## The Academic Effects of United States Child Food Assistance Programs—At Home, School, and In-Between

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While rational expectations (RE) remains the benchmark paradigm in macro-economic modeling, bounded rationality, especially in the form of adaptive learning, has become a mainstream alternative. Under the adaptive learning (AL) approach, economic agents in dynamic, stochastic environments are modeled as adaptive learners forming expectations and making decisions based on forecasting rules that are updated in real time as new data become available. Their decisions are then coordinated each period via the economy’s markets and other relevant institutional architecture, resulting in a time-path of economic aggregates. In this way, the AL approach introduces additional dynamics into the model—dynamics that can be used to address myriad macroeconomic issues and concerns, including, for example, empirical fit and the plausibility of specific rational expectations equilibria. AL can be implemented as reduced-form learning, that is, the implementation of learning at the aggregate level, or alternatively, as discussed in a companion contribution to this Encyclopedia, Evans and McGough, as agent-level learning, which includes pre-aggregation analysis of boundedly rational decision making. Typically learning agents are assumed to use estimated linear forecast models, and a central formulation of AL is least-squares learning in which agents recursively update their estimated model as new data become available. Key questions include whether AL will converge over time to a specified RE equilibrium (REE), in which cases we say the REE is stable under AL; in this case, it is also of interest to examine what type of learning dynamics are observed en route. When multiple REE exist, stability under AL can act as a selection criterion, and global dynamics can involve switching between local basins of attraction. In models with indeterminacy, AL can be used to assess whether agents can learn to coordinate their expectations on sunspots. The key analytical concepts and tools are the E-stability principle together with the E-stability differential equations, and the theory of stochastic recursive algorithms (SRA). While, in general, analysis of SRAs is quite technical, application of the E-stability principle is often straightforward. In addition to equilibrium analysis in macroeconomic models, AL has many applications. In particular, AL has strong implications for the conduct of monetary and fiscal policy, has been used to explain asset price dynamics, has been shown to improve the fit of estimated dynamic stochastic general equilibrium (DSGE) models, and has been proven useful in explaining experimental outcomes.

## Age-Period-Cohort Models

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.

## Aging and Healthcare Costs

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.

## Anthropometrics: The Intersection of Economics and Human Biology

Anthropometrics is a research program that explores the extent to which economic processes affect human biological processes using height and weight as markers. This agenda differs from health economics in the sense that instead of studying diseases or longevity, macro manifestations of well-being, it focuses on cellular-level processes that determine the extent to which the organism thrives in its socio-economic and epidemiological environment. Thus, anthropometric indicators are used as a proxy measure for the biological standard of living as complements to conventional measures based on monetary units. Using physical stature as a marker, we enabled the profession to learn about the well-being of children and youth for whom market-generated monetary data are not abundant even in contemporary societies. It is now clear that economic transformations such as the onset of the Industrial Revolution and modern economic growth were accompanied by negative externalities that were hitherto unknown. Moreover, there is plenty of evidence to indicate that the Welfare States of Western and Northern Europe take better care of the biological needs of their citizens than the market-oriented health-care system of the United States. Obesity has reached pandemic proportions in the United States affecting 40% of the population. It is fostered by a sedentary and harried lifestyle, by the diminution in self-control, the spread of labor-saving technologies, and the rise of instant gratification characteristic of post-industrial society. The spread of television and a fast-food culture in the 1950s were watershed developments in this regard that accelerated the process. Obesity poses a serious health risk including heart disease, stroke, diabetes, and some types of cancer and its cost reaches $150 billion per annum in the United States or about$1,400 per capita. We conclude that the economy influences not only mortality and health but reaches bone-deep into the cellular level of the human organism. In other words, the economy is inextricably intertwined with human biological processes.

## Antitrust Law as a Problem in Economics

“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.

## Applications of Web Scraping in Economics and Finance

The 21st-century economy is increasingly built around data. Firms and individuals upload and store enormous amount of data. Most of the produced data is stored on private servers, but a considerable part is made publicly available across the 1.83 billion websites available online. These data can be accessed by researchers using web-scraping techniques. Web scraping refers to the process of collecting data from web pages either manually or using automation tools or specialized software. Web scraping is possible and relatively simple thanks to the regular structure of the code used for websites designed to be displayed in web browsers. Websites built with HTML can be scraped using standard text-mining tools, either scripts in popular (statistical) programming languages such as Python, Stata, R, or stand-alone dedicated web-scraping tools. Some of those tools do not even require any prior programming skills. Since about 2010, with the omnipresence of social and economic activities on the Internet, web scraping has become increasingly more popular among academic researchers. In contrast to proprietary data, which might not be feasible due to substantial costs, web scraping can make interesting data sources accessible to everyone. Thanks to web scraping, the data are now available in real time and with significantly more details than what has been traditionally offered by statistical offices or commercial data vendors. In fact, many statistical offices have started using web-scraped data, for example, for calculating price indices. Data collected through web scraping has been used in numerous economic and finance projects and can easily complement traditional data sources.

