A linear structure is a family of matrices that satisfy a given set of linear restrictions, such as symmetry or diagonality. We add to the literature on linear structures by studying the family of matrices where all diagonal elements are zero, and discuss two econometric examples where these...

In impulse response analysis estimation uncertainty is typically displayed by constructing bands around estimated impulse response functions. These bands may be based on frequentist or Bayesian methods. If they are based on the joint distribution in the Bayesian framework or the joint asymptotic...

The implied volatility of a European option as a function of strike price and time to maturity forms a volatility surface. Traders price according to the dynamics of this high dimensional surface. Recent developments that employ semiparametric models approximate the implied volatility surface...

A central question in applied research is to estimate the effect of an exogenous intervention or shock on an outcome. The intervention can affect the outcome and controls on impact and over time. Moreover, there can be subsequent feedback between outcomes, controls and the intervention. Many of...

When the number of variables is larger than the number of structural shocks driving the economy, the associated structural VAR system is said to be singular. We propose an identification method for singular structural VAR models contaminated by noise that combines a collapsing procedure with the...

The implied volatility of a European option as a function of strike price and time to maturity forms a volatility surface. Traders price according to the dynamics of this high dimensional surface. Recent developments that employ semiparametric models approximate the implied volatility surface...