Hi, I am trying to estimate ECB’s New Area-Wide Model (NAWM) of Christoffel, Coenen and Warne. In their paper, authors have included a section with the log-linearized model but I am trying to implement the model using the loglinear option in the estimation command instead of using the log-linearized equations but I am having problems figuring out how to include the wage equations. In their log-linearized version, authors note that they use a wage Phillips curve in addition to the equations of the model, but the first order condition characterising the households’ optimal wage setting decision includes an infinite sum (equation 14 in the paper).

In general, there are only two ways: log-linearize manually so that the infinite sum vanishes and enter the FOC in its linearized finite version (the way e.g. Gali (2008) gets rid of the infinite sum in the firm’s Calvo price-setting) or find a recursive representation of the infinite sum so that the non-linear version also has a finite representation that can be entered (e.g. the way
Stephanie Schmitt-Grohé and Martín Uribe, Optimal Simple and Implementable Monetary and Fiscal Rules: Expanded Version, NBER Working Paper No. 12402, July 2006 solved the firm’s Calvo problem).

If you are not able to find a recursive finite representation, you cannot enter the full nonlinear equation to Dynare.