The results of the foregoing chapters are intended to provide empirical researchers with an appreciation of the dangers of taking one's explanatory models too literally, and with tools for coping with the necessity of using models, which by their very nature as human artifacts, may be misspecified to greater or lesser extent.

Chapter 2 of this book motivates use of the method of maximum likelihood in the presence of misspecification and establishes the existence of the quasi-maximum likelihood estimator. We see in Chapter 3 how misspecification can cause quasi-maximum likelihood estimators to fail to be consistent for parameters of interest, but that the QMLE θ generally retains an information theoretic interpretation: it is consistent for a parameter vector θ* that minimizes Kullback-Leibler information. As such,θ depends generally on the specification generating ,θ as well as on the data generation process. In Chapters 4 and 5 we see that in certain special cases, specification correct to a limited extent can allow consistent estimation of parameters of interest. For example, use of exponential family quasi-likelihood functions yields consistent estimators for the parameters of a correctly specified model of the conditional expectation of the dependent variables given the explanatory variables.