Amplification and Asymmetric Effects Without Collateral Constraint: Online Appendix

In this online appendix, beside the additional derivations and analysis for the main paper (Appendices E-J), we present their variants (K, L and M) of the models presented in the main paper. The first variants are models with larger shares of land in the production function or with general CES production functions which generate larger amplification effects. The second variant is a continuous time version of the benchmark model. The Markov equilibrium in this model is similar to the Markov equilibria in He and Krishnamurthy (2013) and Brunnermeier and Sannikov (2014). Thus, we can use the algorithms in their papers to solve for the Markov equilibrium in our model. The last variant of the models is in discrete time, and we allow the households to produce using an inefficient technology. In this model, the households will start producing when the wealth of the entrepreneurs reaches its lower bound.