This is material that is pertinent for computing the Ramsey-optimal equilibrium in environments when the government’s budget constraint can be ignored. This possibility reflects the assumption (sometimes implicit!) that the government has access to lump sum taxes. If the government did not have access to lump sum taxes, then in contemplating a given candidate equilibrium in the search for the optimum, one would have to take into account whatever has to be done to the government’s distortionary taxes (on this, see). This in turn requires explicitly taking into account the government’s budget constraint and the details of the tax system. With lump sum taxes, it is enough to simply include the resource constraint in the analysis.

The following notes describe the equilibrium conditions for each of a series of monetary models, ranging from the simplest possible one to a model with Calvo-style wage and price frictions, habit in preferences, investment adjustment costs and financial frictions.

The following software has the equilibrium conditions coded up in Dynare format for each model in the notes. In addition, the code is set up so that the Ramsey-optimal equilibrium can be computed for each model economy. The code for this is taken from Andrew Levin, Lopez-Salido, J.D., 2004. "Optimal Monetary Policy with Endogenous Capital Accumulation", manuscript, Federal Reserve Board, and Andrew Levin, Onatski, A., Williams, J., Williams, N., 2005. "Monetary Policy under Uncertainty in Microfounded Macroeconometric Models." In: NBER Macroeconomics Annual 2005, Gertler, M., Rogoff, K., eds. Cambridge, MA: MIT Press.

The software in the above zip file is organized into a particular directory structure. When extracting the code, be sure to preserve that directory structure. The different directories correspond to different models and experiments.