Knowledge that Transforms

JN the United States, unemployment insurance benefit payments are financed predominantly by taxes on employers' payrolls. The base of this tax is, however, not the actual payroll but the taxable payroll. Because of the legal provisions according to which the taxable payroll is computed, precise analytical formulae for the taxable payroll can be derived only for certain postulated employment patterns. In a previous theoretical paper (Brechling, 1977a) the determination of the taxable payroll for various types of employment patterns was examined. Further, on the basis of some simplifying assumptions about the employment patterns and some approximations, a fairly general but approximate formula for the taxable payroll was derived. It incorporates all the essential features of the specific formulae. In subsequent research the validity and adequacy of this general formula were examined empirically. This paper contains some theoretical extensions of the previous work as well as the results of the empirical research. The empirical work is unconventional in that it does not consist of tests of hypotheses that arise from assumptions about the behavior of economic agents. Instead it is designed to discover whether a formula which has been derived theoretically on the basis of technical assumptions is, in fact, valid and, hence, useful for practical purposes. Three such practical purposes seem to be especially important: First, theoretical considerations (Brechling, 1977a and b) have led to the conclusion that the taxable payroll may be related positively to labor turnover. Such a relationship implies that there is a tax cost of labor turnover that is influenced by the parameters of the tax structure. Hence changes in these parameters, effected by policy makers, may well affect labor turnover in the economy. Thus it is important that the theoretical relationships between the taxable payroll and its determinants be examined empirically. Second, a correct representation of the taxable payroll is highly desirable in order to be able to model adequately the total tax inflows into the unemployment insurance funds. In many states these funds were depleted substantially in recent years so that some corrective action by policy makers has been called for. Such action is likely to be particularly effective and purposeful if it is based on an adequate model of benefit outflows and tax inflows. Third, for the assessment of the recently enacted employment tax credit, changes in employment levels are approximated by changes in the total taxable payroll of an employer. For an evaluation of the working of this tax credit, it seems essential that the taxable payroll be modelled adequately. For (at least) these three reasons, a theoretical and empirical examination of the determinants of the taxable payroll of the unemployment insurance tax is regarded as an important and relevant research task. This paper is structured as follows: In section lI the formula for the taxable payroll of a particular type of employee is presented and its main implications are highlighted. This section is based on the previous theoretical work (Brechling, 1977a and b) and, hence, is quite brief. In section III, the theoretical analysis is extended. In particular, expressions are derived for a mean taxable payroll for situations in which data for particular types of individual workers are not available. In essence, section III is devoted to dealing with an aggregation problem. In section IV the empirical relationships between taxable payrolls and their determinants are examined. The empirical results lend substantial support to the theoretical models. But some problems still remain to be solved. Received for publication March 27, 1978. Revision accepted for publication February 15, 1979. * University of Maryland. The research underlying this paper was made possible by a contract with the U.S. Department of Labor, ASPER (No. J-9-M-6-0103). Its contents do not necessarily represent the official opinion or policy -of the Department of Labor. The research was undertaken while the author was visiting the Public Research Institute at the Center for Naval Analyses in 1976/77. Kathy Classen Utgoff kindly read and commented on a previous draft of this paper. Her help is acknowledged with gratitude.

William A. Niskanen, Steve H. Hanke, Land Prices Substantially Underestimate the Value of Environmental Quality: A Rejoinder, The Review of Economics and Statistics, Vol. 62, No. 1 (Feb., 1980), p. 156

Asch, Peter, and Joseph J. Seneca, Is Collusion Profitable? this REVIEW 58 (Feb. 1976), 1-12. Block, M. K., F. C. Nold and J. G. Sidak, The Deterrent Effect of Antitrust Enforcement: A Theoretical and Empirical Analysis, Technical Report ISDDE-1-78, Hoover Institution, Dec. 1978. Clabault, James M., and John F. Burton, Jr., Sherman Act Indictments, 1955-1965 (New York: Federal Legal Publications, 1966). Feinberg, Robert M., Structure and Employment Instability, this REVIEW 61 (Nov. 1979), 497-505. , The Lerner Index, Concentration, and the Measurement of Market Power, Southern Economic Journal 46 (Apr. 1980), 1180-1186. Guth, Louis A., Robert A. Schwartz, and David K. Whitcomb, The Use of Buyer Concentration Ratios in Tests of Oligopoly Models, this REVIEW 58 (Nov. 1976), 488-492. Hay, George A., and Daniel Kelley, An Empirical Survey of Price-Fixing Conspiracies, Journal of Law and Economics 17 (Apr. 1974), 13-38. Lustgarten, Steven H., The Impact of Buyer Concentration in Manufacturing Industries, this REVIEW 57 (May 1975), 125-132. , The Use of Buyer Concentration Ratios in Tests of Oligopoly Models: Reply, this REVIEW 58 (Nov. 1976), 492-494. Omstein, Stanley I., Industrial Concentration and Advertising Intensity (Washington, D.C.: American Enterprise Institute, 1977). Palmer, John, The Profit-Performance Effects of the Separation of Ownership from Control in Large U.S. Industrial Corporations, Bell Journal of Economics 4 (Spring 1973), 299-302. Trade Regulation Reporter, Vol. 4, New U.S. Antitrust Cases (Chicago: Commerce Clearing House, 1979).

