Measuring efficiency when competitive prices aggregate differences in product quality and risk

In perfectly competitive markets with homogenous goods, prices aggregate inputs and outputs into a money metric that allows production plans and, hence, firms to be ranked by their profitability. Standard techniques of efficiency measurement use this metric to estimate cost and profit frontiers that identify “best-practice” production, conditioned on these exogenous prices. However, when prices vary due to differences among firms in the quality of outputs and inputs and in how asymmetric informational problems are resolved, both quality and the production of information can be decision variables of the firm, and prices will have endogenous components linked to production decisions. For example, in banking, prices of financial inputs and outputs are linked to credit quality and, hence, to risk and, thus, aggregate both inputs and outputs and their risk characteristics as well as reflect how informational asymmetries in credit markets are ameliorated. This paper argues that these cases pose two serious problems for the standard techniques of efficiency measurement: (1) they underestimate inefficiency because, in conditioning on prices, they fail to account for the effects of suboptimal pricing strategies on profitability; and (2) in ignoring how production plans and pricing strategies affect market-priced risk, the standard techniques neglect the effects of different pricing strategies on the discount rate, on expected profit and, hence, on market value. Two alternative techniques that do not condition their frontiers on prices and that account for risk are described to show how they measure the efficiency of different pricing strategies as well as production plans. These two alternative models for measuring efficiency are employed to study how differences in pricing strategies affect the efficiency and market value of highest-level bank holding companies in the United States in 1994.     

Total factor productivity differences: Appropriate technology vs. efficiency

Recent development and growth accounting studies have established that total factor productivity is an important source of cross-country differences in income levels and growth rates. This paper makes two contributions. First, it examines the sensitivity of the development accounting results to the Cobb-Douglas specification of the production function. Second, within the Cobb-Douglas framework, it weighs evidence of the two alternative explanations of total factor productivity differences: the inefficiency view and the appropriate technology view. To accomplish these tasks, the world production frontier is estimated using a nonparametric deterministic approach known as data envelopment analysis. I find that the fraction of income differences explained by physical and human capital increases from 32% to 55% when departing from the Cobb-Douglas assumption. There is also evidence consistent with the appropriate technology view; countries with an inadequate mix of inputs are unable to access the most productive technologies. Moreover, the world technology frontier appears to be shifting out faster at input combinations close to that of the R&D leader. However, inefficiency appears to be the main explanation for low incomes throughout the world; it explains 43% of output variation in 1995, and its importance has increased over time.     

The measurement of environmental economic inefficiency with pollution-generating technologies

This study introduces the measurement of environmental inefficiency from an economic perspective. We develop our proposal using the latest by-production models that consider two separate and parallel technologies: a standard technology generating good outputs, and a polluting technology for the by-production of bad outputs. While research into environmental inefficiency incorporating undesirable or bad outputs from a technological perspective is well established, no significant attempts have been made to extend it to the economic sphere. Based on the definition of net profits, we develop an economic inefficiency measure that accounts for suboptimal behavior in the form of foregone private revenue and environmental cost excess. We show that economic inefficiency can be consistently decomposed according to technical and allocative criteria, considering the two separate technologies and market prices, respectively. We illustrate the empirical implementation of our approach using a dataset on agriculture at the level of US states.     

Energy price-induced and exogenous technological change: Assessing the economic and environmental outcomes

In this paper, we distinguish between factor/output substitution and shifts in the production technology frontier. Our model includes the by-products of carbon dioxide and sulfur dioxide emissions where the function requires the simultaneous expansion of good outputs and reductions in emissions. We estimate a directional output distance function for 80 countries over the period 1971–2000 to measure the exogenous and oil price-induced technological change. On average, we find substantial oil price-induced technological progress at the world level when long-term oil prices are rising, although the growth rate is more volatile in developed countries than in developing countries. The results also show that developed countries experience higher exogenous technological progress in comparison with developing countries, and the gap between the two has increased during the period of our study.     

