The demand for gambling, 155.—Elasticity of demand, 156.—Demand for bookmaking in Nevada, 157.—Parimutuel betting, 158.—Price, tax, and state revenue, 160.

Regressions containing dummy variables are easily estimated by the familiar expedient of dropping out one of the categories but the result is often awkward to interpret. Since coefficients of dummy variables are determined only up to an additive constant, however, the equation can be transformed into a more easily interpretable form by adding on an appropriately chosen constant to each coefficient. For most regressions the constants should be chosen to force the mean of the transformed coefficients to equal 0. For logarithmic regressions the constants should be chosen to force the sum of the antilogs of the coefficients to equal 1. With logarithmic demand curves fitted to monthly data the resulting antilogs become monthly seasonal indexes. The technical procedure by which dummy variables are used to capture the influence of categorical variables in regression equations is generally familiar (see Goldberger (1964), Kmenta (1971), Johnston (1960), or, to go back near the beginning of things, Suits (1957)). In many cases, particularly where only two classes of observation are involved, results presented in the usual way involve no special problems of interpretation. For example, use of a dummy variable to distinguish pre-war from post-war behavior, or to measure the shift in a relationship during the period of a strike is readily understood by any reader. But where a set of several dummy variables is employed to measure the variation in behavior among a number of classes-regions, education groups, age brackets, and the like-there is often an important difference between the purely mechanical problem of fitting the regression and the quite different problem of presenting the results in the most effective fashion. The purpose of this paper is to call attention to this distinction, and to illustrate by simple examples.

would have received 56 per cent more under TAP. In the case of wheat this pattern is even more pronounced, and it is also present in tobacco; the case of corn has not been investigated. A much larger part of the subsidies to agriculture, therefore, would reach those for whom they are presumably intended. At the same time, by divorcing payments from current production cost TAP avoids the danger of encouraging inefficiency and of perpetuating uneconomic patterns of output. The cost of TAP can only be roughly estimated at the moment; the United States Department of Agriculture should be able to present more accurate calculations on the basis of its extensive market studies. Pending such calculations it appears that the cost of applying TAP to the three principal supported crops (wheat, corn, and cotton) at the rate mentioned earlier would not exceed $I.5 billion in the first year, and would be proportionately less in subsequent years.3 The cost of the present scheme is not known with any exactness but seems to exceed $4 billion per year. Some of the outlays under the existing program (notably those for storage and for the soil bank) would have to continue for some time after the introduction of TAP. Finally, it should be stressed that TAP is a transitional device and is consequently limited to a definite time period. By its very nature an acreage payment cannot be permanent without creating a caste of rural pensioners, and even the most sentimental devotees of the family farm would hardly advocate this. The appeal of this proposal is not to those who want to preserve the present structure of agriculture regardless of the burden on consumers and taxpayers; it is to those who recognize that in a progressive economy agriculture must change along with all other sectors, but who also recognize the wisdom of tempering the wind to the shorn lamb.

IN this paper we present the results of a new study of the demand for passenger automobiles, embodying a number of improvements over the attempts of previous investigators. In particular: (a) some account is taken of the influence of credit conditions on demand; (b) the dynamics of the market derive primarily from the accumulation of a stock of cars rather than from the rate of change of income; (c) the statistical work is carried out in terms of first differences to facilitate testing the influence of the variables. In the final formulation of the demand function, annual retail sales of new passenger automobiles are explained by: (i) real disposable income; (2) the stock of passenger cars on the road, January I; and (3) the average real retail price of new passenger automobiles divided by the average number of months' duration of automobile credit contracts. The price variable is, thus, an index of the monthly payment associated with the purchase of passenger automobiles. Use of this variable involved an estimate of a retail price index and of the number of months' duration of credit contracts. The source and nature of these estimates is taken up in the Appendix. Finally (4), we use a dummy shift variable to account for the special conditions of the automobile market in years of severe production shortage. The demand was estimated by least-squares linear regression with the variables expressed in first differences. For purposes of summary, the results are expressed in Table i as elasticities computed by reference to mean values. The statistical demand schedule fits the observed behavior of the market very well. When the equation is expressed in first differences, the coefficient of multiple correlation is .93. When calculated changes are added to sales of the preceding year, the correlation between actual and predicted levels is .98. It is particularly notable that the sensational rise in demand in

Two quite different issues are raised by the comments of David Davies and Edward Kienzle. The first, raised by both authors, is that use of S (or, for that matter, any other index of tax progressivity) in no way avoids fundamental problems of tax shifting, questions of how income should be measured for proper assessment of tax burden, or how to treat the difference between the distribution of lifetime tax burden compared to what is observed in any given year. The second issue, raised by Davies, deals with the validity of the index S, itself. Estimates of tax incidence differ with the kind of assumptions made about tax shifting. In this regard, the greatest variation occurs among estimates of the distribution of the burden of taxes on property, including the corporate income tax. Kienzle demonstrates this in an interesting way in his Table 2. Whether variant Ic or 3b is employed makes little difference in the value of S calculated for income, sales, or payroll taxes, but taxes on property appear highly progressive under Ic, and virtually proportional under 3b. Davies makes a similar point in noting that the value of S will depend on how income is measured. It would be interesting to see what difference would be produced if the adjustments to income he suggests were made. Likewise, it would be useful to see what happens to S when both income and tax burden are estimated on a lifetime basis. I have made a few attempts to make such calculations, but have so far been defeated by the problems of keeping track of who the taxpayer is, especially with the occurrence of divorce, widowhood, and remarriage. Davies also raises questions about the validity of S itself. His first objection-that no single index can summarize all aspects of a complicated phenomenon-largely duplicates what I said in the original presentation. The limitation is common to all averages and indexes (think of the divergence of individual price behavior concealed in movements of the Consumer Price Index) but we still find them useful. In his concluding remarks, Davies comes close to saying that tax incidence is too complex to permit tax progressivity to be measured at all. If this were true, of course, neither S nor any other such index would make sense. Personally, however, I think some useful things can be said about the relationship of tax burden to income, and that S serves as a good summary measure of those thinvs.