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Productive efficiency analysis with incomplete output information

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Abstract

We present a novel Data Envelopment Analysis (DEA)-type method to evaluate the productive efficiency of Decision Making Units (DMUs) when the empirical analyst has incomplete output information. Our method builds on the Afriat Theorem that was originally proposed in the context of consumer analysis. We translate this result to a production setting and show that it provides a productive basis for cost efficiency analysis in the absence of output information. Our method is versatile in that it can accommodate a continuum of instances characterized by incomplete information on output quantities. We illustrate its practical usefulness through an empirical application that evaluates the productive efficiency performance of countries in producing national welfare.

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Notes

  1. In what follows, complete output information refers to situations where the DMUs’ output levels are fully observed, whereas incomplete output information refers to situations where these output levels are imprecisely observed. In an extreme scenario, incomplete output information boils down to fully unobserved output (see Sections 2.1 and 2.2). We will refer to an intermediate scenario (with some observable information on the output levels) as characterized by “partial” output information (see Section 2.3).

  2. In this respect, we refer to Afriat (1972), Hanoch and Rothschild (1972), Diewert and Parkan (1983) and Varian (1984) for seminal contributions on the nonparametric approach to analyzing producer behavior. Similar to the current paper, these studies also build on the formal analogy between the analysis of consumer and producer behavior. Next, Banker and Maindiratta (1988) provide an early study on the close connection between the nonparametric approach to production analysis and DEA. Importantly, these earlier studies all assume complete output information in the sense that the DMUs’ output levels are fully observed. As motivated above, the main contribution of the current study is that we present tools for analyzing productive efficiency in the absence of such complete output information.

  3. See also Diewert (1973) and Varian (1982) for detailed and insightful discussions of Afriat’s seminal result.

  4. See, for example, Cherchye et al. (2015) and Talla Nobibon et al. (2016) for detailed discussions of this equivalent IP formulation of GARP.

  5. This use of most favorable output orderings reflects the “Benefit of the Doubt” (BoD) interpretation of DEA efficiency analysis. See, for example, Cherchye et al. (2007) and, more recently, Färe and Karagiannis (2014) for detailed discussions of this BoD interpretation of DEA. Whereas this BoD interpretation usually refers to the (unknown) weights that are used for aggregating the inputs and outputs in the DEA efficiency measures, we apply in our setting this BoD principle to the (unknown) output orderings that are used in the efficiency evaluation.

  6. See https://www.rug.nl/ggdc/productivity/pwt/pwt-documentation.

  7. See the Appendix for a list of the countries that we consider. We have cleaned the original data to prevent that our empirical results are severely affected by extreme outliers and noise. To construct Wage we make use of nominal GDP. We obtain output-side nominal GDP by multiplying output-side real GDP by its price level. Given the presence of outliers in the latter, we winsorize it at the 5th and 95th percentile of all observations in the PWT 10.0 data set. We set the average usage cost of capital equal to 0.15, following Gilchrist and Zakrajsek (2007). To avoid potential influences from outliers in the input price data, we winsorize Wage and Capital usage price at the 10th and 90th percentile of all observations in the PWT 10.0 data set. Further, we drop observations with a labor share or a capital share above 1. Last, we drop observations with missing values for the variables under consideration (Real GDP, L, K, Wage, Capital usage price), and limit our analysis to countries for which we have data on all these variables for the years 1990, 2000, 2010, and 2019.

  8. Consistent with our main analysis above, for α > 1.5 we obtain very high average efficiency scores and low standard deviations. These results are available upon request.

  9. Specifically, Kumar and Russell (2002) originally analyzed a sample with 57 countries. We have complete information on the variables under study for the four time periods under consideration for 50 of these 57 countries.

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Authors and Affiliations

  1. Department of Economics, University of Leuven, Leuven, Belgium

    Laurens Cherchye, Bram De Rock, Dieter Saelens & Marijn Verschelde

  2. ECARES, Université Libre de Bruxelles, Brussels, Belgium

    Bram De Rock

  3. National Bank of Belgium, Brussels, Belgium

    Dieter Saelens

  4. IESEG School of Management, Univ. Lille, CNRS, UMR 9221–LEM–Lille Economie Management, F-59000, Lille, France

    Marijn Verschelde

Authors
  1. Laurens Cherchye
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  2. Bram De Rock
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  4. Marijn Verschelde
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Correspondence to Laurens Cherchye.

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Appendix: list of countries used in the empirical application

Appendix: list of countries used in the empirical application

Angola, Argentina, Armenia, Australia, Austria, Azerbaijan, Bahamas, Bahrain, Barbados, Belgium, Benin, Bolivia (Plurinational State of), Bosnia and Herzegovina,Botswana, Brazil, Bulgaria, Burkina Faso, Cabo Verde, Cameroon, Canada, Chile, China, Hong Kong SAR, China, Macao SAR, Colombia, Costa Rica, Croatia, Cyprus, Czech Republic, CÔte d’Ivoire, Denmark, Djibouti, Dominican Republic, Ecuador, Egypt, Estonia, Eswatini, Fiji, Finland, France, Gabon, Germany, Greece, Guatemala, Guinea, Honduras, Hungary, Iceland, India, Indonesia, Iran (Islamic Republic of), Iraq, Ireland, Israel, Italy, Jamaica, Japan, Jordan, Kenya, Kuwait, Kyrgyzstan, Latvia, Lebanon, Lesotho, Lithuania, Luxembourg, Malaysia, Malta, Mauritius, Mexico, Morocco, Namibia, Netherlands, New Zealand, Nicaragua, North Macedonia, Norway, Oman, Panama, Paraguay, Peru, Philippines, Poland, Portugal, Qatar, Republic of Korea, Romania, Rwanda, Sao Tome and Principe, Saudi Arabia, Senegal, Singapore, Slovakia, Slovenia, South Africa, Spain, Sri Lanka, Sudan, Suriname, Sweden, Switzerland, Taiwan, Thailand, Togo, Trinidad and Tobago, Tunisia, Turkey, United Kingdom, United States, Uruguay, Uzbekistan and Zimbabwe.

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Cherchye, L., De Rock, B., Saelens, D. et al. Productive efficiency analysis with incomplete output information. J Prod Anal (2023). https://doi.org/10.1007/s11123-023-00697-w

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