Knowledge that Transforms

Empirical studies of consumer demand or of factor demand have now moved far beyond the Cobb-Douglas functional form and elasticities of interest are no longer estimated as parameters of the system. Instead, such elasticities are typically non-linear functions of the parameters that have been estimated and it is natural to want to be able to say something about the statistical properties of such elasticities. One way of dealing with this is to linearly approximate the elasticity formulas (in terms of the estimated parameters) and use classical statistical procedures to get approximations to the underlying variances. If y-f(x) and x has a variance covariance matrix V, the linear approximation is given by: Var(y) (8f/8x)V(8f/8x). The data needed for such an approximation are estimates of the parameters and of the associated variance-covariance matrix. Some of the earliest references that we have found to uses of this approximation technique in the elasticity context are to Griffin and Gregory (1976), Griffin (1977), and Fuss (1977), while the earliest references to

Partha Dasgupta, Eric Maskin; The Existence of Equilibrium in Discontinuous Economic Games, I: Theory, The Review of Economic Studies, Volume 53, Issue 1, 1 Jan

In his recent study (1985), Joseph Pechman presents estimates of incidence by income classes for several recent years. This study basically updates the earlier work by Pechman and Benjamin Okner (1974), which developed estimates for 1966, using the same methodology but applying it to more recent data to generate estimates of burdens by income class for 1970, 1975, 1980, and 1985. This note points out some peculiarities in the underlying data which suggest there are serious problems with the estimates for the later years. Pechman's major results are displayed in Table 1. Panel A of the table gives average rates for each major by household income deciles in 1966, and panel B presents the estimates for 1980, both for incidence variant ic.' (Ignore the last column in panel B for the moment.) As can be seen, the combined rate for the top decile is estimated to fall between 1966 and 1980 while it rises for the lowest decile. ratio of the rate for the top decile to the rate for the bottom decile declines from 1.8 in 1966 to 1.3 in 1980, a significant decrease in progressivity. Pechman explains the diminished progressivity by noting that the relative importance of various taxes has changed since 1966: The system became less progressive... primarily because the corporation income and the property declined in importance while more emphasis was placed on the payroll tax (p. 10). Although it is true that there has been a change in the relative contribution of various taxes since 1966, this change does not account for the decline in progressivity shown by the 1980 estimates. This is easily demonstrated by scaling up or down each decile's 1966 rate due to each in proportion to the change in the overall rate for that between 1966 and 1980. (For example, since property taxes had fallen from 3.0 percent of total income in 1966 to 2.0 percent in 1980, we would take two-thirds of the 1966 rates, i.e., 1.4 percent for the lowest decile, as an estimate of the 1980 rate due to the diminished importance of the property tax.) last column of panel B shows the results of these calculations, summed over all taxes. These figures suggest that if the only change since 1966 had been due to the change in the relative importance of various taxes, the system in 1980 would have been about as progressive as it was in 1966. Careful inspection of Table 1 clearly indicates that something else besides a change in the relative importance of taxes was responsible for the difference in results between 1966 and 1980. Note in particular the change for payroll taxes (principally the Social Security tax). In 1966, the payroll rate was 2.6 percent for the lowest decile, but in 1980 it is shown as having risen to 8.8 percent, an increase of 223 percent even though payroll taxes as a percent of total income rose by a scant 32 percent over this period. Even more puzzling is how the rate structure of the payroll taxes changed. In 1966, payroll taxes are shown as progressive up through the fifth decile and regressive at higher deciles, but in 1980 they are shown as regressive throughout the entire income distribution. At this point it will be helpful to explain why other studies (as well as Pechman's 1966 estimates) have found payroll taxes to be progressive at the bottom of the income distribution and regressive at the top.2 *Department of Economics, Texas A&M University, College Station, TX 77843. 'Eight different sets of incidence assumptions were used in the Pechman study. Variant Ic tends to embody competitive assumptions regarding the response of the economy to taxes. 2See, for example, my study with William Johnson (1979) or Richard Musgrave, Karl Case, and Herman Leonard (1974).

The concept of an American underclass has become the subject of increasing discussion. Although the term does not enjoy a precise definition, most researchers acknowledge that the underclass condition involves more than being cash poor. Members of the underclass are also believed to have attitudinal and behavioral deficiencies. Other terms that have been used to describe this group over the years include: dangerous classes, other Americans, culture of poverty, and lower classes (see Ken Auletta, 1981). Within this area of inquiry, several researchers have chosen to study what has been termed the black underclass. The purpose of this paper is twofold. First, the appropriateness of the data that are used to characterize members of the black underclass will be examined. Second, the argument that perhaps the most viable solution to the problems of the black underclass are community self-help programs, rather than government programs, will be discussed.