Knowledge that Transforms

I NPUT-OUTPUT analysis can be extended to an economic system with antipollution measures to describe interdependency among economic sectors and antipollution sectors in the economy. Such a model was formulated by Professor Leontief (1970) as a system of equations extending his original input-output framework. This extended model has been extensively discussed by Leontief and Ford (1972), Chen (1973), and Leontief (1973). A linear programming problem of the extended model with substitutions was presented by Lowe (1979). However, counter-examples with unrealistic solutions to the extended model were presented by Flick (1974) and Lee (1975). Validity of Flick's counter-example was questioned by Leontief (1974) and Steenge (1978). There seems to be an unresolved question concerning the existence of a unique nonnegative set of output levels in the extended model for any given nonnegative levels of final demand and tolerated pollution. The structural matrix of Leontief's original input-output model possesses two important properties: (1) off-diagonal elements are nonpositive; (2) all principal minors are positive. These two properties, known as Leontief properties, guarantee the existence of a unique nonnegative solution to Leontief's original model for any given nonnegative final demand. The above-mentioned problem of feasibility arises when the original model is extended to endogenize antipollution sectors and to set the total amount of pollution generated equal to the antipollution output level plus the tolerable pollution level. In this paper, we present a complementarity formulation of the economic system with antipollution measures that overcomes the problem of determining the existence and uniqueness of a feasible solution under Leontief properties, and derive conditions under which the present formulation guarantees these desirable properties when the structural matrix has some positive offdiagonal elements.' We apply the model to solve examples with different final demands and tolerated pollution levels (including Flick's counterexample) to obtain realistic solutions.

In their seminal paper, Chow and Lin (1971) consider the following problem: let X be a (T x k) matrix of high-frequency' (say, quarterly) indicators2 and y a vector of dimension N of low-frequency (say, yearly) observations on the variable to be distributed each year among the q (say, four) intra-annual periods. It is desired to get an estimate (z, vector T x 1, T = Nq) of the unknown quarterly series z possessing some optimal properties and satisfying the condition that the q values of the z se'ries within each period (year) sum up to the observed relevant value of y (consistency requirement). To start with they assume that there exists a multiple regression relation of the kind

Recent economic literature has given a great deal of attention to the behavior of the firm under a regulatory constraint. Such efforts include theoretical extensions of the classic article by Averich and Johnson (1962) by Kennedy (1977), as well as empirical tests of the overcapitalization hypothesis by Leland (1974), Smithson (1978) and Spann (1974). In addition, there have been notable attempts to provide a general theory of regulation by Stigler (1971) and Peltzman (1976). Against this background, surprisingly little attention has been paid to the effect of regulation on the compensation of chief executive officers. The effect of regulation on executive rewards strikes at the heart of why regulated firms appear to behave differently than their less regulated counterparts. The only explicit attempts to relate executive compensation to the presence of regulation appear to be the work of Smyth, Boyes and Peseau (1975) and Ciscel (1977). The apparent oversight of this issue is perhaps best explained by the persistence of the controversy over the nature of the objective function of corporate decision makers introduced as the maximization' hypothesis by Baumol (1967). For the last two decades, the debate over whether corporate decision makers maximize sales or maximize profits has been couched in either-or terms. Proponents of each side of the debate, like Smyth, Boyes and Peseau (1975) and Ciscel (1974) on the managerialist side, and Lewellen and Huntsman (1970) and Masson (1971) on the neoclassical side, have produced evidence for their respective positions. Ciscel and Carroll ( 1980) provide an econometric resolution of the conflict, pointing out the compatibility of the data with both hypotheses, given a proper specification of the compensation-performance equations. Consideration of the impact of regulation on executive rewards has significance for understanding the different rewards in the regulated sectors and it illuminates the implicit incentives for executive behavior in regulated and unregulated firms. Maximum profits or optimal sales can never be directly observed. All that can be measured is whether or not the pattern of executive compensation is consistent with such maximization objectives. This aspect of economic analysis is particularly important when gauging the effect of regulation on executive pay. The impact of the absence of regulation on compensation can be contrasted to two alternatives: regulation establishes maximum prices as is the case in utilities, while regulation prescribed minimum prices as was the case in the transportation sector (see Jordan, 1972). Executive compensation reflects not only incentive changes brought about by the existence of regulation, but also the form regulation takes.

