Knowledge that Transforms

T HE normative principle of horizontal equity in personal income taxation calls for the levying of equal tax liabilities on taxpaying units enjoying identical pretax levels of economic well-being. Unfortunately, the only straightforward application of this principle is the proposition that tax-paying units identical in every other relevant respect should bear equal tax burdens if and only if they enjoy the same level of pretax money income. Economists have long recognized, of course, that the level of money income is only one of several objective factors that determine a tax-paying unit's level of economic well-being its ability to pay. Probably the foremost of the other factors is the number of individuals who must share a given total money income. Economists generally accept the principle that some system of personal exemptions, deductions, tax credits or other technical devices designed to adjust gross money income for the size of the tax-paying unit is necessary to maintain horizontal equity in personal income taxation. The purpose of this paper is to evaluate the structure of personal income tax exemptions for dependent children in the present personal income tax law against the horizontal equity standard stated above.' A review of the literature reveals that this subject has received only a sparse and elementary treatment. Public finance texts go no further than to suggest the qualitative norm that relatively large families should pay somewhat less taxes than averagesize families at a given level of gross money income. A very small number of studies take an approach which we shall pursue in greater depth-the application of a large body of work in consumption economics concerned with the determination of equivalent welfare incomes or for families that differ in size and composition to a quantitative assessment of the personal income tax exemption structure.2 Unfortunately, the direct adaptation of existing equivalence scale results is inappropriate for the purposes of tax policy, as we shall demonstrate in section II of the paper. The major contribution of this study is the estimation of a new set of equivalence scales that can legitimately be applied to the evaluation of aspects of the present tax structure that are relevant to the issue of horizontal equity. Section II of the paper briefly reviews the traditional methodology for estimating equivalence scales and then proceeds to detail the conceptual and pragmatic problems involved in adapting this methodology to our particular problem. Section III presents the statistical model for estimating our new set of equivalence scales and discusses the data source for the estimates. Section IV reports our empirical results and a final, brief section V treats the policy implications of our findings.

R ECENT studies investigating the variability in inter-industry profit rates largely ignore the influence of actual and potential foreign competition [2, 5, 6, 15, 171. This paper examines the influence of foreign competition on industry profitability and concludes that such competition, as represented by the level of imports, appears to exert a significant and negative effect on industry profit rates. The evidence is consistent with the hypothesis that less restrictive trade policies encourage more competitive pricing behavior in domestic industries. Section I of this paper develops the analytical framework within which to view potential foreign competition. Section II describes the model and presents the major empirical results. Section III discusses the implications of the empirical results with respect to foreign trade policies.

T EMPORAL aggregation problems in econometrics pose an important but relatively unexplored set of issues relevant for analyses of economic behavior and policy problems. When the behavior of individuals, firms or other economic entities is analyzed with temporally aggregated data, it is quite possible that a distorted view of parameters' values, lag structures and other aspects of economic behavior can be obtained. Since policy decisions usually depend critically on views regarding parameter values, lag structures, etc., decisions based on results marred by temporal aggregation effects can produce poor results. Further, as emphasized by Orcutt and others, aggregating data temporally or otherwise usually involves a loss of information. In the context of temporal aggregation, aggregation can lead to (a) lower precision of estimation and prediction, (b) lower power for tests, (c) inability to make short-run forecasts and (d) a reduction of the probability of discovering new hypo-theses about short-run behavior from data. It is generally appreciated that when annual data are employed in analyses, it is difficult to obtain satisfactory results pertaining to the intra-year behavior of economic units, for example seasonal effects that are often important in analyzing the variations of such variables as inventories, agricultural prices, agricultural output, etc. Previous work concerned with the theoretical analysis of the effects of temporal aggregation on estimation include Mundlak's [6] and Engle's [3] analyses of distributed lag schemes, Telser's [8] treatment of autoregressive processes and Zellner's results for stock adjustment models [11, 12]. In all these papers, it is shown that when econometric models are implemented with temporally aggregated data for flow variables or stock data pertaining to periods longer than that considered appropriate on a priori grounds, the results of analyses will usually be marred by temporal aggregation effects. Further, empirical analyses of several single equation models using temporally aggregated and disaggregated data have been reported which reveal sensitivity of inferences about lag structures to the level of data aggregation (see, e.g., Bryan [1], Laub [5] and Ranson [7]). While much previous work has concentrated attention on the adverse effects of temporal aggregation, there has not been much attention devoted to the problem of what can be done in analyses when we have to work with temporally aggregated data, perhaps because these are the only data available. The approach to be taken in this paper, also utilized in Zellner [11], is to formulate an economic relation in terms of the time unit, say a week or a month, thought to be appropriate on economic grounds and then to derive logically the implications of the model for explaining the variation of temporally aggregated data. With the implied model for the aggregated data explicitly set forth, the problem of using the aggregated data to make statistical inferences can then be approached. Below we present applications of this approach and make several theoretical and empirical comparisons of results obtained with aggregated data with those obtained from analyses based on disaggregated data. The plan of the paper is as follows: In section II we specify a simple model, derive the implied model, and examine its properties. Then inference procedures for the monthly and quarterly versions of the model are compared and some generalizations of the analysis are indicated. In section III numerical results pertaining to a moneymultiplier model are presented. Finally, in

