Semiparametric Estimation

Semiparametric estimation methods are used to obtain estimators of the parameters of interest — typically the coefficients of an underlying regression function — in an econometric model, without a complete parametric specification of the conditional distribution of the dependent variable given the explanatory variables (regressors). A structural econometric model relates an observable dependent variable y to some observable regressors x; some unknown parameters β, and some unobservable ‘error term’ ε, through some functional y = g(x, β, ε); in this context, a semiparametric estimation problem does not restrict the distribution of ε (given the regressors) to belong to a parametric family determined by a finite number of unknown parameters, but instead imposes only broad restrictions on the distribution of e (for example, independence of ε and x, or symmetry of ε about zero given x) to obtain identification of β and construct consistent estimators of it.