个人所得税的公平性体现(3)

Conceptual Framework

With the Pareto distribution, the distribution of the population over the rangeof wage levels (w), denoted by f(w), that is equal or above

some positive

MARCH–APRIL 200645

threshold w0, expressed as a fraction of total population at each w, is assumedto take the following functional form:

f(w) = β w-α-1, w ≥ w0 > 0,(1)

where β º α wa

coefficient. Hence, this distribution has two parameters: 0 > 0 is a constant and α > 1 is commonly known as the Paretoα and w

equation (1), the cumulative distribution function, denoted by F(w0. Given), of thePareto distribution, which gives the proportion of the population with wagesno greater than w, takes on a particularly simple form. By integrating f(w)over the wage interval [w0, w], one obtains

F(w) = 1 – (w0/w)α.(2)

Hence, the proportion of the population with wages above w is simply 1 –F(w) = (wα0/w). It follows that, if the size of the population is given by N,the number of wage earners with wages above w, denoted by n(w), wouldthen be

n(w) = N (w0/w)α,(3)

which is the most commonly cited formula associated with the Paretodistribution.

The average wage income for the entire population under the Pareto dis-tribution turns out to be13

v = w0 α/(α – 1),(4)

which says that it is proportional to the threshold income w

relatively simple matter with this distribution to ascertain both the number of0. It is also a

wage earners and the total wage income over any wage interval [a, b], whereb > a ≥ w0. The number of wage earners with wage income in this interval,denoted by na,b, is simply the product of N and the definite integral of f(w) over the interval, that is,

na,b = N β (a-α – b-α)/α.(5)

In the similar vein, total wage income in this interval, denoted by wbe the product of N and the definite integral of [w a,b, would

f(w)] over the interval,

that is,

wa,b = N β (a1-α – b1-α)/(α – 1).(6)

Hence, the average wage income in this interval is

46THE CHINESE ECONOMY

va,b ≡ wa,b/na,b = [(a1-α – b1-α)/(a-α – b-α)] [α/(α – 1)].(7)

Model Implementation

The objective is to ascertain the PIT revenue from wage income in each ofthe nine rate bands, for which actual data are not available. Since the basicmonthly allowance of RMB800 is equivalent to having a zero-rate band forincome below the said allowance, one could regard the rate schedule as hav-ing ten rate bands, starting with the zero percent rate and ending with the topmarginal rate of 45 percent. This schedule is given in column 1 of Table 3,with column 2 indicating the width of each band expressed in terms of an-nual wage income.

There are initially three unknown parameters: α, N, and w

w0. However, thegiven monthly allowance permits one to set 0 = 9,600, leaving only twoparameters to be estimated. Figure 1 shows how total PIT revenue behaves in

response to different combinations of α and N. The solution values of thesetwo parameters are found through numerical simulations so that the simu-lated PIT revenue outcome corresponds to the actual PIT revenue collectionin 2002 (see Table 2), for both (1) the global amount of RMB56.1 billion and

(2) the subtotal amount of RMB9.7 billion, which represents the PIT revenuecollected from rate bands from 25 percent to 45 percent. In Figure 2, thecurve G is an iso-PIT revenue contour that traces out the various combina-tions of α and N that would achieve the actual global PIT revenue target,while the curve M is another iso-PIT revenue contour that traces out variouscombinations of α and N that would achieve the actual intermediate PITrevenue target. The point where the two curves intersect provides the (lo-cally) unique combination of α and N that would achieve the global andintermediate targets simultaneously. Specifically, the simulation producedthe following solution values: α = 1.882197575 and N = 48,613,963.

Using these solution values of a and N, columns 3 and 5 of Table 3 can bederived by applying equations (5) and (7), respectively. Column 6 then com-putes the PIT on the average wage in each rate band by applying the rateschedule given in column 1. The total PIT revenue in a given rate band issimply the product of the number of taxpayers and the PIT in that rate band,shown in column 7. Column 9 shows the average PIT rate in each rate band.

The simulation results imply that, in 2002, China had about 49 millionPIT payers14 with an average annual wage income of about RMB20,000. Theaverage PIT rate progresses from about 1 percent (in the 5 percent rate band)to about 31 percent (in the 45 percent top rate band), yielding an overallaverage PIT of about 5.7 percent.15

Not surprisingly, while about 91 percent

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