Knowledge that Transforms

Daniel L. Thornton, Maximum Likelihood Estimates of a Partial Adjustment-Adaptive Expectations Model of the Demand for Money, The Review of Economics and Statistics, Vol. 64, No. 2 (May, 1982), pp. 325-329

URRENT research interest in school finance stems from reforms aimed at narrowing the range of expenditure variations among school districts. These reforms have attempted to compensate for tax base differences by providing state matching aid inversely proportional to tax base.' While expressed in different forms in different states and variously termed Percentage Equalization,' District Power Equalization (DPE), or Guaranteed Tax Base (GTB), these formulas, in their basic form, amount to the state guaranteeing all districts the same tax base per pupil, call it v*. Districts taxing themselves at a tax rate, r (adjusted at the state level to compensate for assessment variations so that r reflects the rate on true market value), are guaranteed revenue equal to rv*. The difference between what is raised locally in a district, rv, and the guarantee at that tax rate is provided through the state aid formula.2 In practice, legislative limitations on aid formulas in most states have led to richer districts maintaining a tax base advantage. For example, districts with a tax base above v* can raise more revenue at the same tax rate than districts at vor below. Also, placing limits on reimbursable expenses (e.g., not to exceed E* = r*v*) means that beyond a certain point, even in districts with tax bases below v*, raising tax rates will not engender any additional state matching aid, as would be required under a strict guarantee. Hence, while the introduction of GTB formulas provided a theoretical improvement, these limits made them equivalent to the foundation aid formulas they were intended to replace, effective improvement coming only when the limits were made more generous.3 In studying these reforms, research has concentrated on models relating current operating expenditures to the following: tax base, some price term reflecting the local share in the matching formula, block grants, and demographic variables. The most popular form has been the single equation log-linear model4 where coefficients are elasticities, which allows for easy comparability of the effects of the independent variables. However, the assumption of constant elasticities and the lack of interaction terms can be misleading in capturing behavioral responses and in making projections. This may be especially true when one is using data from less than equalized systems, where districts are operating in a tax and expenditure range different from what would occur under a fully (tax base) equalized system and when there are different responses to the state aid formula depending upon relative tax burden and educational need. For example, the expenditure response to state aid in poorer districts may be high for small increments in state aid, but, as district expenditures move beyond minimal requirements, increases in state aid may go increasingly into tax relief, depending upon the tax burden. The richer districts, in terms of property, generally face a price of one, i.e., no matching aid at the margin. However, most legislation guarantees some minimal funding for these districts. In order to make aid formulas fully effective, either poorer disReceived for publication October 1, 1981. Revision accepted for publication April 16, 1982. * The American University. This work was supported by National Science Foundation Grant Number SES-8013080. I am indebted to Anthony Boardman for getting me interested in the topic, to Robert Summers, Anita Summers, Janet Pack and Ralph Ginsberg for moral and intellectual support, to numerous people in the Michigan state government, especially Bob Witte and Bob Bosscher, for their expertise and cooperation, and to the School of Public and Urban Policy, University of Pennsylvania, for its encouragement of this research. I Usually property per pupil, which we denote by v. 2 I.e., state aid per pupil is r(v* v). The local share, or net price that the district pays per dollar of educational expenditure, denoted a, is a = v/P*. Under GTB, districts control expenditure levels through their choice of tax rate. 3For a detailed analysis of aid formulas see Reilly (1982). 4 Initially postulated by Feldstein (1975). Park and Carroll of Rand (1979), Black et al. (1979, 1980), and Johnson and Collins (1978, 1979) also use the same model. Other models of local expenditures have been used by Akin and Auten (1976), Barro (1972), Gatti and Tashman (1976, 1978), Grubb and Michelson (1974), Inman (1971, 1978), Ladd (1975), Lovell (1978), Slack (1980), Stem (1973), Welch (1981), and Wentzler (1980).

