Program Evaluation,Treatment Effects And Semiparametric Models:Theory And Applications

The main topics studied in this thesis are policy evaluation,treatment effects and semiparametric models.This thesis consists of five chapters.The first chapter briefly introduces our work.In Chapter 2,we introduce a modification to the method proposed by Hsiao et al.(2012)and compare the performance of the synthetic control method,panel data approach and machine learning method(LASSO and elastic net).In Chapter 3,we show that the economic effect of the city-renaming reform is insignificant.Therefore,policymakers cannot win a“Promotion Tournament”by renaming cities.In finance research,one is frequently interested in estimating the effects of firm-specific financial or economic events on the values of the affected firms.With a small sample size,the test statistics of the traditional market model are no longer valid.In Chapter 4,we propose new inferential methods that do not depend on the sample size or other parametric restrictions.In addition,we provide an approach to identify and estimate the structural parameters of a.heteroscedastic censored regression model with a random coefficient dummy endogenous regressor in Chapter 5.In order to evaluate the treatment effects of policy interventions,social scientists usually face the challenge of estimating the counterfactuals in the absence of interventions.The intervention time series analysis,synthetic control method,panel data approach,and machine learning method are four common methods for evaluating policies when there is only one treated unit.Due to the shortcomings of the intervention time series analysis mentioned in Subsection 3.2,Chapter 2 mainly focuses on comparing the performance of the other three methods.The model selection strategy proposed by Hsiao et al.(2012)has two shortcomings.First,the number of control units must be less than the pre-treatment time periods(N<To).Second,the number of control units cannot be large,otherwise it is not feasible in the calculation.To address the first shortcoming,Gardeazabal and Vega-Bayo(2016)modify the method(referred to here as GV-AICC)such that j=1,…,T0-g,where g is a positive integer less than To.The GV-AICC method is only applicable to small N and To.For example,with N=71 and To=25 and allowing at least 10 degrees of freedom(i.e.,g=10),the GV-AICC method requires the AICC criterion to be used approximately 9.75 x 1014 times to select the best control units for y1t0,which is computationally infeasible.Further,to overcome the first drawback,Li and Bell(2017)divide the control units into m groups such that(m-1)To?N<mTo,and then use the AICC to select the best units in each group.For the same reason,the modified method proposed by Li and Bell(2017)is only applicable to small To.In Chapter 2,we modify the method such that we divide the N-1 control units into n groups,each group contains k control units(referred to here as the k-AICC),where k is a appropriate positive integer less than To-1.This modification not only makes the panel data approach suitable for a variety of situations regardless of the number of control units or pre-treatment time periods,but also allows us to select the best result from a wide range of results.The comparison between the panel data approach and synthetic control method in Gardeazabal and Vega-Bayo(2016)is not convincing because of the poor performance of the modification in Gardeazabal and Vega-Bayo(2016).Using our modification,we re-compare the performance of the synthetic control method,panel data approach and machine learning method in prediction.Under the factor model,we find that the performance of the synthetic control method and panel data approach is comparable.In the study of economics,we should choose between them based on the actual situation.The machine learning method is often used to test the robustness of the empirical results.In China,many cities want to rename themselves to promote economic growth.To explore the impact of city-renaming reform on economic growth,we compare the empirical performance of the synthetic control method,panel data approach and machine learning method(LASSO and elastic net)by the case of Xiangyang,Hubei Province,was renamed on December 9,2010.Based on the two selection criteria of prediction accuracy and interpretation of the model,the panel data approach is a better choice for GDP growth rate data.The panel data approach show that Xiangyang's real GDP growth rate rose by 1.43%after the cityrenaming reform,and this result is significant at the 1%level on the basis of the asymptotic distribution derived in Li and Bell(2017).However,further discussions show that the annual growth rate of the tertiary industry decreased by 1.59%,which contradicts the mechanism of the brand effect of the reform.If multiple policies occur simultaneously,none of the above mentioned methods can identify the effects of different policies.We want to know if the effect of the city-renaming reform is significant.However,the traditional large sample inferential techniques no longer work here.Following the placebo study by Abadie et al.(2010),we construct a distribution of the average treatment effects to determine whether the effect of the city-renaming reform is significant.The statistical inference we implemented in Chapter 3 shows that even if a city did not implement the city-renaming reform in 2010,the probability of obtaining an effect as large as Xiangyang's would be 25.9%.Therefore,the effect of the city-renaming reform is insignificant and other policy interventions—rather than the city-renaming reform—promote economic growth in Xiangyang.In other words,policymakers cannot win a "Promotion Tournament" by renaming cities.In the past,the standard method for measuring the effects of an economic event was estimating a market model.However,econometric methods that bring the idea of machine learning to the panel data setting for studying the impacts of events or policy interventions,such as the synthetic control method and panel data approach,and machine learning methods,such as LASSO and elastic net,can also be used to assess the financial impacts of corporate policy changes,especially if the sample is small.Small samples are quite common in the finance and accounting literature,especially when the firms affected by events are divided into subcategories based on certain criteria.With a small sample size,the test statistics of the traditional market model are no longer valid.In Chapter 4,we compare the forecasting accuracy of the market model,synthetic control method,panel data approach,LASSO and elastic net by examining the effects of stock name changes in the Chinese A-share market,and propose new inferential methods that do not depend on the sample size or other parametric restrictions.Finally,we use stock name changes as an example to illustrate the application of these inferential methods to event studies.Because of the treatment effects of policy interventions(unions,training,schooling,laws,and so on)are different across treated units,random coefficient models are often used to evaluate policies.In addition,censoring often appears in economic applications.For example,many observed economic variables,e.g.,hours worked,expenditure,wealth are censored from above or below due to non-negativity constraints or top coding.Censoring and the impact of interventions are differ across treated units come together is a common phenomena in applied micro-econometrics.Under parametric distributional assumptions,censored regression models with a random coefficient dummy regressor can be translated into censored models with endogenous regressor.Blundell and Powell(2007)and Chernozhukov et al.(2014)used the control function approach to handle censoring and endogeneity that occur simultaneously.However,they required the endogenous regressors to be continuously distributed.Although the methods proposed by Hong and Tamer(2003)and Khan and Tamer(2009)can deal with censoring model with the endogenous regressors are dummy,in addition to lead to a much more computationally intensive estimator in practice,their key identification assumptions will fail if the coefficient of the dummy endogenous variables are random.Abrevaya et al.(2010)proposed a framework only to estimate the sign of the treatment effects rather than the magnitude of these effects in nonlinear models with endogenous regressor.In Chapter 5 we introduce a new structural approach for censored regression models with random coefficient dummy regressors.Our model allows for heteroscedasticity and impose no parametric restriction on the error distribution.The proposed multistage estimator consistently estimates the parameter of interest under general identification conditions and is shown to be asymptotically normal.The Monte Carlo simulations show that the estimator have favorable finite sample properties at various degrees of censoring.Because the proposed estimator has a closed form expression,it is easy to implement regardless of sample size.The approach proposed in this chapter can be readily extended to estimate a heteroscedastic censored regression model with multiple random coefficient dummy endogenous regressors.Finally,we apply our method to evaluate the effect of fertility on mothers' labor supply.