Fair, Ray, and Dwight Jaffee, of for Markets in Disequilibrium, Econometrica 40 (May 1972), 497-514. Fair, Ray, and Harry Kelejian, of for Markets in Disequilibrium: Further Study, Econometrica 42 (Jan. 1974), 177-190. Goldfeld, Stephen, and Richard Quandt, Estimation in a Disequilibrium Model and the Value of Information, Journal of Econometrics 3 (Nov. 1975), 325-348. Hausman, Jerry, Effects of Wages, Taxes, and Fixed Costs on Women's Force Participation, Journal of Public Economics 14 (Oct. 1980), 161-194. McDonald, John, and Robert Moffitt, Uses of Tobit Analysis, this REVIEW 62 (May 1980), 318-321. Maddala, G. S., and Forrest Nelson, Maximum Likelihood Methods for Models of Markets in Disequilibrium, Econometrica 42 (Nov. 1974), 1013-1030. Moffit, Robert, and Kenneth Kehrer, Effect of Tax and Transfer Programs on Supply: The Evidence from the Income Maintenance Experiments, in Ronald Ehrenberg (ed.), Research in Economics, Vol. 4 (Greenwich, Conn.: JAI Press, 1981). Nelson, Forrest, Censored Regression Models with Unobserved, Stochastic Censoring Thresholds, Journal of Econometrics 6 (Nov. 1977), 309-327. Oi, Walter, Labor as a Quasi-Fixed Factor, Journal of Political Economy 70 (Dec. 1962), 538-555. Rosen, Harvey, and Richard Quandt, Estimation of a Disequilibrium Aggregate Market, this REVIEW 60 (Aug. 1978), 371-379. Tobin, James, Estimation of Relationships for Limited Dependent Variables, Econometrica 26 (Jan. 1958), 24-36.

A LTHOUGH many early models of job search assumed that job seekers were unemployed, economists have come to recognize the importance of on-the-job search.' Mattila (1974), for example, found that roughly 60% of quitters experienced no unemployment between jobs, implying that the majority of voluntary job changers engaged in on-the-job search. The choice of search mode (i.e., employed vs. unemployed search) has been modelled in the theoretical search literature (Barron and McCafferty, 1977; Burdett, 1978); however, there have been no attempts to estimate empirically the determinants of this choice.2 Some researchers have, however, examined the resulting wages associated with these two types of search and found a greater wage return to employed than to unemployed search (Mattila, 1969; Black, 1980). However, because voluntarily unemployed search involves forgoing income (Burdett, 1978), while employed search does not (abstracting from voluntary reductions in hours), incomemaximizing job seekers would never quit to search unless the expected net return to unemployed search exceeded that for employed search. Thus, the previously mentioned empirical findings at first glance might appear to contradict the assumption of income maximization by job seekers, because some workers do quit into unemployment.3 In this paper, it is argued that previous attempts to compare the returns of employed and unemployed job search suffer from a selectivity problem. Specifically, searchers who accept offers without experiencing any unemployment are likely to have unobservable variables (such as informal job contacts and ability) which will raise the relative return to employed search compared to that of voluntarily unemployed job seekers,4 providing an explanation for higher wages for on-the-job searchers than for unemployed searchers. This paper estimates the relative wage effects of employed and unemployed search and the determinants of the choice of search mode (i.e., employed vs. unemployed search). Unlike earlier work (Mattila, 1969; Black, 1980), the previously mentioned selectivity problems are accounted for. This is the first attempt to estimate the determinants of choice of search mode.5 Without adjusting for selectivity bias (as regards employed vs. unemployed search), it is found that employed search is associated with greater expected wage offers than unemployed search, controlling for measurable personal characteristics. However, accounting for selectivity, the expected wage offer given unemployed search is greater than that given employed search. Finally, the greater is the difference between the expected offer given unemployed and that given employed search, the more likely one is to choose unemployed search. These findings suggest that quitting to search unemployed may be a wealth-maximizing decision. Received for publication November 5, 1980. Revision accepted for publication August 17, 1981. * University of Illinois at Urbana-Champaign and Arizona State University, respectively. Professor Low is partially supported by a Faculty Grant from the Graduate College at Arizona State University. The authors thank Francine Blau, Wallace Hendricks and two anonymous referees for comments and suggestions. I For a summary of this literature, see Lippman and McCall (1976). 2 Barron and McCafferty ( 1977) do estimate an aggregate time-series model of the log of the proportion of quits entering unemployment as a function of the vacancy rate (proxied by the help wanted advertising index). However, such a model ignores search that does not lead to quits and does not include variables beyond the vacancy rate that influence an individual's choice of search mode. I It is also possible that the forgone earnings due to unemployed search could in principle be less than the possible savings in direct search costs due to unemployed search (relative to employed search)-see Burdett (1978); in this case, a lower wage return to unemployed search could imply that quitting was based on income considerations. Further, individuals may have quit for nonwage reasons. 4 Black ( 1980) found that, other things equal, those who planned to seek new employment but did not quit had significantly lower wage growth than those who did not plan to search and did not quit. This finding strongly suggests the likelihood of a selectivity bias (Black, 1980, p. 227). ' Black's (1976, 1980) data (the Michigan Panel Study of Income Dynamics-PSID) for his work on employed search did not allow him to distinguish employed and unemployed search.

