Knowledge that Transforms

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.

THE hypothesis attributed to Fisher (1930) and more recently the innovative investigation by Fama (1975) have predisposed many economists to treat the expected rate of interest as a constant. At the very least, as a magnitude, the expected interest rate is appealingly viewed as being independent of monetary phenomena. The late 1970s and early 1980s have produced events which force reevaluation of the maintained hypothesis of constancy of the expected rate (hereafter referred to as the real rate). For example, from December 1980 to June 1981 the expected rate of inflation fell by 165 basis points from an annual rate of 10.51 % to an annual rate of 8.86%.' Over the same period 3 month Treasury bill rates continued to remain largely between 14% and 16% with average yields of 15.02% in December 1980 and 14.95% in June 1981. In order to reconcile such facts, one must either believe that security markets no longer fully reflect changes in anticipated inflation in nominal market rates, or that a large drop in anticipated inflation which is not accompanied by a drop of similar magnitude in nominal interest rates, is due to an offsetting rise in the rate.2 Statistical investigations regarding the possibility of movements in the rate have appeared with increasing frequency since publication of Fama's (1975) provocative article.3 Nelson and Schwert (1977) argued that Fama's test of the joint hypothesis of market efficiency and constancy of the rate was not sufficiently powerful and after applying more powerful tests concluded that the data permitted rejection of the hypothesis of constancy of the rate. Other investigations including those by Carlson (1977), Garbade and Wachtel (1978) and Levi and Makin (1979) have rejected the hypothesis of constancy of the rate while tending to support the hypothesis that market interest rates include an efficient inflationary premium. Tanzi (1980) has, along with others, emphasized the role of taxes in interest rate determination. More recently investigators have moved from merely testing the hypothesis of constancy of the rate to searching for an explanation for the rate movements suggested by a large body of statistical evidence. Mishkin (1981) and Fama and Gibbons (1982) have investigated the relationship between the rate and anticipated inflation suggested by Mundell (1963) and Tobin (1965).4 Levi and Makin (1979, 1981), Hartman (1981) and Hartman and Makin (1982) have considered effects of inflation uncertainty on the rate. Dwyer (1981) has found that the rate is independent of predictable changes in the supply. This paper derives a Fisher-type interest rate equation from a structural model similar to that employed by Sargent (1973) for other purposes. The primary differences involve inclusion of a government sector and a simple open economy specification along with introduction of a role for Received for publication February 22, 1982. Revision accepted for publication September 3, 1982. *University of Washington and National Bureau of Economic Research. This work was supported by the National Science Foundation under (irant No. SES-8112687. I would like to thank without implicating Charles Nelson, Richard Hartman and especially Andrew Criswell for excellent help in estimating the equations. An earlier version of this paper was presented at an FMME Conference at NBER where many useful suggestions were provided. ' This figure is based on Livingston survey data for 6 month horizon expectations regarding the consumer price index (CPI). The 12 month horizon figure for CPI also indicated a drop of 165 basis points while 6 and 12 month horizon numbers for WPI indicated drops of 192 and 174 basis points, respectively. Updated Livingston survey data are now compiled by the Federal Reserve Bank of Philadelphia. 2Summers (1982) has argued that nominal interest rates do not adjust by the full amount implied by the Fisher hypothesis modified to allow for marginal tax rates on interest earnings. His results based on both preand post-World War II data arise from equations which employ actual inflation rates in place of anticipated inflation and which generally do not include variables to control for movements in the expected rate. 3Even well before the investigations discussed here Irving Fisher himself reported, based on an investigation of market interest rates during the late 19th and early 20th centuries in London, New York, Berlin, Calcutta and Tokyo, that ' the rate of interest in terms of commodities is from seven to thirteen times as variable as the market rate of interest expressed in terms of money (Fisher (1930), p. 415). 4 Mishkin (198 1) found a significant negative impact upon the rate of a lagged actual (CPI) inflation rate taken as a proxy for anticipated inflation. An ARIMA (0, 1, 1) inflation model with a seasonal MAI term also provided an expected inflation proxy with a significant negative impact on the rate. Mishkin (1982) is discussed below.

An extended Cobb-Douglas production function is developed and estimated in order to examine the extent to which the decline in measured productivity in underground coal mining can be attributed to (1) changes in safety conditions which reflect movement along a product transformation frontier relating safety and marketable output and (2) a shift downward of the entire transformation surface. The model incorporates work-related accidents as a joint output and accounts for the discrete nature of the technological choices available in underground mining. The results indicate that movements along the product transformation curve relating accidents and marketable output do not account for the decline in measured productivity. This decline instead reflects a shift downward of this frontier - a real decline in potential production of marketable output. The non-linear pattern in technological change parameters and differences in these parameters across technologies indicate that a variety of factors have influenced productivity trends including CMHSA and the 1974 contract between union and management. 14 references

A major goal of social programs in a time of fiscal austerity is to focus available assistance on those households in the greatest need. This seemingly simple dictum has become increasingly difficult to follow as the dynamics of poverty have been clarified through analysis of longitudinal panel data in recent years. We can illustrate the importance of these dynamics using the following findings about the future incomes of the 22 million people in poverty in 1967.

