Limit theory is provided for a wide class of covariance functionals of a nonstationary process and stationary time series. The results are relevant to estimation and inference in nonlinear nonstationary regressions that involve unit root, local unit root or fractional processes and they include both parametric and nonparametric regressions. Self normalized versions of these statistics are considered that are useful in inference. Numerical evidence reveals a strong bimodality in the finite sample distributions that persists for very large sample sizes although the limit theory is Gaussian. New self normalized versions are introduced that deliver improved approximations.
We consider a general nonlinear pricing environment with private information. The seller can control both the signal that the buyers receive about their value and the selling mechanism. We characterize the optimal menu and information structure that jointly maximize the seller's profits. The optimal screening mechanism has finitely many items even with a continuum of values. We identify sufficient conditions under which the optimal mechanism has a single item. Thus the seller decreases the variety of items below the efficient level as a by-product of reducing the information rents of the buyer.
We consider a general nonlinear pricing environment with private information. The seller can control both the signal that the buyers receive about their value and the selling mechanism. We characterize the optimal menu and information structure that jointly maximize the seller's profit. The optimal screening mechanism has finitely many items even with a continuum of values. We identify sufficient conditions under which the optimal mechanism has a single item. Thus the seller decreases the variety of items below the efficient level in order to reduce the information rents of the buyers.
In selection processes such as hiring, promotion, and college admissions, implicit bias toward socially-salient attributes such as race, gender, or sexual orientation produces persistent inequality and reduces utility for the decision-maker. Recent works show that interventions like the Rooney Rule, which require a minimum quota of individuals from each affected group, are very effective in improving utility when individuals belong to at most one affected group. However, in several settings, individuals belong to multiple affected groups and, consequently, face more extreme implicit bias due to this intersectionality. We consider independently drawn utilities and show that, with intersectionality, the aforementioned non-intersectional constraints only recover part of the utility achievable in the absence of implicit bias. On the other hand, we show that appropriate lower-bound constraints on the intersections recover almost all the utility achievable in the absence of implicit bias. And, hence, offer an advantage over non-intersectional approaches to reducing inequality.
This paper explores weak identification issues arising in commonly used models of economic and financial time series. Two highly popular configurations are shown to be asymptotically observationally equivalent: one with long memory and weak autoregressive dynamics, the other with antipersistent shocks and a near-unit autoregressive root. We develop a data-driven semiparametric and identification-robust approach to inference that reveals such ambiguities and documents the prevalence of weak identification in many realized volatility and trading volume series. The identification-robust empirical evidence generally favors long memory dynamics in volatility and volume, a conclusion that is corroborated using social-media news flow data.
T. W. Anderson did pathbreaking work in econometrics during his remarkable career as an eminent statistician. His primary contributions to econometrics are reviewed here, including his early research on estimation and inference in simultaneous equations models and reduced rank regression. Some of his later works that connect in important ways to econometrics are also briefly covered, including limit theory in explosive autoregression, asymptotic expansions, and exact distribution theory for econometric estimators. The research is considered in the light of its influence on subsequent and ongoing developments in econometrics, notably confidence interval construction under weak instruments and inference in mildly explosive regressions.
In the presence of bubbles, asset prices consist of a fundamental and a bubble component, with the bubble component following an explosive dynamic. The general idea for bubble identification is to apply explosive root tests to a proxy of the unobservable bubble. Three notable proxies are the real asset prices, log price-payoff ratios, and estimated non-fundamental components. The rationale for all three proxy choices rests on the definition of bubbles, which has been presented in various forms in the literature. This chapter provides a theoretical framework that incorporates several definitions of bubbles (and fundamentals) and offers guidance for selecting proxies. For explosive root tests, we introduce the recursive evolving test of Phillips et al. (2015b,c) along with its asymptotic properties. This procedure can serve as a real-time monitoring device and has been shown to outperform several other tests. Like all other recursive testing procedures, the PSY algorithm faces the issue of multiplicity in testing that contaminates conventional significance values. To address this issue, we propose a multiple-testing algorithm to determine appropriate test critical values and show its satisfactory performance in finite samples by simulations. To illustrate, we conduct a pseudo real-time bubble monitoring exercise in the S&P 500 stock market from January 1990 to June 2020. The empirical results reveal the importance of using a good proxy for bubbles and addressing the multiplicity issue.
A principal privately contracts with a set of agents who then simultaneously make a binary decision. Each contract specifies an individual allocation and the information the agent is given about a fundamental state and other agents' contracts. We study the principal's optimal scheme that induces a desired action profile as the unique rationalizable outcome. Our main result reduces this multiagent problem to a two-step procedure where information is designed agent-by-agent: the principal chooses a fundamental-state-contingent distribution over agent rankings and, separately for each agent, the agent's information about the realized ranking and fundamental states. We illustrate with a team-production application.