Yes, I saw that \theta_t is a first order autoregressive model with mean unity in the paper. In the equation defining \theta_t, \nu_t is an exogenous random variable, the innovation of TFP. They discuss the behaviour of the model with respect to another shock (wealth shock), but I have the impression that when they simulate the model to compare simulated ACF and sample ACF they only consider the productivity shock. Whatever, \nu_t is not a measurement error, \nu_t is the source of aggregate randomness in the model.

I still do not understand if you want to estimate \rho jointly with the modelâs deep parameters, or just want to estimate the TFP stochastic processâŠ If you only seek to estimate \rho independently of the rest of the model, and plug the estimated value \hat \rho in the model, you only have to estimate the AR(1) model with TFP data. You do not need Dynare for that, the OLS estimator is:

\hat\rho = \frac{\sum_{t=2}^T (y_t-\bar y)(y_{t-1}-\bar y)}{\sum_{t=2}^T (y_{t-1}-\bar y)^2}

But if you want to estimate \rho jointly with the rest of the model (which makes sense since the value of \rho does not only affect the dynamic of productivity, but other elasticities in the core model through the expectations), then you need to compute the likelihood of the model (or posterior density) and Dynare may help here.

A latent variable is an unobserved variable. When you estimate a DSGE model, you only observe a subset of the endogenous variables (for instance output, consumption, inflation, âŠ) but a lot of variables are not observed (for instance physical capital stock, productivity, preference shock, âŠ). To evaluate the likelihood of the model a Kalman filter is used, which basically estimate the latent variables with the available data.

Best,

StĂ©phane.