Research And Application Of Breakpoint Regression Design Based On Local Polynomial

In the theoretical research and practical application of regression discontinuity design,non-parametric methods have been favored by the public.Local linear estimate is a standard method for estimating treatment effects in regression discontinuity design.However,for high oscillation functions,local linear estimate is not necessarily the best.Based on the research and application of regression discontinuity design based on local polynomial,this paper systematically reviews the development process of regression discontinuity design.By reviewing the existing theories,it concludes that there are two key issues:(1)the estimation of variance and bias in bandwidth selection and(2)the selection of polynomial order.For question(1),obtaining a better derivative estimation at the boundary point is an intuitive idea to estimate the optimal bandwidth.However,research has shown that for higher-order derivative estimates at the boundary point,the variance will increase as the order increases.For practical problems,it is meaningful to select the optimal bandwidth and the corresponding treatment effect estimate from each order polynomial estimates.For issue(2),since the prior information and error distribution of the regression function in an actual scenario are unknown,we focus on large data set(n = 4000)and small data set(n = 200)in simulation studies.For the large data set,the treatment effect estimates with p=1,2,3,4 perform well,especially the local second-order polynomial estimate has a minimum standard error.For the small data set,the local linear estimate has a minimum standard error.Simulation research shows that the estimate results of each order are likely to reach the optimal result of different design.Therefore,in the application,the robust way is listing the estimate results of each order local polynomial.In real application,we study the winter heating policy of north city in China using regression discontinuity design.From the study results,we find that AQI,SO2 and PM2.5 all increases significantly during the heating period for some northern cities(the large data set)and a specific city-Beijing(the small data set).For the small data set,the treatment effect estimate's with minimum standard error of AQI,SO2 and PM2.5 are 23.064,4.4273 and 48.508.For the large data set,the treatment effect estimate's are 16.92,1.9837 and 18.714.