Another point: Meeks says that we did not include a variable reflecting differences in economic structure. He tried urbanization, found that has no effect on the results, and states that this provides confirmation for the generality of our In fact, the original authors had examined the effect of urbanization, and found (as did Meeks) that did not alter the results. Hence was not mentioned in our article. We therefore do not understand how this provides additional confirmation of his results. A last point: Meeks speculates that it could be that the expenditure effects at other levels take the form of quality rather than quantity changes. But there are some data that rebut that speculation. In a study of school age population, enrollment rates, expenditures per student, and student-teacher ratios (the latter an index of the quality of education) Billsborrow concluded: The empirical results indicate that population growth has not been systematically associated with growth in enrollment rates nor in qualitative deterioration in the education systems of developing countries in the period 1950-1970 (1978, p. 229). In conclusion, we read the data as showing that in MDCs population growth depresses educational expenditures for students, but much less so or not at all in LDCs. We do not know why this difference in results occurs, but differences in the quality of data might play a role. In future work, Meeks' specification of income per adult should be used.

Malthusian theory asserts that high population growth in poor countries retards economic development. 2 authors Simon and Pilarski have recently challenged this theory on the basis of their own research; it is their contention that previous studies of population growth and education (1 of the principal modes by which the Malthusian mechanism is assumed to operate) have been flawed. The defect is felt to lie in the assumption of simple rather than partial associations of the 2 variables education and population growth. On the basis of their tightened specifications they have found demographic variables to be nonsignificant in explaining educational expenditures per child once other relevant regressors have been introduced. Similarly little effect of the demographic variable on primary and tertiary school enrollment rates were found although an effect for secondary school enrollment rates was found. On examination of the theoretical framework and the several explanatory variables however the author concludes that a crucial variable which is sure to have a vital bearing on the conclusions reached has been misspecified in the equations. Further the author asserts that a more thorough specification of the tests of the hypothesis (i.e. that high population growth retards educational investment) actually provides additional support for the Malthusian conclusion on educational expenditures despite unpromising initial indications.

Blinder, Alan S., and Robert M. Solow, 'Does Fiscal Policy Matter?,'' Journal of Public Economic.s 2 (Nov. 1973), 319-337. Christ, Carl, Some Dynamic Theory of Macroeconomic Policy Effects on Income and Prices Under the Government Budget Restraint, Journal o1 Monetary Econo0lmicis (1978), 45-70. Fair, Ray C., A Model of AMI(Horoelonlmi ActivitY (Cambridge, MA: Ballinger Publishing Company, 1976). Kennedy, Peter E., Direct Wealth Effects in Macroeconomic Models: The Saving vs. the Definitional Approach, Journal ,f Monv., Crcdt, and Banking 10 (Feb. 1978), 94-98.

SOME economists have ignored corporate financing decisions on the assumption that they do not affect the investment and production decisions of firms. Yet even if this extreme position is accepted, firms must still make financing decisions which in turn have impacts on other sectors of the economy. Since interest payments on corporate debt are tax deductible, the reliance of firms on debt as opposed to equity financing directly affects the revenue the federal government collects through taxation of corporate profits. The corporate presence in bond markets and corporate borrowing from banks can be expected to affect both interest rates and the demand for money. Thus any large macro model must somehow account for the borrowing behavior of firms. Yet in assessing this portion of the 1965 Brookings Quarterly Econometric Model of the United States, de Leeuw (1965, p. 506) writes that the regressions for business borrowing are the least successful of the model. In this paper we derive an equation for the long-term debt ratio (capital structure) of a firm which can be estimated using available data. Unlike some recent qualitative studies' on the aggregate corporate debt ratio as related to inflation and taxation over time, our primary aim is to explain differences in the debt behavior among individual firms. Tobit estimation results, explicitly allowing for the fact that some firms have no long-term debt, are presented for both U.S. and Japanese firms. Our theoretical model implies that the long-term debt ratio which maximizes the present value of the existing stockholder's equity depends positively on the cost of equity and negatively on the cost of debt, capital productivity, and retained earnings. Our estimation results are generally in agreement with these expectations. In particular, we find that capital productivity, which has not been included as an explanatory variable in most previous studies,2 and the cost of equity capital are both important determinants of the firm's capital structure. Our empirical results also support the view put forward by Komiya3 that debt ratios for Japanese firms are higher than those for U.S. firms in part because the cost of equity has been historically higher in Japan than in the United States in relation to the cost of debt. Other important attempts to explain the debt ratio as a behavioral function of the price of debt and other variables include the studies of de Leeuw (1965) and Goldfeld (1969).4 Certain conceptual problems mar these studies, however. Short-term and long-term debt are not distinguished, despite the fact that long-term debt is usually used to finance capital spending while short-term debt is used to finance inventory and

