DGSE model keeping linear parameters after log-linearisation

Hello! I’m using the model from the paper “House prices, consumption, and monetary policy: a Financial accelerator approach” (Aoki et al. (2004)) and I have some question regarding the log-linearized model.
It seems that the authors keep some parameters that should have been removed after the log-linearisation.

For example, the equation (A-13) in the log-linearized model is: \hat{w_t} = \hat{C_t} + \xi \hat{L_t}. Before the log-linearisation, the autors had: w_t(1-L_t) = \xi C_t (equation (15)). \xi comes from the log-utility function: \log(C_t) + \xi \log(1-L_t). After doing the first orders conditions and log-linearising, the parameter \xi should be removed because it is linear to the other variables. Why is the parameter still there? It happens the same with other equations in the log-linearized model.

I appreciate your help. Thank you so much for your time :slight_smile:

This very much looks like a mistake in the linearized equation. It may simply be a typo or even by present in the final model used. Without the codes, it is impossible to tell.

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Thank you for the reply! I wrote the code in Dynare, and it works fine with \xi and poorly without it. Is it common to keep important parameters after the log-linearization? I thought that maybe it’s a common practice because it gives more economical interpretation and the log-linearized model adapts better to the data.

I don’t understand that point. Log-linearization is a mathematical transformation that preserves equalities. You don’t get to choose which parts to keep. Parameters as exponents becomes multiplicative prefactors. Multiplicative prefactors in fully multiplicative equations drop out.

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I’m trying to make sense of the equations. I find it quite weird to find a mistake in a well cited paper.

Unfortunately, it’s very common. See


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