This paper introduces an estimator for dynamic macroeconomic models where possibly the dynamics and the variables described therein are incomplete representations of a larger, unknown macroeconomic system. We call this estimator projection minimum distance (PMD) and show that it is consistent and asymptotically normal. Many times, PMD can provide consistent estimates of structural parameters even when the dynamics of the macroeconomic model are insufficient to account for the serial correlation of the data or correlation with information omitted from the model. PMD provides an overall specification chi-squared test based on the distance between the impulse responses of the model and their semi-parametric estimates from the data. PMD only requires two, simple, least-squares steps and can be generalized to more complex, nonlinear environments.