S ome recent papers have estimated labor supply functions for the working poor. 1 All have a single objective: To estimate the labor force effects of a negative income tax or related income program. The basic argument is simply that the increase in unearned income leads to an income reduction in the labor supply. This, because leisure is a superior good. Also, most negative income tax schemes entail an increased marginal tax rate, that is the same as a reduced marginal wage rate and this, substitution effect, induces a further contraction in labor supply. This paper presents new estimates of labor supply functions based upon a different set of data from those used in other studies. Our estimate of withdrawal effects is smaller than most,2 even though our measure of nonemployment income includes unemployment compensation, public assistance payments and other components of nonemployment income that result from the hours worked decision. Presumably, the inclusion of these endogenous factors would overstate the true income effect. This underscores a result found by both Fleisher-Porter and Greenberg-Kosters, that the estimated income effect is very sensitive to the income definition used.3

An alternative procedure would be to apply some knowledge of economic history to the problem and see if changes in the financial factors affecting adjustment speeds can explain the changes in investment expenditures by themselves. If so, and my results reported in the original article indicate it is so, then a test for the relative significance of changes in financial factors compared to changes in the gaps between desired and actual capital stocks would be to see which model produces the most stable coefficients for subperiods. One of the things I noted in my article was the stability of the coefficients of the financial variables (the effective yield on railroad bonds and the level of retained earnings), whether estimated for the entire period 1897-1914 or the subperiod 1897-1907. I had no more luck than Morgan, however, in finding stable coefficients for any version of the accelerator model. The net effect of Morgan's work is to give independent support to my original argument that the accelerator model in any form is inappropriate for explaining investment behavior of American railroads during this period of volatile financial changes. lished Ph.D. dissertation Growth, Stability and Financial Innovation in the American Economy, 1897-1914. University of California, Berkeley, 1968.

T HIS study attempts to explore the causes of internal migration in Colombia. Migration rates are first estimated for various groups in the population to clarify who migrates and to where. A model of interregional migration is then set forth and estimated for a sample of Colombian municipalities, from which we can infer the responsiveness of migration to some economic, demographic and political developments in the rural and urban sectors of the society.

FOLKLORE has it that foreign markets are more risky than domestic markets because of political, economic, and social instability abroad. A normative implication of this belief, sometimes mentioned in the literature, is that a firm must establish itself in the domestic market before venturing into foreign markets; otherwise, it is argued, the inherent instability associated with exports might seriously damage the firm's operations. It is shown here that such implications are at variance with the diversification principle in portfolio theory. Specifically, an individual project might be very risky, yet its incorporation with other projects may decrease the overall risk of the portfolio. The overall risk of a group of projects is affected mainly by the relationships among these projects and only slightly by the individual riskiness of each. The hypothesis advanced in this study was that exports, through market diversification, tend to stabilize the firm's sales, and the larger the spread of these exports over several markets the more stable the sales. This hypothesis was tested on data selected from a sample of about 500 firms in Denmark, the Netherlands, and Israel. Results of the test were consistent with the hypothesis: sales stability and diversification of exports are indeed positively correlated.