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This paper investigates the relation between advances in technology and trends in the gender wage gaps in the US service industry. Using quarterly US Current Population Survey data on employment and wages by four major occupations between 1979 and 2001, the paper estimates a constant elasticity of substitution production function (CES) that incorporates male and female labor inputs, a non-labor input and a productivity parameter function that captures non-neutral technological change. The model is estimated by two stage least squares (2SLS) with cross-equation restrictions. The results reveal a narrowing effect of technological change on the female-male wages for the highest skill level occupation (managerial, professional occupations). This effect is robust to controlling for the unexplained gender wage gap and to using direct measures of technological change. The effect of technological change on the gender wage gaps for the other skill levels tends to diminish or disappear altogether once changes in unexplained gender wage gaps are adjusted for. The results highlight the importance of considering the unexplained gender wage gaps in examining the effect of technological change on the gender wage gaps.

This paper uses the Fourier flexible form to jointly approximate utility and service flows from durable and nondurable goods. In contrast, parametric functions are usually not flexible enough to accurately approximate nonseparability and often give inconsistent results. This paper calls these inconsistent results the consumer consumption conundrum. The author calculates Morishima elasticities of substitution because Charles Blackorby and Robert R. Russell (1989) show that the Allen-Uzawa measure of substitution is incorrect. Results show that substitution between commodities are variable over time. Therefore, policy intended to affect consumption should take the variability of substitution into account because constant elasticity of substitution functions may give misleading conclusions. Copyright 1997 by Ohio State University Press.

This paper deals with the problems of partial equlibrium analysis by presenting estimates from a static ten sector computable general equilibrium (CGE) model of the U.S. economy calibrated to the year 1984. Following the introduction, the paper is organized as follows. Section 2 outlines the model. Section 3 details the sources of estimates of premia on preexisting QRs (quota rents) in 1984 and the sources for the parameters describing demand and supply elasticities. Welfare and employment estimates of QR removal are presented by industry and in the aggregate in Section 4. Conclusions follow in Section 5.

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 performance of three frontier steam electric generation estimators is compared in terms of the consideration given to new production technologies and their technical efficiency. The Cobb-Douglas, constant elasticity of substitution, and translog production functions are examined, using the Aigner-Chu linear programming, the sophisticated Aigner-Lovell-Schmidt stochastic frontier, and the direct method of adjusted ordinary least squares frontier estimators. The use of Cobb-Douglas specification is judged to have narrowed the perceived difference between competing estimators. The choice of frontier estimator is concluded to have a greater effect on the plant efficiency than functional form. 19 references. (DCK)

Numerous empirical studies have been undertaken in order to determine those factors that influence manufacturing investment in fixed capital (see Jorgenson, 1971). Most multi-industry studies employ quarterly data for a dozen or more two-digit industry groups. Results consistent across industries are difficult to achieve on account of the wide range of alternative specifications and selection of the best fitting among them. Comparison of results from different studies is further complicated by the use of different time periods, data sources, lag structures, and so on, or by the absence of a post-data model evaluation. Systematic comparisons are found in only a relative handful of empirical studies (see Jorgenson, Hunter, and Nadiri, 1970a, 1970b). This paper presents results for several alternative econometric models of investment in the U.S. iron and steel industry. Two general specifications are dealt with here: first, a nonlinear-neoclassical (N-N) model incorporating a constant elasticity of substitution (CES) production function and, second, a linear-neoclassical (L-N) model incorporating a liquidity variable and a non-specific production function. The empirical results provide a means of discriminating among competing hypotheses on the basis of their performance. However, we avoid unlimited data mining and, consequently, do not explore every possible specification for each model. The paper is divided into three sections. The first section discusses the investment models and presents empirical results based on quarterly data for the period 1960-73. Section II presents forecasts for 1974-76, and section III summarizes the main results from the study and comments on the investment function controversy. Data sources and variable definitions are contained in the appendix. I. The Investment Models and Empirical Results

