We present a multivariate alternative to the voxel-based morphometry (VBM) approach called source-based morphometry (SBM), to study gray matter differences between patients and healthy controls. The SBM approach begins with the same preprocessing procedures as VBM. Next, independent component analysis is used to identify naturally grouping, maximally independent sources. Finally, statistical analyses are used to determine the significant sources and their relationship to other variables. The identified “source networks,” groups of spatially distinct regions with common covariation among subjects, provide information about localization of gray matter changes and their variation among individuals. In this study, we first compared VBM and SBM via a simulation and then applied both methods to real data obtained from 120 chronic schizophrenia patients and 120 healthy controls. SBM identified five gray matter sources as significantly associated with schizophrenia. These included sources in the bilateral temporal lobes, thalamus, basal ganglia, parietal lobe, and frontotemporal regions. None of these showed an effect of sex. Two sources in the bilateral temporal and parietal lobes showed age-related reductions. The most significant source of schizophrenia-related gray matter changes identified by SBM occurred in the bilateral temporal lobe, while the most significant change found by VBM occurred in the thalamus. The SBM approach found changes not identified by VBM in basal ganglia, parietal, and occipital lobe. These findings show that SBM is a multivariate alternative to VBM, with wide applicability to studying changes in brain structure.

JEL classification: C13 C14 G10 G12 Keywords:Variance risk premium Time-varying jump tails Market sentiment and fears Return predictability a b s t r a c tThe variance risk premium, defined as the difference between the actual and risk-neutral expectations of the forward aggregate market variation, helps predict future market returns. Relying on a new essentially model-free estimation procedure, we show that much of this predictability may be attributed to time variation in the part of the variance risk premium associated with the special compensation demanded by investors for bearing jump tail risk, consistent with the idea that market fears play an important role in understanding the return predictability.

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Recent empirical evidence suggests that the variance risk premium predicts aggregate stock market returns. We demonstrate that statistical finite sample biases cannot "explain" this apparent predictability. Further corroborating the existing evidence of the United States, we show that country-specific regressions for France, Germany, Japan, Switzerland, the Netherlands, Belgium, and the United Kingdom result in quite similar patterns. Defining a "global" variance risk premium, we uncover even stronger predictability and almost identical cross-country patterns through the use of panel regressions.