Estimation Of Continuous Treatment Effect Based On Approximately Entropy Balancing Method

Observational data has the advantages of low cost,large sample size,and followup tracking.In the fields of public health,sociology,and psychology,more and more scholars have conducted research based on observational data in recent years.The difficulty in the study of observational data lies in the presence of confounding variables,which can bias the estimated treatment effect.Recently,some researchers have proposed the Entropy Balancing method to estimate the continuous treatment effect.However,using the entropy balance method may encounter such a dilemma:a large number of precise balancing conditions will lead to a reduction in the effective sample size,which will ultimately affect the effect of estimating the continuous treatment effect.Therefore,this paper proposes the Approximately Entropy Balancing method that uses approximately balancing conditions instead of precise balancing conditions,and sets the upper limit of the constraint condition imbalance as the parameter δ.In short,the Approximately Entropy Balancing method relaxes the constraint conditions to increase the effective sample size and improve the estimate.The simulation part compares the performance of the Approximately Entropy Balancing method,the Entropy Balancing method,and the Covariate Balancing Generalized Propensity Score method in two situations.The simulation results show that(1)After relaxing the constraints,the Approximately Entropy Balancing method still has a good performance in the balance of confounding variables;(2)Compared with the other two methods,the Approximately Entropy Balancing method has a higher effective sample size;(3)Compared with the other two methods,the Approximately Entropy Balancing method has the smallest mean absolute percentage error in estimating continuous treatment effects.The empirical part is based on the China Health and Retirement Longitudinal Study waves 2015 and 2018.The Entropy Approximate Balancing method is used to estimate the effect of intergenerational-care duration on the depression levels of middle-aged and elderly people.The results show that when the duration of intergenerational care is short,it will not have a significant impact on the depression level of middle-aged and elderly people;when the duration of intergenerational care exceeds a certain range,intergenerational care will increase the depression level of middle-aged and elderly people.