A Bayesian dynamic stochastic general equilibrium model of stock market bubbles and business cycles

Abstract

This online material contains six appendices to the paper. Appendix A proves Propo-sition 1 in the paper. Appendix B derives the stationary equilibrium. Appendix C stud-ies the bubbly steady state. Appendix D provides the log-linearized equilibrium system around the bubbly steady state. Appendix E presents a table of business cycle moments. Appendix F presents a robustness analysis. Appendix A: Proof of Proposition 1 in the paper We use a conjecture and verification strategy to find the decision rules at the firm level. We first study the optimal investment problem by fixing the capacity utilization rate u j t . Using (14) and (16), we can write firm j's dynamic programming problem as v t ε j t K j t + b ttτ ε j t − v Lt ε j t L j t = max I j t L j t+1 u j t R t K j t − P t I j t − L j t + L j t+1 R f t (A.1) + Q t 1 − δ j t K j t + ε j t I j t + B ttτ − Q Lt L j t+1 subject to the investment constraint 0 ≤ P t I j t ≤ u j t R t K j t − L j t + L j t+1 R f t + η t K j t (A.2)