The Law of One Price in Data Envelopment Analysis: Restricting Weight Flexibility Across Firms

The Law of One Price (LoOP) states that all firms face the same prices for their inputs and outputs in the competitive market equilibrium. This law has powerful implications for productive efficiency analysis, which have remained unexploited thus far. This paper shows how LoOP-based weight restrictions can be incorporated in Data Envelopment Analysis (DEA). Utilizing the relation between the industry level and the firm level cost efficiency measures, we propose to apply a set of input prices that is common for all firms and that maximizes cost efficiency of the industry. Our framework allows for firm-specific output weights and variable returns-to-scale, and preserves the linear programming structure of the standard DEA. We apply the proposed methodology for evaluating research efficiency of economics departments of Dutch Universities. This application shows that the methodology is computationally tractable for practical efficiency analysis, and that it helps in deepening the DEA analysis.Data Envelopment Analysis; Law of One Price; industry-level efficiency; weight restrictions; research efficiency

The Measurement of the Energy Intensity of Manufacturing Industries: A Principal Components Analysis

Energy intensity is the ratio of energy use to output. Most industries deal with several energy sources and outputs. This leads to the usual difficulties of aggregating heterogeneous inputs and outputs. We apply principal components analysis to assess the information derived from six energy intensity indicators. We use two measures of total energy use (thermal and economic) and three measures of industry output (value added, value of production, and value of shipments). The data comes from manufacturing industries in Québec, Ontario, Alberta, and British Columbia from 1976 to 1996. We find that the variation of the six energy intensity indicators that is accounted for by the first principal component is quite large. However, depending on how variables are measured, there may be significant differences in the assessment of the evolution of energy intensity for some industries. There are no particular patterns in this respect. This makes identifying benchmarks that could be used to assess future performance difficult.Energy intensity; aggregation; principal components analysis

Firm and Industry Level Profit Efficiency Analysis Under Incomplete Price Data: A Nonparametric Approach based on Absolute and Uniform Shadow Prices

We discuss the nonparametric approach to profit efficiency analysis at the firm and industry levels in the absence of complete price information, and propose two new insights. First, choosing one commodity (whose price is known) as a numeraire good enables us to measure profit inefficiency in absolute monetary terms. Second, imposing a ‘Law of One Price’ (LoOP) constraint that all firms should be evaluated in terms of the same input-output prices allows us to aggregate firm-level profit inefficiencies to the overall industry inefficiency. Moreover, the LoOP restrictions increase the discriminatory power of the method by better capturing firm-level allocative inefficiencies. Besides the measurement of profit losses, the presented approach enables one to recover absolute price information from quantity data. We conduct a series of Monte Carlo simulations to study the performance of the proposed approach in controlled production environments.Profit Efficiency, Industry Inefficiency, Data Envelopment Analysis, Absolute Prices, Law of One Price, Weight Restrictions, Simulation

On the Efficiency of the Walrasian Mechanism

Central results in economics guarantee the existence of efficient equilibria for various classes of markets. An underlying assumption in early work is that agents are price-takers, i.e., agents honestly report their true demand in response to prices. A line of research in economics, initiated by Hurwicz (1972), is devoted to understanding how such markets perform when agents are strategic about their demands. This is captured by the \emph{Walrasian Mechanism} that proceeds by collecting reported demands, finding clearing prices in the \emph{reported} market via an ascending price t\^{a}tonnement procedure, and returns the resulting allocation. Similar mechanisms are used, for example, in the daily opening of the New York Stock Exchange and the call market for copper and gold in London. In practice, it is commonly observed that agents in such markets reduce their demand leading to behaviors resembling bargaining and to inefficient outcomes. We ask how inefficient the equilibria can be. Our main result is that the welfare of every pure Nash equilibrium of the Walrasian mechanism is at least one quarter of the optimal welfare, when players have gross substitute valuations and do not overbid. Previous analysis of the Walrasian mechanism have resorted to large market assumptions to show convergence to efficiency in the limit. Our result shows that approximate efficiency is guaranteed regardless of the size of the market