Theory And Application Of Assessing The Impact Of Policy Heterogeneity: Policy Depth, Breadth And Marginal Impac

More and more economic researchers pay attention to accurately identifying the causal relationship between policy implementation and individual performance through causal inference,and evaluating the real impact of a policy.Policy evaluation and causal inference are becoming more and more important in economic research.From national policy to micro individual decision-making such as enterprises,families and individuals,many problems can be transformed into policy evaluation.In order to accurately evaluate the impact of a policy,we must first solve the endogenous problem of policy implementation,that is,there is a correlation between policy implementation and unobservable factors affecting individual performance.Researchers usually overcome the potential endogenous problems by means of Instrumental Variables,Difference-in-Differences and Regression Discontinuity Design based on natural experiments or quasi-experiments.However,the prevalence of individual heterogeneity makes the impact of a policy on different individuals different or even completely opposite.If there is significant heterogeneity in policies,but researchers only focus on the average effect of a policy,it is not conducive to a complete assessment of the real impact of policies.However,only taking the average impact of a policy as the basis for policy implementation and reform may lead to misjudgment of the policy and damage social welfare.Therefore,policy evaluation needs to take into account both endogeneity and heterogeneity.In order to comprehensively and accurately assess the impact of policies on social welfare,we must pay attention to the distribution effect or heterogeneous impact of policies.This paper points out for the first time that the heterogeneous impact of policy can be analyzed from three perspectives:Policy depth,policy breadth and marginal impact of a policy.Policy depth refers to the degree of influence of a policy on individuals;The policy breadth refers to the possibility that the policy has a positive（or negative）impact,which can be used to reflect the universality and inclusiveness of the policy impact;The marginal impact of a policy refers to the impact of fine-tuning the intensity of policy implementation,which can be used to reflect the marginal impact of policy intensity adjustment.The existing research mainly focuses on the depth of a policy,and this paper has made some meaningful expansion on how to evaluate the breadth and marginal impact of a policy.Among the cross-sectional data,there are two model frameworks widely used to evaluate the heterogeneity impact of a policy.One is the instrumental variable quantile regression model proposed by Chernozhukov and Hansen（2005,2006,2013）.Chernozhukov and Hansen（2005）defined the quantile treatment effect from different quantiles of unobservable in the potential dependent variable equation,and its core identification condition is rank similarity;The second is the individual selection model proposed by Heckman and Vytlacil（2001,2005）and Carneiro et al（2011）.Heckman and Vytlacil（2005）defined the marginal treatment effect from different quantiles of unobservable in the selection equation,and its core identification condition is the separability restriction on the selection equation.Based on instrumental variable quantile regression model,this paper proposes Outcome Conditioned Quantile Treatment Effect（OCQTE）and Proportion of Gainers（POG）to reflect the policy depth and policy breadth.The outcome conditioned quantile treatment effect defined as ocqte(y_τ0,y_τ1)=E[Y₁-Y₀|y_τ0≤Y<y_τ1],which means the size of policy effect of on individuals between the τ₀,τ₁ quantiles of Y,and can be used to reflect the policy depth.The proportion of gainers defined as pog(y_τ0,y_τ1,c)=Pr(Y₁-Y₀≥c|y_τ0≤Y<y_τ1),which means the proportion individuals between the τ₀,τ₁ quantiles of Y,whose benefit from policy bigger than c,and can be used to reflect the policy breadth.The outcome conditioned quantile treatment effect and the proportion of gainers define the heterogeneous impact of a policy through observable variable Y,which is convenient for researchers to accurately locate the target group.The identification of quantile treatment effect is equivalent to the identification of the marginal distribution of potential dependent variables,while the identification of outcome conditioned quantile treatment effect and the proportion of gainers need to identify the joint distribution of potential dependent variables.Under the assumption of rank invariance,this paper identifies the joint distribution of potential dependent variables and these parameters.Based on Chernozhukov and Hansen（2006）and Wüthrich（2019）,this paper proposes two estimation methods of target parameters respectively,and explains the feasibility and small sample performance of the estimation method through numerical simulation.In addition,based on Athey and Imbens（2006）,this paper discusses how to use the data structure of Difference-in-Differences to identify the joint distribution of potential dependent variables without instrumental variables.Generally speaking,it is difficult for us to observe the change of policy implementation intensity,so it is impossible to identify and estimate the marginal impact of policy.However,under some assumptions,this paper connects the marginal impact of a policy with the marginal treatment effect of micro individuals,and put