In his recent article in this REVIEW, Berndt (1976) reported that estimates of the elasticity of substitution (a) from the constant elasticity of substitution (CES) production function, are "extremely sensitive to differences in measurement and data construction" (p. 59). Almost a decade earlier Nerlove (1967) reached a similar conclusion when he offered his often quoted remark that "even slight variations in the period or concepts tend to produce drastically different estimates of the elasticity" (p. 58). Econometric studies based on cross-sectional data have produced diverse values of the elasticity of substitution. This diversity of results has been explained partly by a variety of hypotheses. ' However, since the publication of the Arrow, Chenery, Minhas, and Solow (ACMS) article in 1961, which introduced the constant elasticity of substitution (CES) production function, direct estimates of a from the "wage equation"2 by Solow (1964), Griliches (1967b), Dhrymes and Zarembka (1970), Zarembka (1970), Zarembka and Chernicoff (1971), and others have assumed that commodity price (P) is constant across regions. Although the assumption of constant commodity price (P) across regions biases3 the estimated value of ar, the assessment of magnitude4 of the bias varies drastically from negligible (Griliches, 1967a) and least important (ACMS, 1961, p. 238), to important (Nerlove, 1967, p. 74). We shall show here that the bias due to the assumption of constant prices can be removed through the introduction of a certain type of "mark-up" prices. Accordingly, in this presentation, we (1) introduce a "mark-up" pricing strategy that sidesteps the ACMS model and relaxes the assumption of constant commodity price, (2) demonstrate that direct estimates of a from the "wage equation" overestimate a, and (3) provide some empirical estimates of the elasticity of substitution for the two-digit manufacturing industries across SMSAs and for the last four Censuses of Manufactures.S5

Historically the problem of negative demand has been encountered in constructing spatial demand cones due to the use of linear demand functions. One solution to this problem is explored in this pap...

T HE CES (constant elasticity of substitution) production function derived by Arrow, Chenery, Minhas, and Solow [2] has become widely known and widely used. Possibly the weakest point of the SMAC (Arrow, Chenery, Minhas and Solow) formulation is the assumption of". . . the existence of a relationship between V/L (value added per unit of labor) and W (the wage rates), independent of the stock of capital" [2, p. 231]. If this assumption does not hold, the value of the elasticity of substitution derived from the estimated CES function may be biased. The CES function is also subject to the limitation that the value of the elasticity of substitution is constant, although not necessarily unity. However, when the capital/ labor ratio varies, due to changes in the factor price ratio, it is possible that the elasticity of substitution will vary as the capital/labor ratio varies. The purposes of this paper are (1) to derive a more general form of the CES production function that does not depend on the SMAC assumption of independence and with a property of variable elasticity of substitution, (2) to examine the elasticity of substitution of the new function, and (3) to present some evidence of the desirability of using the new function.

THE AGGREGATE PRODUCTION FUNCTION is one of the basic tools in the modern theory of economic growth. In recent years the increased interest in this subject has brought forth two types of improvement in the specification of the aggregate production function. First, the form of the production function has been noticeably extended from the constant elasticity of substitution functions (CES [1]) to variable elasticity of substitution functions, such as the linear elasticity of substitution function [17], the production function which combines CES and Cobb-Douglas functions [9] and [4], the production function in which the elasticity of derived demand is constant (CEDD) [14] and [15], etc. Secondly, the problems of specifying and measuring the types of technical progress that are consistent with a given form of the production function have been elucidated. For instance, in a theoretical paper [16] the present authors have studied extensively the implications of various types of " neutral " technical progress that result from the invariant relationships between pairs of important economic variables. Subsequently we have estimated production functions and technical progress on the basis of linear and log-linear invariant relationships between pairs of these variables [3]. The purpose of the present paper is to extend the scope of the above mentioned papers. We proceed by dropping the two-variable restriction and allowing general multi-variate analysis among subsets of production variables. In particular, alternative specifications of production functions and of technical progress will be obtained by specifying linear relationships between rates of change of such production variables as labor-capital ratio, output-capital ratio, wage rate, interest rate, marginal rate of substitution, and profit share. A general differential equation is derived from the linear combination of all these variables. Its solution yields a new class of production functions which includes the CES, Cobb-Douglas and their combination as special cases and for which technical change is factor augmenting. This new class of production functions may appropriately be called the "log-linear production functions." The model is tested against time series data for two digit industries in the United States 1949-65. The question asked is this: what production functions and what types of technical progress are we testing against each other when we

