A conditionally heteroskedastic binary choice model for macro-financial time series

The macro-financial data are characterized by heteroskedasticity which leads to inconsistent estimates and inference from binary choice models (BCMs). To address this problem, we propose a generalized autoregressive conditionally heteroskedastic-type adjustment for the conditional variance of model errors. A data augmentation type algorithm is developed for estimation while Lagrange multiplier (LM)-type tests are derived for testing ARCH effects in BCMs. Simulation results show that the proposed model leads to bias reduction in estimates, while the expected Information matrix-based LM test exhibits smaller size distortions and higher power properties. Empirically, predictions of the US business and financial cycles reaffirm the effectiveness of the extended model.