The Theoretical And Applied Research Of Panel Data Model With Fixed Interaction Effects

The endogeneity of explanatory variables is a common problem in exploring the causal relationship between economic variables.One of its main sources is the miss-ing variable bias,which is often caused by the unobservable individual heterogeneity or the time-varying common impact from the macro level.Although the panel data model provides another sharp tool to solve the two types of missing variable errors,the traditional model usually assumes that the effect of individual heterogeneity does not change over time,which is too strict for some empirical applications.In fact,due to the time span of panel data,the influence of individual heterogeneity is likely to be time-varying with the changes of external macro factors.The error in model setting may lead to the inconsistency of estimation and affect the accuracy of empirical conclusion.The fixed interaction effect model（also known as the time-varying fixed effect model）introduces the product term of individual heterogeneityα_iand common fac-tor F_t,which is more in line with economic reality and avoids the false setting of the model.Moreover,the traditional panel model can be regarded as a special case of this model.However,because the first-order difference and intra group average elimination methods can no longer be used to deal with the interaction effectα_iF_t,researchers have to propose new estimators.According to whether it takes time T tends to infinity,these literatures can be divided into two categories.The literatures under the framework of large T are based on PCA or CCE estimation.In this case,F_tis regarded as a com-mon factor related to the independent variable,whileα_iis the load coefficient to be estimated.These methods have their own advantages,but most of them are difficult to keep the consistency when T is fixed.More and more attention has been paid to the model under the framework of small T.Or building a new quasi difference method,or using the correlation betweenα_iand x_it,existing studies have constructed different es-timation methods.Although they can ensure the consistency of the estimator when the T is fixed,these literatures still have some shortcomings.（1）Most researches based on GMM estimation need to introduce nonlinear moment condition,which not only com-plicates the calculation process,but also may not get the global optimal solution;（2）Most of the models are difficult to identify variables that do not change with time,but their impact may be very important,such as gender discrimination in wage research;（3）Except the Chamberlain-Mundlak projection method,all the estimator need to as-sume that the a dimension is known or estimate it first.In view of this,this paper first constructs a new GLS estimate and a new QMLE estimate under the static panel model,which can not only solve the above problems,improve the estimation efficiency,but also have robustness.We also extend this method to the dynamic panel model and make further expansion.During the empirical research,irrelevant variables will be in-troduced due to the unknowability of the real model,which will lead to the increase of the parameters to be estimated and reduce the estimation effect.In this paper,we use the idea of compressed estimation to construct a new QMLE estimate.It can not only estimate the coefficients,but also screen out the important variables at the same time.In this paper,we first discuss the estimate of a static panel model with fixed in-teraction effects.Referring to and extending the ideas of Mundlak（1978）and Cham-berlain（1984）,a new GLS estimate is constructed by substituting the linear projection ofα_ion the time-varying explanatory variable into the original equation.In order to make this method feasible,we need to estimate the covariance matrix of the error term.We use the ECM algorithm,which is not only simple to calculate,but also can improve the estimation efficiency.Furthermore,referring to Pesaran（2006）,Bai and Li（2014）,this paper also sets another form for the correlation betweenα_iand x_it.On this basis,a new QMLE estimate is constructed,and the ECM algorithm is also used to estimate the covariance matrix of the error term to improve the efficiency.Compared with the existing research,the advantages of this method are as follows.（1）Time invariant variables can be introduced.（2）It is not necessary to assume that the dimension ofα_iis known or to estimate it first.（3）Our estimation has a simpler calculation process and is robust to the different relations between x_itandα_i.（4）The sequence correlation and heteroscedasticity in the permissible error term are allowed.（5）The Monte Carlo simulation results show that the method is more efficient than the existing estimation method,and it can run as well when the T is large.Moreover,the estimate is extended to the dynamic panel,and the strict exoge-nous assumption is relaxed.Due to the complexity of economic law and the fact that the model is unknowable,it is possible to introduce irrelevant variables in regression.Moreover,in the time span of the sample,the influence of some explanatory variables will be time-varying,so it is necessary to construct the cross term between them and time dummy variables for testing.The introduction of irrelevant variables and cross terms will increase the dimension of the coefficient to be estimated and reduce the ac-curacy of the estimation.In order to solve this problem,this paper introduces SCAD penalty function into the newly constructed conditional likelihood function,and real-izes the screening of important variables through compressed estimation.Using lo-cal quadratic approximation and ECM algorithm,the explicit solution of the QMLE estimate and its iterative steps are given.Monte Carlo simulation experiment again confirmed the good performance of this estimation in the limited sample.The new estimator not only inherits the advantages of the static panel model in this paper,but also filters out irrelevant variables at the same time,which further expands the appli-cation scope of fixed interaction effect model in empirical research.The advantages of the estimator are as follows.（1）It inherits the advantages of the two estimation meth-ods in the static panel;（2）The strict exogenous assumption is relaxed;（3）Coefficient estimation and selection of important variables can be carried out simultaneously,the accuracy of estimation is not affected by the number of parameters to be estimated.This paper also uses the above models and methods to study the practical prob-lems.Firstly,with the help of GLS estimation and QMLE estimate,we empirically tests the impact of financial development on PPP landing rate.（1）The financial devel-opment in the region will help to alleviate the financing difficulties of the local govern-ment and improve the PPP landing rate;（2）The promotion incentive of local officials will strengthen the role of financial development.Secondly,we use the QMLE estimate under the dynamic panel model to identify the impact of executive incentive（monetary compensation incentive and equity incentive）on the motivation of enterprises to allo-cate financial assets.（3）The monetary compensation incentive of executives will lead to the improvement of the profit level of financial channels and stimulate enterprises to obtain more short-term benefits through financial speculation.（4）Equity incentive promotes the increase of the share of financial assets and reserves funds for future fixed assets investment.Furthermore,this paper also tests how financial market risk regu-lates the effect of financialization on the efficiency of fixed assets investment.（5）The enterprises’profit of financial channel will reduce the investment efficiency,which is reflected as the”crowding out effect”of financialization.（6）Financial assets allocated by enterprises will improve investment efficiency,reflecting the”reservoir effect”of financialization.（7）Financial market risk can adjust the impact of enterprise finan-cialization on investment efficiency.The rise of risk will strengthen the”crowding out effect”of financial channel profit on investment efficiency and restrain the”reservoir effect”of financial asset share.The above findings help to understand the impact of financial development at the regional level and financialization at the enterprise level,and provide valuable empirical reference for promoting the reform of the financial sys-tem to better serve the development of the real economy.