We study an estimation approach that is robust to misspecifications of the dynamic economic model being estimated. Specifically, the approach allows researchers to focus on a particular sub-problem or sub-period of the optimizing agent’s finite horizon and thus alleviates the need for assumptions regarding expectation formation about the (distant) future. This is accomplished by approximating a pseudo terminal period policy- or value function non-parametrically rather than fully specifying the remaining economic environment anticipated by agents until the terminal period. We illustrate through two Monte Carlo experiments the superior robustness of the approximate estimator compared to a standard full solution estimator.