Idiosyncratic Risk and the Business Cycle: A Likelihood Perspective

This paper asks whether uninsurable idiosyncratic income risk affects aggregate consumption over the business cycle. I explore this question using an incomplete markets business cycle model in which the extent of idiosyncratic risk varies over the business cycle in line with recent empirical findings. I present a method for estimating general equilibrium incomplete markets models with rich household heterogeneity using likelihood-based methods. I use the estimated model to construct a counterfactual series for aggregate consumption under complete markets. The results show that time-varying idiosyncratic risk has substantial effects on the dynamics of aggregate consumption. Had markets been complete, the variance of aggregate consumption growth would have been up to 32% lower and the drop in consumption in the Great Recession up to 1.9 percentage points smaller. ∗[email protected]. I would like to thank Susanto Basu, Simon Gilchrist, Jonathan Parker, Zhongjun Qu, and Ricardo Reis for helpful discussions and Carlos Ramos for excellent research assistance. I am also grateful to seminar participants at PSE/IMF Workshop on Advances in Numerical Methods, BU/BC Greenline Macro Meeting, FRB Chicago, MIT, Brown, ASSA 2014, Columbia, UCL, and the Philadelphia Workshop on Macroeconomics.