Optimal fiscal policy in incomplete market business cycle economies

In this paper, we study how a government should set its fiscal instruments in order to provide insurance to individuals and deal with inequality. We quantitatively evaluate the role of public debt and its interaction with progressive income taxation. To guide our assessment, we develop a DSGEmodelwithincomplete markets that embeds two empirical relevant features that have not been considered by the literature: cyclical idiosyncratic risk and the extensive margin of labor supply. We calibrate the model to beconsistent withthemicroandmacroevidencefortheUSeconomy. We study the importance of time-varying idiosyncratic risk and labor supply elasticity in determining optimal policies by considering two nested versions of the model that shut down one feature at a time. We find that considering both ingredients together significantly increases the optimal debt to output ratio. In addition, we show that the model generates a positive relationship between public debt and income tax progressivity, consistent to what is observed in the data.