Nonparametric Instrumental Variables Method And Applications

The instrumental variables method is an important method in econometrics which is used to solve the endogeneity problem of explanatory variables.Instrumental variables method needs to find the variables which are related to the endogenous explanatory variables,and the variables are independent of error,that is,instrumental variables.This method is of great value in theory and application,in theory,it establishes a set of methods,in application,it solves a lot of problems in economic,educational,medical and other fields.In practical application,we use instrumental variables method with parameters,we need to set models.But the relationship between independent variables and dependent variables is often complex,we do not know the exact relationship between them.So we need a way to approximate this relationship,nonparametric instrumental variables method is one of them,nonparametric instrumental variable method uses a series of orthonormal basis to approximate relationship between independent variables and endogenous dependent variables,nonparametric instrumental variables method has good large sample properties and easy to compute.The relationship between logarithm of average daily passenger volume and log fare examples reveal the same points and differences between the parametric instrumental variables method and the nonparametric instrumental variables method.First,we find that logarithmic fare is an endogenous explanatory variable,then we find the instrumental variable,which is the market share of the biggest carrier.When we use ordinary least squares method and two stage least squares method,we find that we must control logarithm of distance and the logarithm of the square of the distance.The logarithm of distance and logarithm of fare is relevant,which implies that there is a nonlinear relationship between the logarithm of the average daily passenger volume and logarithm of fare,finally we use nonparametric instrumental variables method to obtain the nonlinear relationship.At the end of the paper,we discuss the prospect of nonparametric instrumental variables method.Since the nonparametric instrumental variables method has the characteristics that lager the sample size is,the more accurate the model fitting we obtained.So nonparametric instrumental variables method is a way of unlimited potential.