## Asset Pricing: Time-Series Predictability

Asset returns change with fundamentals and other factors, such as technical information and sentiment over time. In modeling time-varying expected returns, this article focuses on the out-of-sample predictability of the aggregate stock market return via extensions of the conventional predictive regression approach. The extensions are designed to improve out-of-sample performance in realistic environments characterized by large information sets and noisy data. Large information sets are relevant because there are a plethora of plausible stock return predictors. The information sets include variables typically associated with a rational time-varying market risk premium, as well as variables more likely to reflect market inefficiencies resulting from behavioral influences and information frictions. Noisy data stem from the intrinsically large unpredictable component in stock returns. When forecasting with large information sets and noisy data, it is vital to employ methods that incorporate the relevant information in the large set of predictors in a manner that guards against overfitting the data. Methods that improve out-of-sample market return prediction include forecast combination, principal component regression, partial least squares, the LASSO and elastic net from machine learning, and a newly developed C-ENet approach that relies on the elastic net to refine the simple combination forecast. Employing these methods, a number of studies provide statistically and economically significant evidence that the aggregate market return is predictable on an out-of-sample basis. Out-of-sample market return predictability based on a rich set of predictors thus appears to be a well-established empirical result in asset pricing.

## A Survey of Econometric Approaches to Convergence Tests of Emissions and Measures of Environmental Quality

The analysis of convergence behavior with respect to emissions and measures of environmental quality can be categorized into four types of tests: absolute and conditional β-convergence, σ-convergence, club convergence, and stochastic convergence. In the context of emissions, absolute β-convergence occurs when countries with high initial levels of emissions have a lower emission growth rate than countries with low initial levels of emissions. Conditional β-convergence allows for possible differences among countries through the inclusion of exogenous variables to capture country-specific effects. Given that absolute and conditional β-convergence do not account for the dynamics of the growth process, which can potentially lead to dynamic panel data bias, σ-convergence evaluates the dynamics and intradistributional aspects of emissions to determine whether the cross-section variance of emissions decreases over time. The more recent club convergence approach tests the decline in the cross-sectional variation in emissions among countries over time and whether heterogeneous time-varying idiosyncratic components converge over time after controlling for a common growth component in emissions among countries. In essence, the club convergence approach evaluates both conditional σ- and β-convergence within a panel framework. Finally, stochastic convergence examines the time series behavior of a country’s emissions relative to another country or group of countries. Using univariate or panel unit root/stationarity tests, stochastic convergence is present if relative emissions, defined as the log of emissions for a particular country relative to another country or group of countries, is trend-stationary. The majority of the empirical literature analyzes carbon dioxide emissions and varies in terms of both the convergence tests deployed and the results. While the results supportive of emissions convergence for large global country coverage are limited, empirical studies that focus on country groupings defined by income classification, geographic region, or institutional structure (i.e., EU, OECD, etc.) are more likely to provide support for emissions convergence. The vast majority of studies have relied on tests of stochastic convergence with tests of σ-convergence and the distributional dynamics of emissions less so. With respect to tests of stochastic convergence, an alternative testing procedure accounts for structural breaks and cross-correlations simultaneously is presented. Using data for OECD countries, the results based on the inclusion of both structural breaks and cross-correlations through a factor structure provides less support for stochastic convergence when compared to unit root tests with the inclusion of just structural breaks. Future studies should increase focus on other air pollutants to include greenhouse gas emissions and their components, not to mention expanding the range of geographical regions analyzed and more robust analysis of the various types of convergence tests to render a more comprehensive view of convergence behavior. The examination of convergence through the use of eco-efficiency indicators that capture both the environmental and economic effects of production may be more fruitful in contributing to the debate on mitigation strategies and allocation mechanisms.

## Bayesian Statistical Economic Evaluation Methods for Health Technology Assessment

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: Applications

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.

## Bayesian Vector Autoregressions: Estimation

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.

