Household Heterogeneity and the Value of Government Spending Multiplier: an Analytical Characterization

This paper provides an analytical formula for the government spending multiplier in economy populated with heterogeneous households that face uninsured idiosyncratic risk. To derive this expression I use the canonical Bewley-Huggett-Aiyagari model extended to capture frictional product market. In my analysis I relax several assumptions that were made in the literature to obtain closed-form solutions in heterogeneous agent models such as: partial equilibrium (e.g., Auclert (2017)), extreme illiquidity (e.g., Krusell et al. (2011)) and constant real interest rates (e.g., Auclert et al. (2018)). The resulting formula for the multiplier is decomposed into interpretable, model-based channels. Calibrated model is used to estimate their magnitude under alternative fiscal and monetary policy rules. Quantitative exploration indicates that household heterogeneity plays a crucial role in the propagation of government expenditures shocks.