T HE effective tax rate on individual returns (to be denoted etr) remained approximately constant at 23.4 per cent from 1955 to 1962, while taxable income increased more than 50 per cent. Since the individual income tax structure is progressive, this seems at first glance to be a strange result. Explanations which exist in the literature allude to the possibility that shifting between types of returns has occurred, that the pattern of deductions and exemptions has changed over time, and that the tax rate of new taxpayers has been less than the existing average. The objectives of this paper are to evaluate these arguments and to analyse in detail the nature of the etr constancy. The first problem in analysing the etr is to decide whether or not the constancy is in fact a surprising result. That is, although almost everyone would be willing to predict a larger etr as a result of a taxable income increase of 50 per cent, most would be hard pressed to predict the magnitude of the increase. Yet the constancy can hardly be considered a curiosum if the etr is, in general, very insensitive to taxable income growth. In fact it should be realized that under certain general conditions an increase in the taxable income of every taxpayer will result in a decrease in the etr. Assume first that only incomes in the lowest tax bracket increase, and that no income increases sufficiently to move it to a higher tax bracket. Then the overall etr will decrease since the lowest bracket rate is weighted relatively more heavily. But clearly a reduction in the etr may result without such extreme assumptions. What is required is that taxable income in low brackets grows sufficiently rapidly (relative to taxable income in high brackets) to enable the effect of increased densities of returns with marginal tax rates less than the average, to offset the effect of higher rates on certain incomes. Since marginal rates in the two lowest brackets are less than 23.4 per cent, rapid taxable income growth at these income levels will tend to prevent the etr from rising, and may in fact even cause it to decline.1 Further, the etr may be reduced even without an increase in the density of returns with marginal rates less than the average. Suppose, for example, that a joint return taxable at $5,000 in 1955 increases to $9,000 by 1962, thus decreasing the density of returns with marginal rates below the aggregate etr, and increasing the density of those with marginal rates above. But the growth from $5,000 to $9,000 consists of an increase in income of $3,000 taxable at 22 per cent and $1,000 taxable at 26 per cent which is equivalent to adding $4,000 at 23 per cent, and hence the aggregate etr of 23.4 per cent will be reduced. Similarly, the average and not the marginal rate on a new return is the relevant factor in determining whether or not the aggregate etr will decline when the return becomes taxable. For example a new return with a marginal tax rate of 26 per cent will also involve income taxable at 20 and 22 per cent, and provided the weighted average of the rates is less than the aggregate etr, the latter will fall. The extent to which taxable income growth diverges from proportionality (across individuals) is therefore of great interest. There are three major reasons for expecting taxable income growth to be nonproportional. First, proportional growth of adjusted gross income (to be denoted AGI) is probably a more realistic assumption than proportional growth of taxable income.2 Second, the annual distribution of new taxpayers probably differs from the distribution of existing taxpayers. Third, the growth in deductions and exemptions differs for various income levels. As discussed below all

SINCE 1953, Congress has enacted several changes in the income tax laws which provide subsidies to investment. Depreciation rules were amended in 1954 to allow taxpayers to use various accelerated depreciation methods, such as sum of the years digits or double declining balance, as a substitute for straight line depreciation. In 1962 the tax laws were changed to shorten the lives over which assets could be depreciated, and to provide a tax credit on investment in equipment. The 1954 acceleration and the tax credit were suspended in 1966 and reimposed in 1967. Although these subsidies have been incorporated in many econometric and theoretical studies of investment behaviour, the latter have been concerned exclusively with the partial equilibrium impacts on investment and on the interaction between investment and income in a short-run Keynesian framework.' Partial equilibrium effects are certainly of interest and the use of these subsidies for countercyclical purposes has been emphasized by recent policy decisions. However it should be recalled that one of the major reasons for instituting these policies was to stimulate economic growth. Consequently in this paper an attempt is made to analyse in a general equilibrium context the long-run steady state implications of investment subsidies in general, and of the tax credit and of a change in depreciation methods in particular. Of course this method ignores all problems arising from cyclical fluctuations in aggregate demand.