N the past two decades our understanding of the investment process has expanded greatly. Central to this expansion is the notion that the "desired" or "optimal" stock of capital depends, not only upon the level of output, but also upon such factors as prices, interest rates, technological change, and tax policy. Equally central is the closely related proposition that the actual stock of capital adjusts to its optimal value only after a considerable lag, possibly several years. In contrast, dynamic input-output forecasting models typically treat investment in much the same fashion as early accelerator theories: for each industry net investment is given by the change in output multiplied by a fixed capital coefficient. Thus lags and endogenously determined changes in the "optimal" capital coefficients cannot be accounted for without considerable difficulty. However valuable this traditional treatment may have been in the past (and there is no doubt that it was), a wholly different approach is now required if input-output models are to benefit fully from accumulated knowledge about the investment process. In particular, fitted investment equations, rather than matrices of capital coefficients, should be the basis for forecasts. A primary purpose of this paper is to estimate such a set of equations for 68 equipment purchasing sectors as defined in the 1958 inputoutput study [10]. The regression model, first developed by the author in [19] and subsequently used by Robert Coen [3], is a generalization of work done by Robert Hall and Dale Jorgenson [11]. Their model, in addition to handling the conventional determinants of investment, is able to account for changes in a wide variety of tax policy variables: depreciation methods, tax lives, emergency amortization provisions, and investment tax credits. These variables affect investment by altering the user cost of capital and, consequently, the optimal stock of capital. Unfortunately, the extent to which changes in the user cost affect the optimal stock of capital is not estimated by Hall and Jorgenson. Rather, the effect is constrained by assuming a Cobb-Douglas production function. To remedy this deficiency, the generalized approach presented here actually estimates the impact of the user cost on optimal stocks with the aid of a constant elasticity of substitution (CES) production function [1]. Since the Cobb-Douglas is a special case of the CES, estimates of the generalized model provide a test of the Hall-Jorgenson hypothesis. The plan of the paper is as follows. Sections II and III outline the theory of investment underlying the regression model and explain the various assumptions and sources relied upon in the construction of the data. Then, section IV presents the regression results and summarizes the most important findings. Finally, in order to illustrate the usefulness of the fitted equations, section V estimates the impact on investment of a hypothetical repeal of the tax credit for 1962-1967.

The paper describes a Fortran IV program for estimation of a non‐linear‐in‐the‐parameters production function known as the Constant Elasticity of Substitution (CES) model (see Arrow et al., 1961). This model, specified with multiplicative errors, is estimated by applying an approximate modified Newton method in which second‐order derivatives are not computed; the method is discussed in connection with the technique used for restraining the parameters in the iterative process and ensuring non‐negative marginal products. The program has been tested for a large number of samples the estimation of which has been shown sufficiently accurate and rapid.

The elasticity of substitution between capital and labor is a fundamental parameter describing the structure of production in an economy or its component sectors. This elasticity is a measure of the relative ease with which these factors may be substituted in production; and for this reason, it plays a crucial role in most modern partial and general equilibrium models of income distribution [1, 3, 8, 11, 12, 13, 14, 15, 21, 22, 23, 25, 27, 28, 37, 38], international trade [3, 24, 26], and economic growth [1, 3, 13, 31, 36, and comments on 31, in 6, 32]. Following the introduction of the constant elasticity of substitution (CES) production function by Arrow, Chenery, Minhas, and Solow (referred to hereafter as ACMS) [3], a great deal of professional interest has centered on the estimation of the elasticity of substitution (a) in the aggregate U.S. economy and among its industries or sectors. In particular, ACMS showed that under the assumptions of (i) constant returns to scale, and (ii) purely competitive product and factor markets, the elasticity of substitution could be estimated from the

