Knowledge that Transforms

IN recent years number of economists have found, or taken for granted, substantial positive interest elasticity of private saving, and several have concluded that the taxation of property income has played major role in depressing and investment and therefore economic welfare.' Thus, probably the most quoted of these studies, by Michael Boskin (1978), finds that a variety of functional forms, estimation methods and definitions of the real-after-tax rate of return invariably lead to the conclusion of substantial positive interest elasticity of private saving (p. 3). As consequence he states, current tax treatment of income from capital significantly retards capital accumulation... Rough estimates of the lost welfare $50 billion per year... . The most recent of these studies, by Lawrence Summers (1981), uses the Boskin empirical results to check corresponding findings based on assumed values of the relevant parameters in life-cycle model of aggregate behavior. Summers raises the ante in his estimate of the welfare gain associated with the elimination of capital income taxation, claiming it would exceed $150 billion annually, and noting that this conclusion rests on high positive interest elasticity of (p. 533). Summers notes that his larger interest rate effect reflects his additional allowance for wealth changes. Since these findings on interest elasticity are inconsistent with earlier studies,2 and have received widespread attention by political activists, it is important to determine how much confidence can be placed in the underlying analysis. This paper will demonstrate that there is little scientific justification for the recent literature purporting to show strong positive interest elasticity of saving, so that government tax policies predicated on such behavior rest on dubious foundation. The evidence to be presented will indicate that at the present stage of knowledge, we have no sound basis for alleging either strong positive or negative after-tax rate of return effect on saving. The only prior published examination of these recent potentially important findings of strong positive interest elasticity of private has been brief reference to the Boskin results in paper by Howrey and Hymans (1978), which was largely devoted to an analysis of what the authors call personal cash or loanable funds rather than private saving. These authors report that the significance of Boskin's results is sensitive to estimation period, inclusion of lagged unemployment, and use of alternative interest rate variables. They do not report the results of the alternative estimations, however, nor do they present consistent instrumental variable estimations, despite the fact that the latter provide Boskin with what he considers to be his best results. In this paper in striking contrast to the Boskin analysis, we show that using the best available proxies for the relevant interest rate variables (real expected after-tax rates of return, estimated both on an ex ante and on an ex post basis), the estimated interest elasticity of household and private is generally found to be either statistically insignificant or significantly negative and only rarely significantly positive, with the result depending on the specific interest rate series, period and consumption function used. Nor is this finding altered when the single equation estimation of this or consumption function is replaced by an instrumental variable, consistent estimation. As result, there does not seem to be much basis to Boskin's or Summers' strong criticism of the earlier literature which generally concluded that there was Received for publication May 14, 1982. Revision accepted for publication November 23, 1982. *University of Pennsylvania. See Boskin (1978), Gylfason (1981) and Summers (1981). 2 See the consumption function in either the Wharton model (The Wharton Mark IV Quarterly Econometric Model, Philadelphia, 1977 and updates) or the MPS Model (The Quarterly Econometric Model, Board of Governors of the Federal Reserve System, 1978 and updates).

even if it does not eliminate them completely. The primary effect of using individual expectations data rather than cross-sectional averages as a regressor is to introduce additional measurement error. Finally, the distinction between expectations and full informational efficiency is more than a semantic one. The failure to make this distinction seems to be the cause of substantial confusion in the literature. The distinction has become increasingly important with the advent of expectations macroeconomic models (see Lucas, 1973; Barro, 1976) which are driven by imperfections and asymmetries of information, yet in which each economic agent is assumed to process rationally the information he possesses. In particular, empirical tests which depend upon full informational efficiency can provide little evidence on the validity of the rational expectations hypothesis as that term has come to be used in macroeconomics.

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.

The article focuses on the relationships between the macroeconomic performance of political administration and their popularity or vote getting ability. All of the studies that has been performed to analyze the relationships agree that votes and popularity can be explained well by models which suppose that voters judge policy makers on the basis of retrospective evaluation of past macroeconomic outcomes. While conventional popularity functions assume that voters simply punish inflation and reward output or low unemployment, voters who understand the long and short run relationships noted above would evaluate policymakers differently. Inflation in a given period is largely determined by past expectations of inflation, which cannot easily be controlled by current policy choices. The results of a study done by the author, show that data on presidential popularity are consistent with the hypothesis that voters are concerned with the future consequences of current economic policy choices and are aware of the nature of constraints imposed by economic reality.

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