Estimation with data in levels

Estimation
1

Dear all,

I’m trying to estimate an RBC model with stochastic growth (labour augmenting technology) as in the “Guide to Specifying Observation Equations” where the model is stationarized. However, I want to use the observed variables in (log) levels rather than in growth rates for the estimation. Is that possible in Dynare? Or is it only possible with deterministic trends? If so, can you suggest some reference or code to look at?

I have read several posts in here about this, but I’m still quite confused about whether this is Dynare constraint or is a broader situation with DSGE modelling.

Thanks all in advance.

2

It’s a general issue related to perturbation techniques and modeling. Your DSGE model is approximated around a steady state that needs to exist. So you need to work with a detrended model. Now the data itself is trending. If you want to link the stationary model and the trending data, you need to take a stand on what gives rise to the trend in the data, i.e. you need to specify the data generating process. It either features a deterministic or stochastic trend.

3

Professor, Thank you for your answer.

In many of the models replicated in your website with stochastic trends (Aguiar&Gopinath, GPU, Smets&Wouters) the estimation is in growth rates. Is it possible to estimate those models with the data in (log) levels in Dynare?

4

No, but there is also no reason to use the level. The only difference between levels and growth rates is that the initial condition is not used.

5

@jpfeifer, hello! I want to try to estimate a model without log-linearization, just linearized in levels (nonlinear model without exp(x)). So the model variable y represents level deviations from steady state. You mentioned in the Guide to Specifying Observation Equation that typically the HP filter is applied to log(GDP per capita) to get a stationary series to make scale invariant. But since my model is in levels, should I instead detrend just GDP per capita in levels (without taking logs) and demeaned to match the model? And my observation equations would be yobs=y-steady_state(y).

6

You could theoretically do that, but it would imply that you really need the model to match the level and therefore also the units of the actual data. That is the reason why people always use the log of the data.