AN ATTEMPT TO EXPLAIN DIFFERENCES IN ECONOMIC GROWTH: A STOCHASTIC FRONTIER APPROACH

Total factor productivity (TFP), factor accumulation, and growth are analysed for a panel of 40 countries in 2001–11. TFP growth and technical inefficiency are estimated using a stochastic frontier model. Environmental variables are found to have an important role in explaining differences in inefficiency across countries. Over 2001–11, the general improvement in technical efficiency of countries is almost outweighed by technological regress. Results indicate that differences in factor accumulation between OECD and emerging economies are more important than differences in TFP change to explain differences in economic growth. Results also indicate negative and significant random shocks for the OECD countries.     

Substitution and expansion effects in production theory: The case of joint production

This paper is concerned with a systematic examination of what happens when a firm that has been in equilibrium at certain prices of inputs and prices of outputs experiences a change in these prices. The mutual effects between inputs and between outputs and the cross effects between inputs and outputs are explored by means of various kinds of decomposition equations in production theory. A definition of the “normal” technology is given to show that inputs are not gross substitutes, nor are outputs, and that the input-output relations are not regressive.     

Productivity growth and catching up: a technology gap explanation

This paper seeks to explain why some countries have managed to catch up in terms of labor productivity over the period 1993–2007 in 76 countries. By integrating the technology gap research within the standard growth-accounting approach, we introduce a methodology which allows us to split total factor productivity (TFP) change into two components: conditional technical inefficiency and the magnitude of the technology gap. We find that labor productivity growth depends both on investment in fixed capital and TFP. Fast emerging economies exhibit patterns of growth based in particular on the reduction of the technology gap, confirming the role of investment in technological capabilities to spur productivity catch-up. Looking at change in the distribution of labor productivity, emerging countries managed to shift from low productivity toward a medium level of productivity thanks to technology accumulation. Less advanced countries cannot rely only on technology diffusion and learning by doing, policies for technological capabilities accumulation are necessary.     

中国制造业资本存量永续盘存法估计

KLEMS 项目的目的是在北美,欧洲和亚洲进行生产率的多国比较。本文讨论了 KLEMS 研究中估计资本存量的基本方法一永续盘存法及其经济含义。在这个研究中,根据中国的现有数据,应用永续盘存法估计了1985—1995年间,中国制造业分部门的资本存量。本文详细地分析了估计中所使用的数据,并讨论了所使用的假设与必要的数据调整,以及这些假设与数据调整所可能带来的估计中的误差。     

A micro,econometric investigation of choice of technology

This paper reports on a micro study of the determinants of technological choice utilizing a sample of observations at the man-machine level from operating plants. The large sample size permits econometric modelling - based on engineering and process analytic principles - of the production relationships involved. It also allows statistical testing of hypotheses. Among the determinants analyzed in the context of differentiated inputs and outputs are policies affecting prices on the factor and product markets. The particular case examined is the choice between imported and locally made looms for cotton textile weaving in Korea. However, methodological concerns are given equal weight in the discussion.     

Public and private inputs in aggregate production and growth: a cross-country efficiency approach

In a cross section of OECD countries, we replace the macroeconomic production function by a production possibility frontier, total factor productivity being the composite effect of efficiency scores and possibility frontier changes. We consider, for the periods 1970, 1980, 1990 and 2000 one output – GDP per worker – and three inputs – human capital, public physical capital per worker and private physical capital per worker. We use a semi-parametric analysis, computing Malmquist productivity indexes, and we also resort to stochastic frontier analysis. Results show that private capital is important for growth, although public and human capital also contribute positively. A governance indicator, a nondiscretionary input, explains inefficiency. Better governance helps countries to achieve a better performance. Nonparametric and parametric results coincide rather closely on the movements of the countries vis-à-vis the possibility frontier and on their relative distances to the frontier.     