Edna Loehman, Vo Hu De, Application of Stochastic Choice Modeling to Policy Analysis of Public Goods: A Case Study of Air Quality Improvements, The Review of Economics and Statistics, Vol. 64, No. 3 (Aug., 1982), pp. 474-480

SMALL businesses are prevalent in some sectors of the economy and relatively scarce in others. If we use two frequently employed definitions of small business-firms with annual sales at or below $500,000 or $5 million'-we can see the relative patterns in table 1: Agriculture, construction, wholesale and retail trade, and services are areas in which small businesses are relatively important; mining and manufacturing are areas in which they are less important. Why does small business flourish in some sectors and not in others? This question has been tackled in a qualitative fashion by a number of authors.2 But, to this author's knowledge, there have been no quantitative efforts to establish the determinants of small business prevalence. The closest approximations in the economics literature are, in effect, the inverse: the efforts to explain concentration in individual industries (e.g., efforts to explain the sizes of the four-firm or eight-firm concentration ratios across industries).3 Some of these concentration data have also been analyzed in the context of discussions about small business.4 But the concentration data provide only indirect evidence for the small business question. This paper will provide some direct cross-section evidence on the determinants of the relative importance of small business. Our sample will be limited to the manufacturing sector, largely for reasons of data availability, but the results should have general economy-wide applicability. Section II will discuss the major hypotheses to be tested. Section III will describe the data. Section IV will describe the results of the tests. And section V will provide some brief conclusions.

A SSUMPTIONS regarding the depreciation ,AX rate for housing play an important role in the urban economics literature.1 The notion that houses filter down from higher to lower quality is prevalent in both academic and policy discussions of the nature of urban problems. Yet there has been no attempt to specify which depreciation rates are appropriate to these discussions, and little empirical investigation of depreciation in housing. This paper presents estimates of depreciation rates for housing which are appropriate to consideration of the filtering hypothesis. Estimates of these depreciation rates must be pursued differently from estimates of the depreciation rates for the aggregate capital stock of housing. A brief review of previous studies, which points out some of the difficulties which confound observation of depreciation rates, is presented in section I. Section II discusses specification, and section III describes the data and estimation technique used. Results are presented in section IV. Section V is a brief conclusion.