Theory And Application Of Panel Data Model With The Interaction Effect

Panel data model in the theory and application of econometric studies had been paid more and more attention, whether in the field of micro econometrics or macro econometrics, panel data model will be a mainstream direction of development. For example, in the field of micro econometrics, the panel probit model and panel tobit model are the expansion of the discrete dependent variable model about the panel data, which is belonging to the forefront research areas of the microeconometrics; the stochastic dynamic equilibrium (DSGE) widely used by macroeconometrics has expanded into the panel data model to build transnational DSGE model, which also belongs to the field of macroeconometric cutting-edge research. Therefore, in view of important position of the panel data model in econometric theory and applied research, the in-depth reseach of the panel data model has significant value.Traditional panel data models included individual effects and time effects in the composite error term and the individual effects and the time effects have been introduced into the model through the form of the addition, there exits the obvious defects to such model setting form; The addition setting form of the time effect and the individual effect mean that the coefficient of the time effect and the individual effect for all the different individual are the same, this is equivalent to a constraint which is applied to the model, this constraint is clearly not in line with the economic realities. For example, in the analysis of the impact of education to wages which is concerned widely in labor economics, the individual effects tend to be interpreted as unobserved individual endowments, the personal endowment are often important explanatory variables to wage level, so individual endowment has been included in the model to effectively prevent the omitted variable bias; but the addition setting form makes the impact of individual endowment to wage unchangable over time, which is obviously not in line with economic common sense; the possible improvement method is the introduction of the interaction between the personal endowment and the time factor, so it can be observed that the pricing track of the personal endowment which is changeable over time. Also for example, in the empirical study of macroeconomics about inflation, if the selected sample contains not only the panel data from all provinces which affect the provincial inflation, but also contains such time series variable as interest rate and exchange rate and so on; in this case, the variable of such time series as the interest rate and so on is a time effect, if the introduced form of the interest rates is an addition, it means that the response of the provincial inflation to interest rate change is consistent, which is obviously not logical; an improvement on this issue is also that the interaction term between the interest rate and the individual effect should be introduced into the model, it will be able to capture the different sensitivity of every province to interest rate change through the individual effect in the interaction term. Therefore, the introduction of the interaction in the panel data model can make a substantial improvement and innovation to the panel data model.The content of this study is to introduce the product terms of the individual effects and time effects into panel models to get panel data model with interactive effects.To comprehensively study the impact of interaction effect to panel data model, this paper analyzed and discoursed in detailed such various situations as single equation and multiple equation, static and dynamic, linear and nonlinear.Specifically, this paper consists mainly of the following aspects:Firstly, this paper introduced the interactive effects into the static single equation panel data model and put forward the setting form of the model and parameter estimation method. Based on the data of medical price and its influencing factors,,the paper gives a case study to compare the advantages of the interaction static panel data model relativelyto the traditional panel data model.Secondly, this paper introduced the interactive effects into the dynamic single equation panel data model and constructed the dynamic single equation panel data model with the interaction effect. For this model this paper put forward a nonlinear parameter estimation method of instrumental variable and give the Monte Carlo simulation results of the estimation method.Again, this paper introduced the non-linear conversion mechanism into the single equation panel data model with the interaction effect and extended panel data model with the interaction effect into the nonlinear field. For the nonlinear panel data model with interaction effects, this paper proposes a parameter estimation method based on grid search and gives an application case study of the consumption structure.Finally, this paper introduced the interactive effect into the panel structural VAR model and constructed a dynamic panel structural VAR model with the interaction effect and gives the parameter estimation method of the IEPSVAR model and case study of the formation mechanism of inflation.