An econometric application of the theory of the farm-household

Employing a Cobb-Douglas specification for the production function and a modified linear expenditure system, the paper presents an econometric model of household production, consumption and labor supply behaviour for a semi-commercial farm with a competitive labor market. The model, estimated from primary, cross-sectional, Malaysian data, is used to analyse the impact of migration, output price intervention and technological change on the agricultural sector. In doing so, the wage-rate is treated as an endogenous variable to be determined by the interaction of aggregate labor demand and supply curves obtained from the estimated micro functions.     

Biases in technical efficiency scores caused by intra-input aggregation: mathematical analysis and a DEA application using simulated data

In Data Envelopment Analysis (DEA) applications involving multiple inputs and outputs, inputs are aggregated into the total amounts of each type of input. For example, if input types ‘labour’ and ‘capital’ are used to produce multiple outputs, the total amount of labour used to produce all outputs is treated as one aggregated input and the total amount of capital as another. Resources are not disaggregated into input variables measuring the amount of labour used to produce the first output, the amount of labour used to produce the second output, the amount of labour used to produce the third output and so on, for both labour and capital. It is shown that such intra-input aggregation causes downward bias in reported technical efficiency scores, with variations in bias unrelated to true technical efficiency. Therefore, with few exceptions, any technical efficiency comparisons among DMUs are invalid. The presence of intra-input aggregation bias is demonstrated mathematically, simulation is used to exhibit its severity, and the exceptions that permit intra-input aggregation without causing bias are identified. It is concluded that, for multiple-input, multiple-output DEA applications, inputs must be disaggregated into the amounts used to produce each output in order to validly report technical efficiency, unless one of the exceptions is present.     

Using panel data analysis to estimate confidence intervals for the DEA efficiency of individual decision making units

This article demonstrates a methodology using panel data analysis to estimate confidence intervals for the data envelopment analysis efficiency of individual decision making units (DMUs), and the statistical significance of trends in individual DMU efficiency. The procedure accounts for stochastic variations of the inputs and outputs of the target DMU as well as stochastic variations of the inputs and outputs of its efficient benchmark peers. The procedure is demonstrated using 9 years of data from 34 Canadian paratransit agencies.     

Measuring efficiency under fixed proportion technologies

Data Envelopment Analysis (DEA) applications frequently involve nonsubstitutable inputs and nonsubstitutable outputs (that is, fixed proportion technologies). However, DEA theory requires substitutability. In this paper, we illustrate the consequences of nonsubstitutability on DEA efficiency estimates, and we develop new efficiency indicators that are similar to those of conventional DEA models except that they require nonsubstitutability. Then, using simulated and real-world datasets that encompass fixed proportion technologies, we compare DEA efficiency estimates with those of the new indicators. The examples demonstrate that DEA efficiency estimates are biased when inputs and outputs are nonsubstitutable. The degree of bias varies considerably among Decision Making Units, resulting in substantial differences in efficiency rankings between DEA and the new measures. And, over 90% of the units that DEA identifies as efficient are, in truth, not efficient. We conclude that when inputs and outputs are not substituted for either technological or other reasons, conventional DEA models should be replaced with models that account for nonsubstitutability.     

Impact of input substitution and output transformation on data envelopment analysis decisions

Data envelopment analysis (DEA) can aid managerial decision-making because it offers an opportunity to measure organizational performance in a holistic manner, aggregating data from partial indicators into a single comprehensive measure. However, there are some methodological hazards associated with the use of DEA that are especially relevant to managerial decisions, but which have been largely ignored in the literature. Herein, we identify and show the impact of a ubiquitous methodological hazard in DEA modelling – the economic assumptions regarding input substitutions and output transformations.     

Bias and precision in the DEA two-stage method

In Data Envelopment Analysis (DEA), the two-stage method is a popular procedure for accounting for exogenous influences on efficiency. With the conventional two-stage method, a DEA is first conducted using only traditional (endogenous) inputs and outputs. Then, the first-stage DEA scores are regressed on the environmental/contextual (exogenous) inputs of interest. The regression outcomes are used to identify exogenous inputs that influence the first-stage DEA scores to a statistically significant degree, and to adjust DEA scores to account for these influences. Herein, it is demonstrated empirically that the conventional method exhibits substantial bias and low precision, with the degree of bias and precision affected by input variance and correlation. A reverse two-stage procedure that yields estimates without the bias and precision problems that compromise the validity of the conventional method's estimates is suggested.