The response of nominal interest rates to price increases has been intensively studied since the onset of substantial inflation and historically high interest rates in the late 1960s. Early empirical investigations (Yohe and Karnosky (1969), Gibson (1972), and Pyle (1972)) tested the Fisher hypothesis that nominal rates react one-for-one to changes in the expected inflation rate. Paralleling results in the wage-price literature, these studies often found that nominal rates appeared to adjust too little to imply neutrality with respect to expected inflation. Theoretical work by Mundell (1963) and Tobin (1965) that incorporated wealth effects, by Sargent (1972) that considered an extended macromodel, and by Darby (1975) and Feldstein (1976) that allowed for income tax effects, however, suggested that additional variables, like measures of fiscal and monetary policy, may be relevant and that nominal rates may change by either more or less than unity in response to a one unit change in expected inflation. Two puzzling features of the response of nominal rates to expected inflation remain. First, even when other factors are included, estimates of that response are unstable for the postwar period (see Cargill and Meyer (1977)). Second, empirical studies to date have failed to produce any statistically discernible impact of expected inflation on interest rates during the 1950s (see Cargill and Meyer (1974) and Cargill (1976)). Similarly striking is the sizeable residual autocorrelation exhibited by nearly all estimates that include the 1950s. These symptoms of model misspecification imply that an important factor may have been omitted from previous models. A reduced form model of nominal interest rates that allows for an additional impact, that of factor supply shocks, is advanced in section II. The empirical tests in section III show that, once this variable is included, a significant relation between interest rates and expected inflation emerges for the 1950s. We also show that our specification is stable over the entire post-Accord period. Section IV concludes.

T HERE is no professional consensus about the process of aggregate wage inflation. A spectrum of opinion exists between the following extreme poles: (1) That wages are determined instantaneously in markets where participants have rational expectations and can anticipate in their behavior the long-run consequences of any consistent pattern of macro policy making;' and (2) that wages are determined largely by institutional forces including considerations of equity, normal historical wage patterns, union strength, and current bargaining conditions.2 Adherents of these polar positions have little respect for wage adjustment equations of the Phillips (1958) or Phelps (1967)-Friedman (1968) variety in which wages are related structurally to aggregate unemployment rates. These adjustment equations occupy a middle ground in the spectrum and are currently used in large scale econometric models to explain how the effects of a change in demand are distributed into real and price components. Between the poles are several alternative justifications of wage-unemployment relationships. Among these are the following views: That wages are determined as in (1) above except for the existence of long-run contracts;3 that the determination of expectations about future prices can be fairly approximated by a distributed lag on past prices;4 that it is past prices rather than expectations of future prices that are important;5 and that economic conditions are but one of a set of factors to be included in the current bargaining conditions that determine wages.6 Which of these views best describes the process of wage determination is an empirical question, but the question is quite complicated and does not appear to be capable of resolution through a single, conclusive test. Many issues are involved simultaneously and no one has been able to find a set of workable assumptions that can be agreed upon by all as being a sensible way to proceed. The question of wage determination continues to divide macroeconomic opinion more than any other single issue. This paper reports results of empirical work on wage equations in which a strategy of disaggregation has been followed. It is part of a larger project to estimate the dependence of the natural rate of unemployment on the distributions of the supply and demand for labor according to location and occupation. As an estimation strategy, disaggregation can avoid problems of identification and could, in principle, provide a way to distinguish among the many competing hypotheses in this area. In practice, the disagreements are so fundamental and the possible tests so limited that the results can be offered as no more than an extension of the wage equation literature rather than as a resolution of the issue of whether wage equations should be treated as structural relations or, of even greater ambition, what those relations might be. The extension provided follows the direction of Baily and Tobin (1977, 1978) who hypothesized that the rate of wage change in a single labor force group should depend on the unemployment rate of that group and its wage relative to the wages of other groups. The results are interesting for several reasons. First, the wage data that are used in these tests come from a survey not previously used in the estimation of aggregate wage equations. The data are from the National Survey of Professional Administrative, Technical and Clerical Pay (PATC).7 This survey is conducted annually by the Bureau Received for publication September 18. 1981. Revision accepted for publication May 4, 1982. * The University of Wisconsin. The author wishes to thank Gregory Krohn and Bruce Chapman for their excellent research assistance. Helpful comments were received from Paul Gertler and the participants at a seminar at the National Commission for Employment Policy. This research was supported by Grant Number 99-0-2289-50-11 from the National Commission for Employment Policy, and Contract Number 20-06-08-11 from the Employment and Training Administration, U.S. Department of Labor. ' See, for example, Lucas (1973) and Sargent and Wallace (1975). 2See Dunlop (1977). 3See Phelps and Taylor (1977) and Fischer (1977). 4McNees (1979) provides a way to distinguish this position from the one in the subsequent phrase. 5 See Okun (1978) for a summary of studies of this kind. 6See Hicks (1955) and (1974, pp. 59-85). Bureau of Labor Statistics (1980).

