Research of Decision Variables of Tax Revenue Based on Nonparametric Selection Approach - Innovative Management in Information and Production - page 306

= /

where Y is a random

variable which represents the error. We selected nine decision variables of tax
revenue using linear model of parameters method. The nine decision variables
are as follows: the proportion of the agriculture to GDP x 6 , per capita GDP x 1 ,
Population density x 2 , industrial gross output index x 13 , foreign direct investment
x 12 , the proportion of the third industry to GDP x 11 , The proportion of the second
industry to GDP x 7 , financial expenditure x 5 , and area x 10 .

T GDP is the proportion of tax revenue to GDP, and ε

2.2 Variable Selection of Stepwise Regression Method

Here we use the backward stepwise regression and start from the model containing
all the variables; a variable would be taken out from the model every time.
The method is to calculate the value of AIC after a variable is taken out and
choose the model of the smallest value of AIC as the best model; remove any
variables in the model until the value of AIC would not become smaller:

AIC ( M )= − 2 l ( M )+ 2 p , (2)

where l(M) denotes logarithm likelihood function of training set of data and p is the
number of variables in the model M .
By the stepwise regression method, we eliminated non significant variables one
by one in the model with AIC criterion, eliminating the two variables of the real-
estate investment and population density. We obtained 15 decision variables of tax
revenue using parameters method of stepwise regression: per capita GDP x 1 ,the
fixed assets investment x 3 , retail sales of consumer goods x 4 , financial expenditure
x 5 , The proportion of the agriculture to GDP x 6 , the proportion of the second
industry to GDP x 7 , long-term investments x 8 ,area x 10 , the proportion of the third
industry to GDP x 11 , foreign direct investment x 12 , industrial gross output index
x 13 , amount of imports x 14 , amount of exports x 15 , current assets x 16 , total profit x 17 ,
area x 10 .
The mean square error of the estimation obtained by the stepwise regression
method, nearly unchanged after eliminating irrelevant variables, but the mean square
error of linear regression increased by 14.3 %. It seems the method of stepwise
regression is better than linear parameters method, but stepwise regression retained
too much explanatory variables, and the calculation was relatively complex; it
couldn't find out the main decision variables. Further, in these two methods, there
are several regression variables in which the coefficient test is not significant; it
implies that there is no necessary linear relationship between several explanatory
variables and the explained variables of tax burden. Next we will consider nonpara-
metric method and try to use the nonlinear method to study the decision variables
of tax.