structures. For multiple horizon forecasting, the topic of MIDAS regressions also relates to research regarding direct versus iterated forecasting.
Pieter van Baal and Hendriek Boshuizen
In most countries, non-communicable diseases have taken over infectious diseases as the most important causes of death. Many non-communicable diseases that were previously lethal diseases have become chronic, and this has changed the healthcare landscape in terms of treatment and prevention options. Currently, a large part of healthcare spending is targeted at curing and caring for the elderly, who have multiple chronic diseases. In this context prevention plays an important role as there are many risk factors amenable to prevention policies that are related to multiple chronic diseases.
This article discusses the use of simulation modeling to better understand the relations between chronic diseases and their risk factors with the aim to inform health policy. Simulation modeling sheds light on important policy questions related to population aging and priority setting. The focus is on the modeling of multiple chronic diseases in the general population and how to consistently model the relations between chronic diseases and their risk factors by combining various data sources. Methodological issues in chronic disease modeling and how these relate to the availability of data are discussed. Here, a distinction is made between (a) issues related to the construction of the epidemiological simulation model and (b) issues related to linking outcomes of the epidemiological simulation model to economic relevant outcomes such as quality of life, healthcare spending and labor market participation. Based on this distinction, several simulation models are discussed that link risk factors to multiple chronic diseases in order to explore how these issues are handled in practice. Recommendations for future research are provided.
Karla DiazOrdaz and Richard Grieve
Health economic evaluations face the issues of noncompliance and missing data. Here, noncompliance is defined as non-adherence to a specific treatment, and occurs within randomized controlled trials (RCTs) when participants depart from their random assignment. Missing data arises if, for example, there is loss-to-follow-up, survey non-response, or the information available from routine data sources is incomplete. Appropriate statistical methods for handling noncompliance and missing data have been developed, but they have rarely been applied in health economics studies. Here, we illustrate the issues and outline some of the appropriate methods with which to handle these with application to health economic evaluation that uses data from an RCT.
In an RCT the random assignment can be used as an instrument-for-treatment receipt, to obtain consistent estimates of the complier average causal effect, provided the underlying assumptions are met. Instrumental variable methods can accommodate essential features of the health economic context such as the correlation between individuals’ costs and outcomes in cost-effectiveness studies. Methodological guidance for handling missing data encourages approaches such as multiple imputation or inverse probability weighting, which assume the data are Missing At Random, but also sensitivity analyses that recognize the data may be missing according to the true, unobserved values, that is, Missing Not at Random.
Future studies should subject the assumptions behind methods for handling noncompliance and missing data to thorough sensitivity analyses. Modern machine-learning methods can help reduce reliance on correct model specification. Further research is required to develop flexible methods for handling more complex forms of noncompliance and missing data.
Many nonlinear time series models have been around for a long time and have originated outside of time series econometrics. The stochastic models popular univariate, dynamic single-equation, and vector autoregressive are presented and their properties considered. Deterministic nonlinear models are not reviewed. The use of nonlinear vector autoregressive models in macroeconometrics seems to be increasing, and because this may be viewed as a rather recent development, they receive somewhat more attention than their univariate counterparts. Vector threshold autoregressive, smooth transition autoregressive, Markov-switching, and random coefficient autoregressive models are covered along with nonlinear generalizations of vector autoregressive models with cointegrated variables. Two nonlinear panel models, although they cannot be argued to be typically macroeconometric models, have, however, been frequently applied to macroeconomic data as well. The use of all these models in macroeconomics is highlighted with applications in which model selection, an often difficult issue in nonlinear models, has received due attention. Given the large amount of nonlinear time series models, no unique best method of choosing between them seems to be available.