Dear Professor Pfeifer,
I hope you are doing well. I do have a question regarding the measurement equations used during the estimation process. I know that measurement equations are for matching the data with a model. However, I am confused by the use of exogenous variables in the measurement equations.
For example: dyt = y(t)-y(t-1)+trend, for output growth (in Smets and Wouters (2007) and many papers). I understand this equation.
Another example: dyt= y(t)-y(t-1)+z(t)+ctrend (in FRBNY DSGE model paper by Del Negro et al (2013). I got confused here. I get entirely different time-series of smoothed output (y_t) when I use the productivity term in the measurement equation.
My concern is that while making a model economy, we believe that there are different types of shocks affecting the economic variables. However, the second type of measurement equation says that output growth is primarily driven by productivity shock only. Is the assumption in the measurement equation not in contrast with the model? Or am I wrong in understanding the measurement equation?
I wonder if you could help me understand this issue?