Balance on unbalanced growth

Conclusions In his paper Baumol raised a number of important issues. Included are several knotty problems of an empirical nature: Can measures of outputs which we normally classify as services be reasonably divorced from measurement of the inputs of labor involved in their provision? Can commodities be satisfactorily divided into two classes: those for which the technology of production is inherently stagnant, and those for which technological progress is possible? It should be clear that in this paper no attempt has been made to address these or any other factual questions.What has been attempted is a demonstration that, on their own grounds, Baumol's rather pessimistic propositions about the behavior of an economy undergoing unbalanced productivity change can be balanced by rather more positive ones. Furthermore, those grounds have themselves been questioned: It has been argued that few normative implications can be drawn from the movement of relative prices, especially in the one-factor world used illustratively by Baumol, that a balanced expansion path is unlikely to be desired in such a world, and that little significance can be attached to changes in a real output index in this context. Finally, it has been shown that assuming a one-factor world results in hiding some of the important possibilities (for relative commodity and factor price behavior) under unbalanced growth. In particular, with not very unlikely sorts of factor complementarity, two of Baumol's propositions no longer hold.With 6 FiguresThe author is assistant professor of economics at Princeton University. He wishes to thank the Brookings Institution and the Ford Foundation for financial support which facilitated the writing of this paper, and to acknowledge helpful discussions with colleagues William J. Baumol, Richard R. Cornwall and Dennis E. Smallwood.     

A dynamic profit function with adjustment costs for outputs

It is well known that there are adjustment costs associated with many input factors, which delays firms response to changes in relative prices. Although adjustment costs are implicitly acknowledged when a cost rather than profit function is used, little attention has been given to adjustment costs for outputs. However, in many cases there will also be adjustment costs associated with changes in the product mix for multioutput firms. In this paper we formulate a firm’s optimization problem in a profit maximizing set up that allows adjustment costs for all netputs from which it follows that adjustment cost for some factors affect the adjustment of both inputs and outputs. We also show that one can test whether a factor is quasi-fixed or fully fixed.      

中国制造业技术投入与产出绩效的统计分析

为考察中国制造业技术进步情况,本文将中国26个制造业划分为高、中、低技术含量产业,并分析了各类产业的技术投入与产出绩效统计指标。分析结果表明,在技术投入方面中国制造业总体技术开发投入显著增加,高技术含量制造业的技术投入较其他产业明显占优,一些中低技术含量产业技术投入增长很快,表明有关产业已由单纯依靠劳动力成本竞争逐渐转向依靠技术进步进行市场竞争,但各产业普遍存在着人力投入增长速度落后于物力投入的情况。在技术产出方面,各制造产业的劳动生产率显著提高,高技术含量的产业相对其他产业更加突出,在产品创新方面高技术含量产业总体情况优于中等技术含量产业,后者又优于低技术含量产业,表明产品创新在高、中、低技术含量产业间的分布呈结构优化的趋势。不同产业对提高劳动生产率和产品创新两种市场竞争方式的侧重点有所不同。     

A hedonic-output-index-based approach to modeling polluting technologies

Despite some recent criticisms, the conventional radial distance function, which treats undesirable by-products as either frontier shifters or inputs, remains a popular go-to formulation of polluting production processes among practitioners. This unfading popularity is arguably driven by the ability of radial distance functions, unlike alternative directional distance functions, to allow for unit-free multiplicative changes in arguments as well as, by implicitly postulating the radial direction, to free researchers from the dilemma of having to explicitly choose the directional vector. In this paper, we offer a generalization of the standard radial distance function to polluting technologies that can accommodate undesirable by-products in a more economically meaningful way. Specifically, we propose modeling undesirable outputs via a hedonic output index, which is meant to ensure that pollutants are treated as outputs, as opposed to inputs or theoretically unregulated frontier shifters, while also recognizing their undesirable nature. By using a radial input distance function generalized to encompass an (unobservable) hedonic output index of desirable and undesirable outputs, we are able to meaningfully describe relationships between different products (including the complementarity of desirable and undesirable outputs) within producible output sets as well as to represent technically feasible polluting production possibilities given inputs. An empirical application of our methodology to the case of Dutch dairy farms in 2001–2009 demonstrates the complexity of interactions between outputs, thereby attesting to the value of more elaborate representations of production possibilities.     