This paper explores the implications of regional income convergence for measures of inequality at the national level. In general, such convergence occurs as poorer regions overtake more developed ones. It is difficult to imagine any realistic scenario in which rising incomes in poorer regions would not have the effect of reducing absolute poverty. At the same time, it seems reasonable to assume that national inequality would fall as the mean incomes in the various regions converge. Given these general presumptions, the recent economic history of regional convergence between the southern United States and the rest of the nation is quite puzzling. Over the last twenty-five years mean family income in the southern United States has gone from about 80% of the national mean to about 93%. At the same time inequality in the South and that in the non-South have been changing only slightly when measured by Gini coefficients. Under these circumstances with no serious deterioration in intraregional measures of inequality, we would expect to observe a substantial reduction in national inequality as these two broad regions converge in mean incomes. Nevertheless, there has been no significant decline in the national Gini coefficient.' This apparent paradox is in contrast to an earlier period in U.S. history in which regional convergence occurred while national inequality was falling (Smolensky, 1961, 1963). The purpose of this paper is to demonstrate that the relationship between regional convergence and overall inequality is far from obvious. In particular, we shot that the convergence of mean incomes among regions, ceteris paribus, is not a sufficient condition for a reduction in common measures of ov erall inequality such as the Gini coefficient. The ceteris paribas conditions here are that the distribution of population across regions and the relative distribution of income within each region are held constant. The proof of this assertion is made in section II. In section III, we demonstrate the relevance of this analysis to the U.S. case. We show that the simple mean convergence of family incomes between the southern United States and the rest of the nation over the last twenty-five years should not have been expected to have a direct effect on national inequality. The naive link between regional income convergence and national income distribution does not hold up in this important case. Hence the arguments of section II are more than analytical curiosa. In a situation where the direct effects of income convergence are insufficient to reduce overall inequality there is the possibility that the broader process of regional convergence achieves this result more indirectly. Regional convergence may involve economic changes that work on intra-regional income distributions or the distribution of population across regions in ways favorable to greater national equality. In section IV we speculate on such indirect effects. From a theoretical point of view we conclude that the direction and extent of such interactions are not obvious.

P REVIOUS studies of the effects of U.S. tariffs and quotas on U.S. real income and its distribution have concluded that these effects are minimal. Moreover, this conclusion has

N this paper I investigate proposition that price-cost margin of a producer goods industry will vary systematically with what I call industry's importance of its output in costs of its industrial customers. The empirical results indicate that price-cost margins are indeed negatively associated with cost-importance, particularly in highly concentrated industries. In these industries at least, evidence seems to confirm the importance of being unimportant. In section I, I present relationship between derived demand elasticity for an industry's output and cost-importance of its output, and also analyze ways in which industry pricing coordination and transaction costs of changing input suppliers interact with cost-importance to influence industry price-cost margins. In sections II and III I describe process of sample selection and a method for calculating a measure of cost-importance for producer goods industries. In section IV I present empirical results of estimating relation between price-cost margins and cost-importance for a broad sample of producer goods industries, and in section V I summarize my findings and suggest some promising avenues for future research.