DESPITE A VAST LITERATURE ON THE DETERMINANTS of investment behavior, questions about the way in which relative prices and output influence investment expenditures have not been satisfactorily resolved. In the "neoclassical" investment models, relative prices and output are commonly introduced as a composite variable, a procedure that does not allow for the possibility of separate and distinct effects of these two determinants on the level of investment expenditures.' Yet separation of these effects is critical * I am indebted to members of the Brookings panel for their important and considerate comments. I have benefited greatly from the competent assistance of Edward Matluck and Veena Gupta; I am grateful to Rose Ferro and Laura Chasen for their efficient secretarial help. 1. The neoclassical specification follows from the assumption about the form of the underlying production function. If the production function is considered to be CobbDouglas, the elasticity of investment with respect to relative prices and output is, by assumption, unity. If the production function is constant elasticity of substitution, and a vintage model of capital is assumed, the pattern of responses of investment to price changes and to output changes will differ. See Charles W. Bischoff, "The Effect of Alternative Lag Distributions," in Gary Fromm (ed.), Tax Incentives and Capital Spending (Brookings Institution, 1971), pp. 61-125. For a survey of the empirical performance of several econometric investment models, see Charles W. Bischoff, "Business Investment in the 1970s: A Comparison of Models," Brookings Papers on Economic Activity (1: 1971), pp. 13-58. Intermingling of rental prices and output is also defended on the grounds that the data on rental prices are subject to substantial errors of measurement. See Arnold Harberger's discussion in Tax Incentives, pp. 256-62. This argument is spurious, for if the price component of the synthesized variable is subject to measurement errors of unknown magnitude, the resulting estimates of the investment equations are certainly unreliable.

BY exploitation, we mean that a factor of production is receiving less than its marginal revenue product. Relative exploitation connotes that the marginal rate of technical substitution of two factors is not equal to the ratio of their scarcity prices. Hence, either both factors may be exploited, but in different degrees, or one factor may be exploited while the other is not. In the present paper, a measure of the change in relative exploitation of capital and labor is presented together with empirical results for three two-digit industries (machinery except electric, primary metal industries, and electric and gas utilities), where the observations are drawn from the period, 1948-1960. Knowledge of variations in relative exploitation is useful in quantifying and explaining the sources of change in the distribution of income between the factors of production. This, in itself, is sufficient justification for focusing on the change in relative exploitation rather than the level. Although there may be more intrinsic interest in a measure of the level of exploitation as defined above, the framework used below does not lend itself to such a measure. The paper is laid out in the following manner. An elementary model of exploitation within a constant elasticity of substitution (CES) framework is presented first. This is followed by an econometric specification of one of the equations which must be tested in order to derive the required measure, while the succeeding section is devoted to the direct estimation method of the second required equation, the CES production function. Next, the empirical results for three selected industries are presented and discussed. The subsequent section contains the quantification of the changes in relative exploitation. In a later section, some problems with the framework and measuring procedures are discussed.

Обсуждаются следующие темы: чистая теория производства, функциональное распределение дохода, технический прогресс, источники международных конкурентных преимуществ. Анализируются эластичность замещения между трудом и капиталом в обрабатывающей промышленности; производственные функции различного типа.

W ITH the pathbreaking article by Arrow, Al Chenery, Minhas and Solow [1] introducing the constant elasticity of substitution (CES) production function, interest in production theory has multiplied. No longer is the Cobb-Douglas function the workhorse for neoclassical theory; rather, the role of the production function has been examined anew in the theory of the firm, in growth theory, and in the theory of international trade. This re-examination has taken the form (1) of theoretical analysis of the role of the elasticity of substitution, (2) of empirical estimation of the elasticity, and (3) of the introduction of new forms for the production relation, e.g., Zellner and Revankar [14] and Revankar [8]. Unfortunately, knowledge about the appropriate micro-economic or macro-economic production function seems further away now than before 1961, the year of the ACMS article [1]. Nerlove [7, p. 58] reports that "even slight variations in the period or concepts tend to produce drastically different estimates of the elasticity [of substitution] " and he presents a summary of empirical studies of the CES production function to support his conclusion. In this paper it is first shown that Nerlove's conclusion on the definition of time periods is an inappropriate interpretation of previous estimates (however, part of the difficulty was outside Nerlove's control); that in fact changes in period do not produce significantly different estimates of the elasticity. To demonstrate this contention, estimates of the elasticity from the factor demand equation for labor for two consecutive years are obtained. However, evidence of serial correlation leads to a correction of the labor and wage rate variables for quality variation in the workers over states. Since this correction does not remove the serial correlation, the estimation is then undertaken using the efficient estimation technique of Zellner [12] and the results suggest that use of different time periods does not produce different estimates of the elasticity. Second, the estimates of the elasticity are constrained to be equal for the two years and the efficient estimation techniques are again used with the labor quality correction included. A test on the null hypothesis that the elasticity of substitution equals one for each industry indicates that the elasticity does not in general depart significantly from one. This conclusion from estimates of the labor demand equation supports a similar conclusion of Griliches [3, p. 292] based upon least squares regressions for two-digit manufacturing industries. However, he uses a smaller sample (only 1958 data) than here, and his estimates are biased toward one because labor quality variation was not included in his two-digit industry estimates (he only considers labor quality variation in his estimates for manufacturing as a whole). Third, direct estimates of the CES production function are obtained for each industry using Kmenta's approximation [5]. Again, using efficient estimation and correcting for labor quality differences across states, the elasticity of substitution is not in general significantly different from one. It is incidentally shown that returns to scale can be accepted as being equal to unity for most industries.

