This chapter provides a selective review of the factor-augmented regression (FAR) models, where the factors are usually estimated from a large set of observed data, and then as “generated regressors” enter into the next stage of regression. It begins with an introduction to the large-dimensional factor models and the widely used principal component analysis (PCA) estimator. Then we review FAR models with time series data, the extensions of FAR to some nonlinear models, and the factor-augmented panel regressions. Lastly, we briefly introduce some applications of FAR to financial markets.

This chapter overviews three recently developed posterior test statistics for hypothesis testing based on posterior output. These three statistics can be viewed as the posterior version of the trinity of test statistics based on maximum likelihood (ML), namely, the likelihood ratio (LR) test, the Lagrange multiplier (LM) test, and the Wald test. The asymptotic distributions of the test statistics are discussed under repeated sampling. Furthermore, based on the Bernstein–von Mises theorem, the equivalence of the confidence interval construction between the set of posterior tests and their frequentist counterparts is developed, giving the posterior tests a frequentist asymptotic justification. The three statistics are applicable to many popular financial econometric models, including asset pricing models,copula models, and so on. Studies based on simulated data and real data in the context of several financial econometric models are carried out to illustrate the finite sample behavior and the usefulness of the test statistics.

Recent years have seen a surge of econometric development of infill asymptotic theory. Unlike the traditional large-sample theory which assumes that an increasing sample size is due to an increasing time span (denoted as the long-span asymptotic theory in this chapter), infill asymptotic theory assumes that the sample size increases because the sampling frequency shrinks toward zero. The limit of the infill asymptotics of the estimators are those based on a continuous record. Not surprisingly, a development of infill asymptotic theory is closely linked to the increased popularity of continuous time models in applied economics and finance. This chapter reviews the literature on the infill asymptotic theory and applications in financial econometrics, such as unit root testing, bootstrap, and structural break models. In many applications, nonstandard limiting distribution arises. In some cases, the initial condition shows up in the limiting distributions. Monte Carlo studies are carried out to check the performance of the infill asymptotic theory relative to the long-span asymptotic theory.

What happens when agents can choose their information at a cost? What kinds of cost functions lead to behavior typically observed in economics and psychology experiments?

Agents are forward-looking and incorporate their future behavior into today’s decisions. This is captured by the Bellman equation. We break this axiomatically into preference for flexibility and rational expectations.

How do people choose between risky prospects? I discuss the model of random expected utility and its axiomatic characterization. Other models are discussed too, including models of nonexpected utility and models with additive shocks.

Dynamic discrete choice models, such as dynamic logit, are used extensively in industrial organization. This chapter exposits various classes of these models and studies their properties.

Sometimes agents don’t pay attention to all the items on the menu but restrict themselves to what is called a consideration set. We review a number of classical model of consideration sets.

Are fast choices better or worse than slow ones? This chapter explores models of stopping times, including sequential sampling models from statistics and drift-diffusion models from cognitive science.