This dissertation develops efficient semiparametric estimation of parameters and expectations in dynamic nonlinear systems and analyzes the role of environmental factors in productivity growth accounting. The first essay considers the estimation of a general class of dynamic nonlinear systems. The semiparametric efficiency bound and efficient score are established for the problems. Using an M-estimator based on the efficient score, the feasible form of the semiparametric efficient estimators is worked out for several explicit assumptions regarding the degree of dependence between the predetermined variables and the disturbances of the model. Using this result, the second essay develops semiparametric estimation of the expectation of known functions of observable variables and unknown parameters in the class of dynamic nonlinear models. The semiparametric efficiency bound for this problem is established and an estimator that achieves the bound is worked out for two explicit assumptions. For the assumption of independence, the residual-based predictors proposed by Brown and Mariano (1989) are shown to be semiparametric efficient. Under unconditional mean zero assumption, I proposed an improved heteroskedastic autocorrelation consistent estimator. The third essay explores the directional distance function method to analyze productivity growth. The method explicitly evaluates the role of undesirable outputs of the economy, such as carbon dioxide and other green-house gases, have on the frontier production process which we specify as a piecewise linear and convex boundary function. We decompose productivity growth into efficiency change (catching up) and technology change (innovation). We test the statistical significance of the estimates using recently developed bootstrap method. We also explore implications for growth of total factor productivity in the OECD and Asia economies.