• • Title: Testing general linear hypotheses under a high-dimensional multivariate regression model with spiked noise covariance

  • Abstract: We consider the problem of testing linear hypotheses under a multivariate regression model with a high-dimensional response and spiked noise covariance. The proposed family of tests consists of test statistics based on a weighted sum of projections of the data onto the estimated latent factor directions, with the weights acting as the regularization parameters. We establish asymptotic normality of the test statistics under the null hypothesis. We also establish the power characteristics of the tests and propose a data-driven choice of the regularization parameters under a family of local alternatives. The performance of the proposed tests is evaluated through a simulation study. Finally, the proposed tests are applied to the Human Connectome Project data to test for the presence of associations between volumetric measurements of human brain and behavioral variables. 

• • Title: Common Trends and Long-Run Multipliers in Nonlinear Structural VARs

  • Abstract: While it is widely recognised that linear (structural) VARs may omit important features of macroeconomic time series, the use of nonlinear SVARs has to date been almost entirely confined to the modelling of stationary time series, because of a lack of understanding as to how common stochastic trends may be accommodated within nonlinear models. This has unfortunately circumscribed the range of macroeconomic series to which such models can be applied -- and/or required that these series be first transformed to stationarity, a potential source of misspecification -- and prevented the use of long-run identifying restrictions in these models. To address these problems, we develop a flexible class of nonlinear SVARs, which subsume models with threshold-type endogenous regime switching, both of the piecewise linear and smooth transition varieties. We extend the Granger-Johansen representation theorem to this class of models, obtaining conditions that specialise exactly to the usual ones when the model is linear. These models are shown capable of supporting both linear and nonlinear forms of cointegration, where the latter is understood in the profound sense of series having common nonlinear stochastic trends, with possibly nonlinear cointegrating relations between those trends. We further show that, as a consequence, these models are capable of supporting the same kinds of long-run identifying restrictions as are available in linearly cointegrated SVARs.

• • Title: The econometrics of financial duration models: likelihood-based estimation and asymptotics

  • Abstract: Financial durations models are widely used in finance to model time between events such as trades, stock price movements, or other financial events. A workhorse in the literature is the ACD(1,1) model by Engle and Russell (Econometrica, 1998). We show although the likelihood of the model resembles the Gaussian (G)ARCH likelihood, the asymptotic theory for ACD non-standard and different from GARCH asymptotics. In particular, the behavior of likelihood estimators in ACD models is highly sensitive to the tail behavior of the financial durations, with asymptotic normality breaking down when the tail indices of the durations are smaller than unity. Our results exploit the fact that for duration data the number of observations within any given time span is random.

Title: The econometrics of financial duration models: bootstrap-based testing and inference

Abstract: ACD models are a workhorse in the literature of financial duration modeling. Because of their similarity with GARCH models, estimation is usually carried out using quasi maximum likelihood. However, the asymptotics properties of the MLE are non-standard, with the finite sample distributions being different from its asymptotic approximation. We discuss the theory for the bootstrap in this framework. Because for duration data the number of observations within any given time span is random, bootstrap implementations are non-standard; extant bootstrap algorithms such those discussed in the literature on the general class of so-called multiplicative error models are not valid in the ACD setting. We propose discuss a novel bootstrap which works irrespectively of the tail index of the durations. The implications of our results to different point process and renewal models are also discussed.

Title: Local asymptotic minimax inference for set-identified impulse responses

Abstract: This paper considers a local asymptotic minimax inference for set-identified impulse responses. Structural impulse responses, the key causal parameters in applied macroeconomic models, are only identified as a set without stringent restrictions. Under set-identification, the bounds of the identified set are typically characterized as the maximum or minimum of some parametric functions, which may be non-differentiable, e.g.  when multiple structural models are consistent with the boundary parameter value. In this case, the standard "plug-in" approach leads to invalid inference. In addition, robust Bayesian credible sets by Giacomini and Kitagawa (2021) are no longer valid confidence regions in the frequentist perspective. We demonstrate that our local asymptotic minimax framework provides adequate tools for defining estimator optimality and conducting inference even when these existing methods do not apply. The proposed confidence regions achieve desired asymptotic sizes, and are optimal in terms of the average volume. As an empirical illustration, we study inference for impulse responses to the monetary policy shock using the dataset in Jarocinski and Karadi (2020).

Title: Dynamic spatial interaction models for a leader's resource allocation and followers' multiple activities 

Abstract: This paper introduces a new spatial interaction model designed to explore the decision-making processes of two types of agents: a leader and followers. In our empirical study, these agents symbolize the central and local governments. The model's objective is to account for three pivotal features: (i) resource allocations from the leader to the followers, along with the resulting strategic interactions, (ii) followers' multiple activities, and (iii) interactions among followers. We develop a network game to delve into the micro-foundations of these processes. Within this game, the followers undertake multiple activities while the leader distributes resources among them. The game's Nash equilibrium (NE) subsequently informs our econometric framework. By producing equilibrium measures, this NE facilitates understanding the short-run impacts of changes in followers' characteristics and their long-term consequences. For estimating agent payoff parameters, we adopt the quasi-maximum likelihood (QML) method and study the asymptotic properties of the QML estimator, ensuring robust statistical inferences. Empirically, we explore interactions among U.S. states in public welfare and housing development, examining how federal grants influence these expenditures. Our findings indicate positive spillovers in states’ welfare spending and suggest that welfare and housing expenditures act as substitutes. Additionally, we observe significant positive effects of federal grants on both types of expenditures.