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Vector Autoregression (VAR) has been a standard empirical tool used in macroeconomics and finance. In this paper we discuss how to compare alternative VAR models after they are estimated by Bayesian MCMC methods. In particular we apply a robust version of deviance information criterion (RDIC) recently developed in Li, Zeng, and Yu (2014b) to determine the best candidate model. RDIC is a better information criterion than the widely used deviance information criterion (DIC) when latent variables are involved in candidate models. Empirical analysis using US data shows that the optimal model selected by RDIC can be different from that by DIC.

This chapter examines the limit properties of information criteria (such as AIC, BIC, and HQIC) for distinguishing between the unit-root (UR) model and the various kinds of explosive models. The explosive models include the local-to-unit-root model from the explosive side the mildly explosive (ME) model, and the regular explosive model. Initial conditions with different orders of magnitude are considered. Both the OLS estimator and the indirect inference estimator are studied. It is found that BIC and HQIC, but not AIC, consistently select the UR model when data come from the UR model. When data come from the local-to-unit-root model from the explosive side, both BIC and HQIC select the wrong model with probability approaching 1 while AIC has a positive probability of selecting the right model in the limit. When data come from the regular explosive model or from the ME model in the form of 1 + n^α/n with α ∈ (0, 1), all three information criteria consistently select the true model. Indirect inference estimation can increase or decrease the probability for information criteria to select the right model asymptotically relative to OLS, depending on the information criteria and the true model. Simulation results confirm our asymptotic results in finite sample.

In this chapter we develop and implement a method for maximum simulated likelihood estimation of the continuous time stochastic volatility model with the constant elasticity of volatility. The approach does not require observations on option prices, nor volatility. To integrate out latent volatility from the joint density of return and volatility, a modified efficient importance sampling technique is used after the continuous time model is approximated using the Euler–Maruyama scheme. The Monte Carlo studies show that the method works well and the empirical applications illustrate usefulness of the method. Empirical results provide strong evidence against the Heston model.

This chapter derives asymptotic properties of the least squares (LS) estimator of the autoregressive (AR) parameter in local to unity processes with errors being fractional Gaussian noise (FGN) with the Hurst parameter H∈(0,1). It is shown that the estimator is consistent for all values of H∈(0,1). Moreover, the rate of convergence is n−1 when H∈[0.5,1). The rate of convergence is n−2H when H∈(0,0.5). Furthermore, the limiting distribution of the centered LS estimator depends on H. When H=0.5, the limiting distribution is the same as that obtained in Phillips (1987a) for the local to unity model with errors for which the standard functional central limit theorem is applicable. When H > 0.5 or when H < 0.5, the limiting distributions are new to the literature. The asymptotic properties of the LS estimator with fitted intercept are also derived. Simulation studies are performed to check the reliability of the asymptotic approximation for different values of sample size.

This chapter presents an evaluation of the literature on the effect of the pandemic on mental health. It draws mainly on the existing economics literature and presents the state of the art of the COVID-19 effect on mental health. While paying particular attention to how the deterioration of mental health evolved over time and across countries, this chapter also considers variation of mental health across individual demographic characteristics as well as different circumstances through which mental health has been affected. Moreover, it provides a general assessment of the methodological aspects of various studies, by discussing the sample and data used, measures of mental health as well as causality issues. Overall, researchers for various countries around the world adopting different measures of mental health, often non-comparable samples and different methodologies document consistently that the level of mental health has been deteriorated during the pandemic, with the negative effect of the lockdown on mental health being evident in the early stage of the pandemic and on the whole population. Findings point out to a high degree of heterogeneity within demographic groups.

This study contributes to the understanding of the health effects of pesticides exposure and of how pesticides have been and should be regulated.

This study presents literature reviews for the period 2000–2013 on (i) the health effects of pesticides and on (ii) preference valuation of health risks related to pesticides, as well as a discussion of the role of benefit-cost analysis applied to pesticide regulatory measures.

This study indicates that the health literature has focused on individuals with direct exposure to pesticides, i.e. farmers, while the literature on preference valuation has focused on those with indirect exposure, i.e. consumers. The discussion highlights the need to clarify the rationale for regulating pesticides, the role of risk perceptions in benefit-cost analysis, and the importance of inter-disciplinary research in this area.

This study relates findings of different disciplines (health, economics, public policy) regarding pesticides, and identifies gaps for future research.