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Supplementary material for Laureys, Meeks, and Wanengkirtyo: “Optimal simple objectives for monetary policy when banks matter”
Appendix A. Model
This section contains a full description of the model and derivations of its equilibrium conditions.
Appendix B. Complete Set of Equilibrium Conditions
Appendix C. Steady State
Appendix D. The Linearized Model
The decentralized allocation:38
To close the model, specify monetary policy.
Appendix E. Estimation
We plot the observables used for the estimation in Figure E.1. Additionally, we also plot the one-step ahead forecasts, as implied by the model under the posterior mode calibration used in the optimal policy exercises. Effectively, these are the fitted values of the model. The model matches the real observables fairly well. Note that this exercise would almost always lead to a ‘poor’ fit of the variables with a data-rich strategy. As we use measurement errors to allow data-rich estimation, but following the literature, these shocks are set to be i.i.d. However, in reality, the wedge between the data-rich observables (for example, between GDP deflator and CPI inflation) tends to be fairly persistent. A one-step ahead forecast would not contain this persistence. Thus, almost by construction, the data-rich observables like inflation and spreads do not have a fit as close as the other variables.
The impulse responses to a one standard deviation shock (of the estimated variances) are in Figures E.2 and E.3. The structural parameters and the forcing processes are also calibrated to their posterior mode estimates. Overall, the model behaves as expected to categories of shocks. A negative TFP shock reduces real activity, and also raises inflation sharply as it raises marginal costs. There is also a rise in credit spreads as net worth of banks fall when firms are less productive and consequently demand less capital, which amplifies the initial adverse shock somewhat. A one standard deviation TFP shock also appears to have a quantitatively large real effect relative to other shocks, as the variance decompositions in Table E.1 highlight that TFP shocks account for a sizeable proportion of the fluctuations in output and consumption. Mark-up shocks also have expected effects as cost-push shocks—increases inflation and dampens real activity.