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The generating mechanism of these latent shocks is a censored regression model, where linear combinations of lagged explanatory variables lead to positive shocks, while otherwise shocks are equal to zero. We apply this censored latent effects autoregression to monthly US unemployment, where the positive shocks are found to be predictable using various leading indicators. The model fits the data well and its out\u2010of\u2010sample forecasts appear to improve on those from alternative models. 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