In this paper [the authors discuss] five procedures for incorporating demographic variables into theoretically plausible demand systems: translating scaling and the Gorman reverse Gorman and implicit Prais-Houthakker procedures.... These five procedures are used to incorporate a single demographic variable--the number of children in a household--into the generalized CES demand system using household budget data for the United Kingdom for the period 1966-1972 (EXCERPT)

Robert A. Pollak, Terence J. Wales, Comparison of the Quadratic Expenditure System and Translog Demand Systems with Alternative Specifications of Demographic Effects, Econometrica, Vol. 48, No. 3 (Apr., 1980), pp. 595-612

In this paper we estimate a complete system of demand equations making full use of the restrictions implied by economic theory. Our theoretical model is based on the Klein-Rubin linear expenditure system which was first estimated by Stone. We place primary emphasis on maximum likelihood estimates obtained using annual time series observations of prices and per capita consumption for the U.S. economy in the period 1948-1965. The plan of the paper is as follows: Section 1 begins with a discussion of the problems involved in making systematic use of economic theory to estimate demand functions; this is followed by a brief description of the linear expenditure system and discussion of the specification of its dynamic and stochastic structure. In Section 2 we describe three methods of estimating the linear expenditure system, including the maximum likelihood procedure which we believe is most appropriate. We report our results in Section 3 and our conclusions in Section 4. 1 A. INTRODUCTION The pure theory of consumer behavior is concerned with individual demand functions. An individual's preferences are assumed to be representable by a well behaved utility function, U(x1, .. . , x), where xi denotes the rate of consumption of the ith good. He is supposed to maximize U subject to the budget constraint n (1) E PkXk =I k = 1

In this paper, we introduce three flexible consumer demand systems in which expenditures on goods are quadratic functions of income. We view these alternatives as to the demand systems used heretofore in the empirical modeling of rank-three demands, namely those in which expenditure shares are quadratic functions of the logarithm of income. Curvature conditions required by theory can be imposed locally during the estimation for each, and a semiflexible version can be estimated. For illustrative purposes, we estimate various forms of two of the systems using Canadian data on seven categories of goods for the period 1947 to 1995.

Robert A. Pollak, Terence J. Wales, Price-Augmenting Returns to Scale: An Application to Nonseparable Two-Stage Technologies, The Review of Economics and Statistics, Vol. 74, No. 2 (May, 1992), pp. 213-220

Pooling consumption data from different countries for demand system estimation is attractive because it increases both sample size and therange of v ariation of relative prices and income. The major objection to pooling is that d ifferent countries may have different demand system parameters. This paper propo sed and estimates specifications that permit pooling while allowing both short-r un andlong-run demand systems to differ across countries. Using data from Belgi um, the United Kingdom, and the United States, the authors findthat, although p ooling was accepted for some pairs of countries and some specifications, it was rejected for most. They conclude that caution is appropriate in pooling internat ional consumption data.

M ANY cross-section studies exist in the literature attempting to explain variations in per capita state and local expenditures on such services as highways, municipal services, health, and education. Differences in per capita expenditures across states are explained in terms of such factors as differences in population densities, urban-rural distributions, average income levels, age distributions, and numbers of school-age children.' In most of these studies, however, the underlying theory has not been carefully spelled out and, in particular, it is never made clear whether the demographic variables are thought to enter on the demand side or on the supply side of the market for state and local services. In the first part of this paper we look at the theory underlying such regression studies of the determinants of state and local expenditures. We attempt to distinguish between the demand side of the market for such services and the supply (cost) side. In the second part of the paper we obtain empirical estimates of price and income elasticities of demand for state and local services for three broad classifications of services. Finally we discuss a number of interesting applications of our results.