In this talk, I will present a new general sufficient condition for the consistency of maximum likelihood estimator (MLE) for partially observed diffusions, which is stated explicitly via the stationary distribution of the fully observed system. This result is then applied to a model of market microstructure with latent (unobserved) price process, for which the estimation is performed using real market data for liquid NASDAQ stocks. In particular, we obtain the estimates of the price impact coefficient, as well as of the micro-level volatility and drift of the latent price process (the latter is responsible for the concavity of expected price impact of large meta-orders). Joint work with I. Cialenco and Y. Yin.