forward the parameters of Marginal Intensity Effect（MIE）of a policy.Taking the China’s enrollment expansion of colleges and universities in 1999 as an example,the intensity of the enrollment expansion policy is the enrollment number and enrollment rate.Under the assumption of constant local equilibrium,the marginal impact of enrollment expansion is the rate of higher education return of individuals locating on the admission boundary.Then we can connect the enrollment expansion policy at the macro level with the heterogeneous rate of higher education return at the micro level,and then indirectly identify and estimate the marginal impact of the enrollment expansion policy.For the New Rural Pension Scheme（NRPS）with the basic policy purpose of"ensuring basic and wide coverage",we should not only pay attention to its size on the welfare of rural residents,but also pay attention to whether it is inclusive,that is,whether it benefits the vast majority of rural residents.Therefore,we must pay attention to the depth and breadth of the new rural insurance policy at the same time.Based on the rural data in the national baseline survey conducted by CHARLS from 2011 to 2012,this paper makes an in-depth study with the help of the quantile processing effect of dependent variables and the proportion of policy benefits.Although in the average sense,the impact of the NSPR on rural residents’family income,consumption and labor supply is not significant.However,this study found that the new rural insurance has a heterogeneous impact on the family income,consumption and labor supply of the rural middle-aged and elderly in China.The specific manifestations are as follows:i)the NSPR has a general role in promoting the family income of low-income and middle families.For families with an annual income of 1090 yuan～23600 yuan,the income increasing role of the new rural insurance is 500～1600 yuan.ii)The NSPR has a general promoting effect on the family consumption of rural residents,and the higher the consumption,the greater the promoting effect on the family.For the family with an annual consumption of more than 4295 yuan,the consumption promoting effect of the NSPR exceeds 1000 yuan.iii)The impact of the NSPR on the labor supply of rural residents is not consistent.The NRPS restrains the labor supply of low labor supply groups,but increases labor supply of high labor supply groups.In addition,with the help of the heterogeneous impact of the new rural insurance on labor supply,this paper explains why the promotion effect of the new rural insurance policy on family income and consumption is greater than the benchmark payment amount of pension（660 yuan/year）.This paper finds that the new rural insurance promotes the high labor supply individuals to increase labor supply,and therefore promotes the improvement of family income and consumptionThe enrollment expansion of colleges and universities in 1999 is a landmark event in the development of China’s higher education,which has a far-reaching impact on the human capital accumulation and the higher education return.Based on the individual decision-making model under incomplete information,this paper expounds the law of diminishing marginal effect of enrollment expansion policy on human capital accumulation from the perspective of heterogeneous rate of higher education return.This paper studies the marginal impact of enrollment expansion policy according to the marginal intensity effect parameter of policy,and explains the reliability of the empirical results by testing the core identification hypothesis and robustness analysis.The empirical study found that:i)On average,the expansion of university enrollment has a positive impact on improving the social human capital accumulation.The average rate of higher education return of individuals who can enter colleges and universities due to the enrollment expansion policy is 71%;ii)The rate of higher education return varies from person to person,and the contribution of college to the accumulation of some individual human capital is not as good as the work of corresponding years;iii)Due to the existence of individual heterogeneity,the marginal effect of enrollment expansion policy decreases with the increase of admission rate.Under the admission rate of 55.5%,the marginal effect of enrollment expansion policy is 4.43%and is not significant.This paper is helpful to comprehensively and accurately evaluate the impact of college enrollment expansion in 1999 on China’s human capital accumulation,and has some enlightenment for the current policy design of graduate enrollment expansion.Therefore,the main contributions of this paper are as follows:i)Based on Rubin latent variable model,this paper discusses the specific meaning of policy depth,policy breadth and policy marginal impact;ii)Based on the instrumental variables quantile regression model,it is proposed to reflect the depth and breadth of policy respectively-outcome conditioned quantile treatment effect and the proportion of gainers;iii)Through the above parameters,this paper studies the heterogeneous impact of the New Rural Pension Scheme on rural residents’income,consumption and labor supply;iv)Based on the individual selection model,this paper links the marginal impact of enrollment expansion policy with the heterogeneous rate of individual higher education return,and expounds and verifies the law of diminishing marginal effect of enrollment expansion policy on human capital accumulation with the help of micro survey data.