James A. Dunlevy, Don Bellante, Net Migration, Endogenous Incomes and the Speed of Adjustment to the North-South Differential, The Review of Economics and Statistics, Vol. 65, No. 1 (Feb., 1983), pp. 66-75

SUPPLY behavior in international trade has been notoriously difficult to capture empirically. Indeed, so few published supply studies exist that Stern, Francis, and Schumacher's (1976) bibliographical survey of price elasticities in international trade devotes over 350 pages to demand estimates but barely 10 pages to supply estimates. In recent years, only Goldstein and Khan (1978) and Dunlevy (1980), using simultaneous-equation estimation techniques, have reported estimates of supply behavior in international trade.' Exogenous shocks to demand and supply for traded goods in general influence both quantity and price. For supply estimates, it is unclear a priori whether the response is more appropriately specified with quantity or price as the dependent variable. However, if supplying firms in an uncertain world pursue pricing strategies based on past market performance (as in Zabel (1981)), the appropriate specification is a supply-price equation. In this case, prices respond to lagged quantities, which implies that the traditional supply-quantity specification (with present and past prices as explanatory variables) cannot capture the dynamic supply behavior. In this study, we explore the hypothesis that previous attempts to estimate supply behavior have generally failed not only because of the well-known problem of simultaneity bias, but also because quantity rather than price was specified as the dependent variable. Section II presents and discusses traditional supply-quantity equations based on quarterly data for aggregate exports and imports for the United Kingdom and the United States from 1947 to 1979. Section III briefly discusses the theoretical rationale of a supply-price specification and presents estimates of supply-price equations based on the same data. Section IV evaluates the empirical evidence to determine whether a supply-quantity or supply-price formulation is more appropriate, and compares estimates of long-run price elasticities of supply based on the two approaches. A final section summarizes the conclusions.

Stephen E. Haynes, Joe A. Stone, Secular and Cyclical Responses of U.S. Trade to Income: An Evaluation of Traditional Models, The Review of Economics and Statistics, Vol. 65, No. 1 (Feb., 1983), pp. 87-95

This paper reports on another attempt to statistically uncover evidence of embodied technological change as an explanation of changes in labor productivity in the United States. In this version of the test, an interregional cross-section, time-series sample of data was used. While the hypothesis has a lot of appeal, it has proven difficult to find manifestations of embodiment in econometric tests. This study has proven to be no exception. Despite the unique data set, results were again not supportive of the hypothesis. A possible limitation of this test is that the time period studied may have been too short. REFERENCES

Many commentators believe that the phenomenon of urban sprawl, which is characterized by vigorous spatial expansion of urban areas, is a symptom of an economic system gone awry. By transforming pastoral farmland into often-unattractive suburbs, sprawl is thought to disrupt a natural balance between urban and non-urban land uses, leading to a deplorable degradation of the landscape.' This sentiment is often translated into policy through zoning restrictions designed to inhibit the conversion of land from agricultural to urban use (see Bryant and Conklin (1975)). The economist's view of urban expansion stands in stark contrast to this emotionally-charged indictment of sprawl. Economists believe that urban spatial size is determined by an orderly market process which correctly allocates land between urban and agricultural uses. The model underlying this view, which was originally developed by Muth (1969) and Mills (1972) and more completely analyzed by Wheaton (1974), suggests that urban spatial size is determined in a straightforward way by a number of exogenous variables. By showing empirically that urban size is related to the given variables (population, income, agricultural rent, and commuting cost) in the manner predicted by the model, the present paper achieves two goals. First, the empirical results suggest that the economist's view of urban sprawl is justified: rather than being determined by a process which indiscriminately consumes agricultural land, urban sizes are the result of an orderly market equilibrium where competing claims to the land are appropriately balanced.2 Second, by confirming the urban size predictions of the underlying model, the empirical results constitute yet another piece of evidence validating the basic framework of urban economic analysis.3 The plan of the paper is as follows. Section II sketches the structure of the Muth-Mills model and presents the main comparative static results relevant to urban sprawl. With the model's predictions in focus, section III discusses the sample and the data, and section IV presents the empirical results. Section V offers conclusions.

N recent years a great deal of research has been directed to the modelling and measurement of technical and allocative efficiency in production. With few exceptions this research has been restricted to single-product firms.' However, recent developments in duality theory have facilitated the extension of this research to multi-product firms. The main purpose of this paper is to develop a model of the multiproduct firm in which the possibilities of both technical and allocative inefficiency are incorporated in an econometrically useful way. The first model we develop includes a nonneutral2 type of technical inefficiency and three distinguishable types of allocative inefficiency-output mix, input mix, and scale. Each type of inefficiency is costly to the firm, in the sense that each causes a reduction in profit beneath the maximum value attainable under full efficiency. The cost of each type of inefficiency depends on the magnitude of the inefficiency and the structure of the underlying production technology. In the second model we develop, technical inefficiency remains nonneutral, but allocative inefficiency is not generally decomposable into output mix, input mix and scale components. However, both technical and allocative inefficiency remain costly to the firm, the cost of each type of inefficiency depending on its magnitude and the structure of the underlying production technology. We model the technology of a competitive profit maximizing multi-product firm with the dual profit function. This enables us to use Hotelling's Lemma to generate a system of profit maximizing output supply and input demand equations. These equations are then modified to allow for the possibility of technical and three types of allocative inefficiency. A virtue of using the profit function to represent production technology is that it permits a straightforward comparison of maximum profit under full efficiency with actual profit, and with the profit that would result from any combination of the four types of inefficiency. This enables us to allocate the cost of inefficiency to each of four components. Our model of inefficiency is parametric, and is embedded in a Generalized Leontief profit function, although any flexible specification of the profit function can be used. The model is developed in sections II-IV. Estimation of the model is considered in section V. An empirical example designed to illustrate the workings of the model is discussed in section VI. Section VII concludes.