## Behavioral and Social Corporate Finance

Corporate finance is about understanding the determinants and consequences of the investment and financing policies of corporations. In a standard neoclassical profit maximization framework, rational agents, that is, managers, make corporate finance decisions on behalf of rational principals, that is, shareholders. Over the past two decades, there has been a rapidly growing interest in augmenting standard finance frameworks with novel insights from cognitive psychology, and more recently, social psychology and sociology. This emerging subfield in finance research has been dubbed behavioral corporate finance, which differentiates between rational and behavioral agents and principals. The presence of behavioral shareholders, that is, principals, may lead to market timing and catering behavior by rational managers. Such managers will opportunistically time the market and exploit mispricing by investing capital, issuing securities, or borrowing debt when costs of capital are low and shunning equity, divesting assets, repurchasing securities, and paying back debt when costs of capital are high. Rational managers will also incite mispricing, for example, cater to non-standard preferences of shareholders through earnings management or by transitioning their firms into an in-fashion category to boost the stock’s price. The interaction of behavioral managers, that is, agents, with rational shareholders can also lead to distortions in corporate decision making. For example, managers may perceive fundamental values differently and systematically diverge from optimal decisions. Several personal traits, for example, overconfidence or narcissism, and environmental factors, for example, fatal natural disasters, shape behavioral managers’ preferences and beliefs, short or long term. These factors may bias the value perception by managers and thus lead to inferior decision making. An extension of behavioral corporate finance is social corporate finance, where agents and principals do not make decisions in a vacuum but rather are embedded in a dynamic social environment. Since managers and shareholders take a social position within and across markets, social psychology and sociology can be useful to understand how social traits, states, and activities shape corporate decision making if an individual’s psychology is not directly observable.

## Behavioral Corporate Finance: The Life Cycle of a CEO Career

One of the fastest-growing areas of finance research is the study of managerial biases and their implications for firm outcomes. Since the mid-2000s, this strand of behavioral corporate finance has provided theoretical and empirical evidence on the influence of biases in the corporate realm, such as overconfidence, experience effects, and the sunk-cost fallacy. The field has been a leading force in dismantling the argument that traditional economic mechanisms—selection, learning, and market discipline—would suffice to uphold the rational-manager paradigm. Instead, the evidence reveals that behavioral forces exert a significant influence at every stage of a chief executive officer’s (CEO’s) career. First, at the appointment stage, selection does not impede the promotion of behavioral managers. Instead, competitive environments oftentimes promote their advancement, even under value-maximizing selection mechanisms. Second, while at the helm of the company, learning opportunities are limited, since many managerial decisions occur at low frequency, and their causal effects are clouded by self-attribution bias and difficult to disentangle from those of concurrent events. Third, at the dismissal stage, market discipline does not ensure the firing of biased decision-makers as board members themselves are subject to biases in their evaluation of CEOs. By documenting how biases affect even the most educated and influential decision-makers, such as CEOs, the field has generated important insights into the hard-wiring of biases. Biases do not simply stem from a lack of education, nor are they restricted to low-ability agents. Instead, biases are significant elements of human decision-making at the highest levels of organizations. An important question for future research is how to limit, in each CEO career phase, the adverse effects of managerial biases. Potential approaches include refining selection mechanisms, designing and implementing corporate repairs, and reshaping corporate governance to account not only for incentive misalignments, but also for biased decision-making.

## Behavioral Development Economics

Economics, like all behavioral sciences, incorporates premises about how people think. Behavioral economics emerged in reaction to the extreme assumption in neoclassical economics that agents have unbounded cognitive capacity and exogenous, fixed preferences. There have been two waves of behavioral economics, and both have enriched development economics. The first wave takes into account that cognitive capacity is bounded and that individuals in many situations act predictably irrationally: there are universal human biases. Behavioral development economics in this first wave has shown that low-cost interventions can be “small miracles” that increase productivity and well-being by making it easier for people to make the rational choice. The second wave of behavioral economics explicitly takes into account that humans are products of culture as well as nature. From their experience and exposure to communities, humans adopt beliefs that shape their perception, construals, and behavior. This second wave helps explain why long-run paths of economic development may diverge across countries with different histories. The second wave also suggests a new kind of intervention: Policies that give individuals new experiences or new role models may change their perceptions and preferences. New perceptions and preferences change behavior. This is a very different perspective than that of neoclassical economics, in which changing behavior requires ongoing interventions.

## Behavioral Experiments in Health Economics

The state-of-the-art literature at the interface between experimental and behavioral economics and health economics is reviewed by identifying and discussing 10 areas of potential debate about behavioral experiments in health. By doing so, the different streams and areas of application of the growing field of behavioral experiments in health are reviewed, by discussing which significant questions remain to be discussed, and by highlighting the rationale and the scope for the further development of behavioral experiments in health in the years to come.