Jon P. Nelson, George R. Neumann, Ronald M. Crandall, A Comparison of Alternative Econometric Models of Iron and Steel Investment Behavior, The Review of Economics and Statistics, Vol. 62, No. 1 (Feb., 1980), pp. 122-127

T HE presence of adjustment costs for a firm altering its labour force or capital stock creates considerable problems for econometric work involving firm behaviour, either on the employment or the investment side. The usual way of handling these costs is to derive a so-called desired level for the choice variables based on an optimization assuming there are no adjustment costs and then to add an ad hoc lagged adjustment process, the nature of which however is not derived explicitly from the actual costs of adjustment. There are two problems with this. First, as noted by Nerlove (1972), the resulting paths would not in general be optimal for a profitmaximizing firm so there is an inconsistency between equilibrium behaviour and adjustment behaviour. Second, by allowing the adjustment process to be data determined without imposing the restrictions implied by optimization over adjustment costs, one makes it harder to discriminate between models on the basis of the data. This makes it difficult to test the appropriateness of assumptions about the underlying economic model (for example, the form of the production function used). The problem with including the adjustment costs in the optimization is of course that it leads to formulations that are intractable for empirical work. This paper is an attempt to avoid that problem by looking more carefully at labour costs and to see what can be said about the underlying production model without using ad hoc dynamic assumptions. In particular it recognizes the fact that, even for small firms, the wage rate for operatives is a step function in hours worked; up to a certain number of normal hours an operative is paid at one hourly wage rate but above that number of hours is paid at a higher, overtime rate. Of course, a firm would only use labour at the overtime rate if it cost less overall than hiring more labour at the normal rate. But since firms do regularly employ overtime labour, this suggests that they must face either a rising supply curve for labour or else a fixed cost in hiring additional employees; Since the latter enables one to retain price-taking behaviour in the labour market and can also provide an explanation for short-time working, that is what will be investigated here. What is relevant to the production decisions of a firm is of course the marginal cost of an additional hour of labour, provided, that is, that the average cost is not so high that it is unprofitable to produce at all. For a firm that has employees on short-time working, the marginal cost is the normal hourly wage rate. For a firm with employees on overtime, the marginal cost is the hourly overtime rate. These observations are formalized in the next section of the paper. In succeeding sections they are applied to models based on the Constant Elasticity of Substitution (CES) production function and to the vintage model of Malcomson and Prior (1979).

The results presented below demonstrate that the structural modeling approach to interest rate determination not only stands apart from the sectoral disaggregation question conceptually but also performs fairly well without sectoral disaggregation empirically. This paper presents estimation and dynamic simulation results for an aggregated equivalent to the disaggregated model of the determination of bond yields developed in Friedman (1977; 1979). Instead of six bond demand and two bond supply equations, here there are but one demand and one supply equation. The empirical results show that, while disaggregation is of value in structural interest rate modeling (that is, the disaggregated model outperforms the aggregated one), even the aggregated structural model performs very well in comparison with familiar unrestricted reduced-form term structure equations.

straints that are imposed, the price vectors chosen to generate the data, and the functional form used for the cost function approximation. It is also fair to say that if input-output coefficients are the ones of interest, since these are obtained for each of the points used in the generation, it may be better to seek some approximating functions for these directly rather than seek an approximating function for the cost function and then derive the input-output coefficients. All these comments do not imply that the pseudo data approach should be given up. It is, however, important to sort out the aims of the analysis. There are some problems (like studying the effects of changes in environmental regulations) where one cannot get any answers from time series and one has to use the process analysis models that have detailed specification of technology and the constraints. But for this the appropriate thing is to do a simulation analysis of the process model itself and not seek a single equation approximation of the complex technology. What distin,guishes Griffin's approach from the garden variety simulation analyses of process models is this distillation in a single equation.