AT least since Kaldor (1935), a number of economists have argued that indivisibilities and accompanying economies of scale in spatially extended economies can negate the zero profit result generally associated with free entry.' The essential argument is that if there are industries in which transportation costs are non-negligible and size economies call for firms that are large relative to local demand, even the most intense competition need not result in a zero profit equilibrium. Recently, Eaton and Lipsey (1978) have provided the analytical underpinnings for Kaldor's largely intuitive argument and demonstrate that pure profits can remain even with free entry of new firms and price competition. Eaton and Lipsey (1978, p. 467) suggest that their result depends critically on the.existence of the following conditions: (1) the average total cost curve is declining over some initial range; (2) customers are geographically spread out and intermingled with firms; (3) transport is costly; and (4) once the firm enters the market it has location-specific sunk costs.2 This paper offers an empirical investigation of the non-zero profit argument as applied to the U.S. cement industry. On a priori grounds, the cement appears to meet the necessary conditions for existence of positive, site associated profits. The existence, or at least the belief that the a priori conditions are satisfied has provided a basis for using the as a representative case. Scherer (1980, pp. 252-258), for instance, offers a textbook example of entry deterrence through plant location strategy that combines elements of space and the standard deterrence argument.3 Scherer then notes that, In an interview study of plant-size and location decisions in 12 industries across six nations, the author observed by far the strongest emphasis on geographic space packing as an entry-deterring strategy in the cement industry (p. 257). Scherer's example of entry deterrence via strategic plant proliferation is an extension of the Kaldor non-zero profit argument. However, the non-zero profit argument has at least one major drawback: profits in the cement have not been significantly above normal for any sustained period. The first section of this paper considers the evidence of the cement industry's approximation to the Eaton and Lipsey conditions and its historical profitability. Given the contradictory results between apparent satisfaction of the a priori conditions and the lack of supernormal profits a reformulation of the basic model is presented. An explanation offered here for the absence of supernormal profits is derivable from the property rights paradigm. The usual procedure in analyzing the reaction to new entrants in a spatially extended model has been to assign either initial locations to a set of firms or provide for a prearranged pattern of sequential entry. Both procedures implicitly assign property rights to locational rents and ignore the vital element that there will be competition to be the first plant in a given location.4 With demand for the product growing, competition to be first at a given location will insure that the timing of construction of the

RECENT economic developments have aroused substantial interest in the treatment in the Consumer Price Index (CPI) of the cost of shelter for homeowners.' From December 1977, when the latest version of the CPI was introduced, until December 1980, the all-items CPI increased at an average annual rate of 11.6%, while the homeownership component increased at an average annual rate of 16.2%. Relative to all of the other goods and services in the CPI, the homeownership component has increased by 17.5% over the same time period. If the relative price of homeownership had remained constant the growth rate of the CPI would have been reduced to 10.1%. The question which has been raised is whether the rapid relative increase in the homeownership component, which has had such an important impact on the CPI, truly reflects changes in the cost of shelter. This question is not only important, but difficult, encompassing many subsidiary questions and auxiliary issues. The purposes of this paper are threefold: (1) to outline briefly a conceptual framework for the CPI, which leads to a straightforward specification of what the shelter component of the CPI should measure, (2) to evaluate the theoretical properties of alternative procedures designed to approximate this measurement objective and (3) present empirical evidence on the operational difficulties involved in pursuing a new approach to shelter cost measurement. Two main conclusions are reached. First, on both theoretical and empirical grounds, a approach to measuring shelter costs for owner-occupants is preferred. Second, an estimated rental equivalence measure has grown more slowly over (at least) the past six years, than the official CPI homeownership component. Given the way in which the CPI is used to escalate both private and public expenditures, these results demonstrate that the choice of measurement technique has important distributional implications.

13'1 rev . .:. Division of Agricultural Sciences UNIVERSITY OF~IFORNLA Working Paper No. 139 R.I>J:~ FUTURES MARKET EFFICIENCY IN THE SOYBEAN COMPLEX Gordon C. Rausser and Colin Carter GIANNINI FOUNDATION OF AGRICULTURAL. ECONOMICS L.IBRAIli'V iM· ( California Agric'u l tural ElqIeriment Station Giannini Foundation of Agricultural Economics March 1982