JN recent years, economists have presented empirical evidence that improvements in efficiency have accounted for most of the growth in aggregate output in the United States and many other countries during the past half century. Robert M. Solow has presented a Cobb-Douglas production function model in which he explicitly assumes that this increased efficiency (technical progress) is due to improvements which are embodied in new physical equipment.' The model is easily extended to the case in which improvements may be embodied in new physical equipment, or may be due to other causes (i.e., disembodied improvements).2 Furthermore, Solow has demonstrated that the explicit assumption that technical progress must be embodied in new physical equipment can be incorporated in a constant elasticity of substitution (CES) production function model.3 Such a model is more general than the embodied Cobb-Douglas model in that the latter implies that the elasticity of substitution is not only a constant, but also equal to one. Solow did not consider the case in which technical progress may also be disembodied, but again it is easy to incorporate this into the CES model. This will be done below. The purpose of this paper is to point out one striking difference between Solow's Cobb-Douglas, and his CES model, when it is assumed that technical progress may be either embodied or disembodied. Embodied technical progress in the Cobb-Douglas model has no influence on the elasticities of output with respect to labor and with respect to the net capital stock. In that model, it is not possible to isolate the influence of embodied technical progress from that of disembodied progress. In the case of the CES model, however, the elasticity of output with respect to capital relative to the elasticity with respect to labor is influenced by the rate of embodied progress. Another feature of the CES model is that it is possible to state output per labor unit as a function of the marginal product of labor, and of a time shift factor which is accounted for only by disembodied technical progress. Given these facts, given data on output, labor, and the net capital stock, and finally, given the assumption that labor and capital tend to be paid their marginal products, it is possible to obtain upper and lower bound estimates of the influence of embodied and disembodied progress on output. The procedure in this paper will be: first, to outline the derivation of the Cobb-Douglas model in which progress is assumed to be either embodied or disembodied; second, to describe the extension to the CES model; and third, to demonstrate how the CES model allows us to distinguish between the effects of embodied and disembodied progress on output, and to discuss some of the implications of the CES model.

In recent years the elasticity of substitution between capital and labour has been recognized as a basic characteristic of the technology of an industry or an entire economy with important implications for international trade, distribution, growth and taxation. A substantial number of studies have now provided estimates of the substitution elasticity for the United States economy and for individual American industries[2, 4, 6, 7, 8, 10, 11, 12, 13, 15, 20].2 No estimates for Britain have been reported previously. The current study began by estimating the elasticity of substitution using British inter-industry data. The values obtained by using the "indirect" estimation procedure originally proposed by Arrow et al. [2, referred to below as ACMS] vary substantially from year to year. An alternative "direct" method of estimation was then applied; these results suggest a substantially higher elasticity. Section I of this article reviews the basic theory of the constant elasticity of substitution (CES) production function and presents the estimates obtained for Britain. Some objections to the traditional indirect estimation method are discussed in Section II. Section III describes an alternative procedure and presents the resulting estimates. Section IV comments on several other CES estimation procedures.