Shadow directional distance functions with bads: GMM estimation of optimal directions and efficiencies

Because of its greater flexibility, the directional distance function (DDF) has been employed with increasing frequency to estimate multiple-input and multiple-output production, where inputs and outputs can be good or bad. However, typically researchers make three restrictive assumptions. First, they assume a direction of movement of firm production toward the frontier. Second, they assume that actual quantities of inputs and outputs are allocatively or price efficient. Third, they assume exogeneity of all inputs and all outputs, except for the normalized one. The first contribution of this paper is to include parameters to estimate optimal directions which correspond to the firm’s profit-maximizing (PM) position. The second contribution is to generalize the DDF to a shadow-quantity DDF. This entails adding distortion parameters to each input and output quantity of the DDF, creating shadow quantities. To estimate the shadow quantities and the structural parameters, we form the shadow DDF system, which includes the shadow DDF and all the first-order price equations from the shadow-PM problem. These include prices for bad inputs and bad outputs, where we approximate their missing prices for use in their first-order price equations. The third contribution is that we estimate the shadow DDF system using a Generalized Method of Moments approach, where all variables are potentially endogenous. This approach is simpler than the Bayesian one employed in Atkinson et al. (Estimating efficient production with bad inputs and outputs using latent prices and optimal directions. Working paper, University of Georgia, Athens, 2016), which estimated shadow prices and optimal directions. Using the same data set, both sets of results are qualitatively very similar, although they differ somewhat quantitatively.     

Luenberger and Malmquist Productivity Indices: Theoretical Comparisons and Empirical Illustration

This contribution establishes, from a theoretical viewpoint, the relations between the Malmquist productivity indices, that measure in either input or output orientations, and the Luenberger productivity indices, that can simultaneously contract inputs and expand outputs, but that can also measure in either input or output orientations. The main result is that a Malmquist productivity index overestimates productivity changes, since it provides productivity measures that are nearly twice those given by the Luenberger productivity index looking for simultaneous contractions of inputs and expansions of outputs. This relationship is empirically illustrated using data from 20 OECD countries over the 1974–97 period.     

Analysing the Performance of Firms Using a Decomposable Ideal Index Number to Link Profit, Prices and Productivity

This article reviews an index number framework that links changes in aggregate performance measures (such as profit, revenue, cost and total factor productivity) to changes in both the prices and quantities of key outputs and inputs. The framework provides a way of linking the aggregate performance measures to outcomes for individual customer groups, employees and owners of businesses. This information is useful to policy makers in evaluating the outcomes of economic reform, including the distributional consequences. It is also useful to regulators who need to understand and monitor both the consequences of their regulation and the response to their decisions by those being regulated. The article demonstrates that the logarithmic version of Fisher's Ideal index offers a useful way of integrating changes in profit, productivity and prices into a single analysis. The usefulness of the framework is illustrated by applying it to a data set for Australian National.     

Misallocation and aggregate productivity across time and space

Productivity is at the core of the large differences in income per capita across countries. What accounts for international productivity differences? I discuss cross‐country differences in the allocation of inputs across heterogeneous production units—misallocation—as a potential factor in accounting for aggregate productivity. Policies and institutions generating misallocation are prevalent in poor and developing countries and may also be responsible for differences in the selection of operating producers and technology used, contributing substantially to aggregate productivity differences across countries.     

Jointness In Production and Factor-Price Equalization *

This paper argues that the presence of activities which yield outputs jointly does not damage the case for factor-price equalization. the crucial condition for equalization is similar to that in the no-joint production case: the number of common activities with independent input vectors that are actively used in both countries at least match the number of factors, and factor endowments lie sufficiently close. Indeed, joint production may increase the range of commodity prices for which factor prices are equalized by commodity trade.     

Are sports teams multiproduct firms?

The appropriate conception of team outputs is investigated by estimating a two-output factor demand system for baseball teams, relative to which single-output models are rejected. This finding is robust to alternative approaches to testing and model choice. The factor demands are those of the symmetric generalized McFadden cost function, which has several advantages in this context. The team factor inputs are the skill characteristics of players, the prices of which are obtained hedonically. In addition to investigating one- versus two-output models, the estimation results are used to obtain demand and substitution elasticities, factor input elasticities with respect to output, cost elasticities, and measures of economies of scale and scope. Although the results support a multiproduct conception of team production, output separability is not rejected, suggesting that team outputs may sometimes be adequately treated as a production aggregate.