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This article investigates the robustness of impulse response estimators to near unit roots and near cointegration in vector autoregressive (VAR) models. We compare estimators based on VAR specifications determined by pretests for unit roots and cointegration as well as unrestricted VAR specifications in levels. Our main finding is that the impulse response estimators obtained from the levels specification tend to be most robust when the magnitude of the roots is not known. The pretest specification works well only when the restrictions imposed by the model are satisfied. Its performance deteriorates even for small deviations from the exact unit root for one or more model variables. We illustrate the practical relevance of our results through simulation examples and an empirical application.

It is widely documented that while contemporaneous spot and forward financial prices trace each other extremely closely, their difference is often highly persistent and the conventional cointegration tests may suggest lack of cointegration. This chapter studies the possibility of having cointegrated errors that are characterized simultaneously by high persistence (near-unit root behavior) and very small (near zero) variance. The proposed dual parameterization induces the cointegration error process to be stochastically bounded which prevents the variables in the cointegrating system from drifting apart over a reasonably long horizon. More specifically, this chapter develops the appropriate asymptotic theory (rate of convergence and asymptotic distribution) for the estimators in unconditional and conditional vector error correction models (VECM) when the error correction term is parameterized as a dampened near-unit root process (local-to-unity process with local-to-zero variance). The important differences in the limiting behavior of the estimators and their implications for empirical analysis are discussed. Simulation results and an empirical analysis of the forward premium regressions are also provided.

Using a novel measure incorporating stylistic and acoustic data on recorded music from 1967 to 2017, we search for trends in the evolution of musical diversity in 125,340 albums. We find that temporal patterns of diversity differ for stylistic and acoustic data. We also find that the patterns differ dramatically by genre. Some genres, such as blues, jazz, and pop-rock, decrease in diversity over time; most other genres increase in diversity. The causes of these different trends present a puzzle for future research. We also find different patterns for recordings that made the Billboard 200 charts compared to all recordings, suggesting an association between selection processes driven by consumer popularity and diversity. Moreover, associations of diversity and industry structure found in prior research do not hold when we analyze data beyond the smaller sample of the more popular recordings found in Billboard. These findings have implications for many prior studies based exclusively on best-selling recordings