Convert DSGE paper to structural econometrics, anything to be noted？

Question

I'm intent to bring some insights of a DSGE paper to a structural econometric model. The paper is Liu, Wang and Zha's 2013 Econometrica paper on land collateral channel. Now I have some good datasets containing firm's land holding information, so I want to "estimate" than "assume and simulate". However, my coauthors and I are largely macro guy and know only a little about structural estimation.

(1). We are focusing on firm's investment decision (purchasing land or real estate asset) and borrow behavior. In Liu et al, they also modeled the household sector. So for our purpose , we can safely ignore the household sector, and treat (land) price exogenous ,right?

(2). The macro paper normally contains dozen of shocks, some of which we are interested (like the "collateral shocks"), some we are not (habit persistence). Then we just treat those we are interested in as parameters to be estimated , and others as unobservable impact?

Personally, I don't quite believe the DSGE model which specifies dozens of shocks . I want to "bring some insights" and replicate from the LWZ paper. Most DSGE studies struggle to meet the general equilibrium condition, which , in my opinion, is one of their weakness. The price are too complicated and hard to fully capture, so if you are concerning something else, why just keep it exogenous and put other more realistic stuff.

Answer 1

There's no correct method to do this. DSGE guys will estimate the model by doing something like this: plugging in priors for their parameters and then running an optimization that minimizes the distance between model and data moments while maximizing the log likelihood from the priors. The data moments for them will be well known values of variances and covariance of the deviations of c, y, i, p from trend.

Structural estimation guys will do any number of things: a) take a model predicted relationship, like a investment to q relationship, $i=b\cdot f(q)$ where b is a parameter, estimated the relationship and infer the value of b; b) general method of moments or simulated method of moments or indirect inference: use a characterization of the data into moments or auxiliary statistics, and then find parameter values such that the model (analytically or with simulations) replicates the values of these moments or auxiliary statistics.

Which moments / statistics to use? Who knows! Follow tradition!

Which macro variances or covariances? Who knows! Follow tradition! (plus the values of these maybe change dramatically depending on how and when you calculate them....)