At the beginning, please allow me to provide some background information about the DSGE and SVAR models regarding expectations.
So DSGE is the workhorse model for macroeconomic analysis. It entirely stems from economic theories. Each structural equation represents the decision rule for one or a group of economic agents. Normally, we have many more structural parameters than the number of equations. We can either calibrate those parameters based on traditions in the literature or estimate them using maximum likelihood. For the estimation, the common practice is to match the hypothetical reaction of DSGE to economic shocks with empirical evidence generated by some data-driven models, such as SVAR. The impulse responses produced by SVAR provide meaningful guidance to the estimation of DSGE.
But here comes the problem: the SVAR is inherently backward-looking, while DSGE is typically embedded with rational expectations. Rational expectations become the unbridgeable gap between the two most popular models in macroeconomics.
The efforts to fill this gap have been relentless, but the majority of them show interest in another type of expectation — news-driven expectations which are formed on exogenous information. Practitioners can either include forward-looking variables as an information block or recognize noise shock with future information. Less endeavor has been made on the rational expectation side.