1. James Cordeiro, State University of New York (Brockport), USA Joseph Sarkis, Clark University, USA Diego Vazquez & Jeroen Dijkshoorn, BRASS Center, Cardiff University, Wales, UK GIN CONFERENCE 2008 (Leeuwarden, Netherlands) A Stochastic Frontier Analysis of Estimates and Correlates of the Efficiency of Solid Waste Management in Welsh SMEs

2. Purpose of the Study Primary Purpose: To identify the technical efficiency of 299 solid waste recycling efforts of Welsh SMEs in 2003 by using a sophisticated econometric technique called Stochastic Frontier Analysis (SFA) Secondary purposes:  To identify the extent to which environmental practices such as waste monitoring, auditing, publication of environmental policies, and use of local support groups are related to the efficiency scores  To check whether the SFA efficiency scores correlate significantly with those obtained using Data Envelopment Analysis (DEA) approaches

3. Efficiency Analyses Efficiency analyses focus on the efficiency of some production process (e.g. solid waste processing) in transforming inputs into outputs. Frontier methods use an efficient frontier to identify the efficiency of individual organizations relative to a reference set of organizations  DEA is a non-parametric approach that uses mathematical programming to identify the efficient frontier.  SFA is a parametric approach that hypothesizes a functional form and use the data to econometrically estimate the parameters of that function using the entire set of DMUs The measure of efficiency is normally one of either :  The distance between observed and maximum possible output for given inputs (output efficiency)  The distance between observed and minimum possible input for given outputs (input efficiency)

4. Overview of Study Sample and Variables Study Focus: Efficiency of solid waste management (a subject of major environmental significance and legislation in Wales) Study sample: 299 Welsh Small and Medium-sized manufacturing Organizations (SMES) in 19 industries who responded to a BRASS survey in 2003 Methodology: Stochastic Frontier Analysis (SFA) Study Variables:  Output: Ln (Proportion of total solid waste recycled)  Inputs: (a) Ln (Total recycling cost expended per ton) (b) Ln(Organization size i.e.,#employees))  Variables use to explain inefficiencies: Dummy indicators (0,1) of waste auditing, waste monitoring, publication of environmental policies, use of local support groups

5. Methodology: SFA and DEA compared to each other and to OLS Regression DEA creates virtual units that serve as benchmarks for measuring DMUs comparative efficiency SFA uses an hypothesized function to calculate estimates of the efficiencies of individual DMUs Only SFA can separate random noise from efficiency; DEA incorporates noise as part of the efficiency score. SFA and OLS regression methods reveal overall sample-based information. DEA reveals unit-specific data type of returns to scale, productivity change 246810 2 4 6 8 12 0 Input A B E F D C G H DEA OLS Regression Output SFA I1I2 O2 O1 X Y Output Efficiency of F: F0/YO Input Efficiency of E: XI/XF

6. SFA Results (Base Model) Model Parameters: Constant 0.031 *** Ln (Treatment cost per ton of solid waste) -0.002*** Ln (Number of Employees) -0.010 *** Model Statistics: Lambda 0.000 Log-Likelihood -527.27 Wald Chi 2 (Prob. > Chi 2 ) 460280.49(.000) Model of Predictors of Variance of Inefficiency Scores (this section of the model is re-estimated as part of the original model): Constant 2.493 *** Firm Monitors Waste 0.159 Firm Audits Waste -0.418 * Firm Publishes Environmental Policy 0.192 Firm Uses Local Business Support Group -0.495 ***

7. Rank Correlations of SFA with DEA Efficiency Rankings SFA technical efficiency score rankings were correlated (using Kendall’s Tau) with the DEA efficiency score rankings for two different DEA approaches:  CCR approach (correlation is.87)  Slack-based CCR approach (correlation is.87) Thus our confidence that SFA and DEA provide similar efficiency rankings of the Welsh SMEs is very high  this is encouraging given the different assumptions underlying these two approaches

8. Summary of Findings SFA was used to obtain technical efficiency scores for 299 Welsh SMEs and the two inputs specified were both found to be significant The SFA scores correlate with those obtained by DEA  increasing our confidence in our estimates of the SMEs efficiency rankings Some initial evidence that waste auditing and use of local business support groups may impact efficiencies of the SMEs Further research: We are focusing on panel data collection of SME inputs and outputs to answer important questions like:  Which industries have been improving their efficiencies faster over time?  Which waste management practices have the most impact over time?  Can more sophisticated input and output models be developed for the rankings?  Can the model be successfully applied to other waste management approaches?  How do SMEs compare to larger firms? Different countries?

9. Thanks!

10. DEA Numeric Example

11. Five LP models are run (for each firm A to E) to find the efficient frontier for DEA

12. CRS Input-Oriented DEA Solution

13. CRS Input-Oriented Example of DEA Frontier 1) TE (technical efficiency) of Firm 3 is 0.833, i.e., Firm 3 could reduce all inputs (x 1,x 2 ) by 16.7% to produce the same amount of y. 2) Thus, firm 3 project to 3 ’,on a line joining 2 and 5 and firm 4 to 4’ 3) The line joining 2 and 5 is called the “ Frontier ” and firm 2 and 5 are referred to as “targets” or “peers” for firms 3 and 4.

14. Start with a Set of Observed DMUS and their Input - Output Correspondences

15. By virtue of interpolation between C and D all input - output correspondences on CD are feasible

16. Using interpolations between observed units the set of all feasible input -output correspondences is constructed and its boundary identified

17. Using the set of all feasible input output correspondences the comparative efficiency and other information in respect of a unit (e.g. unit E) is derived as illustrated here:  Output Efficiency of E: FE/FG  Output benchmarks for E: Units C and D Scope for output augmentation at E: EG  Returns to scale (increasing, decreasing, constant): Revealed by the intercepts of the segments of the efficient boundary.  Scale elasticity revealed by the slope of the segments on the efficient boundary.  Input Efficiency of E: HI/HE  Scope for resource conservation at E: IE Examining DMU Efficiencies in DEA

18. Consider a production function for I DMUs and K inputs: PARAMETRIC METHODS FOR COMPARATIVE EFFICIENCY MEASUREMENT Where y is output, x ik are inputs, and e i is the residual for DMU I It is the residual e i the captures any inefficiency in this model The residual also captures other noise or random effects (e.g. omitted variables, measurement error, etc.) SFA attempts to decompose the error term into inefficiency and noise components for each DMU i [1]

19. SFA Model for I DMUs and K inputs We decompose the error term into two components: v is an identically distributed conventional two-sided error term with zero mean. It stands for random noise, omitted variables etc. u is an identically distributed one-sided error term with a non-zero mean. It stands for inefficiency. u is typically assumed to be exponential, half-normal or truncated normal

20. Stochastic Frontier Example Frontier: y= exp(x β) y i = exp(x β +v i ) v i is noise due to random events if v i >0  above frontier if vi<0  under frontier;

21. The exponential or half-normal distributions often assumed for SFA inefficiencies (u) acknowledge that larger inefficiency values are less likely

22. The Stochastic Frontier

23. The SFA model is usually fitted using Maximum Likelihood estimation We need to estimate the inefficiency of the ith producer (u i ) by using its composed residual   = v i - u i. Depending on the assumption we make about the distribution (e.g. half-normal, exponential) of the inefficiency u i we arrive at a different formula for the conditional value We plug into this formula the values of   and other values we derive from the   to arrive at an estimate of the conditional inefficiency u i of the ith DMU. The formulae for differs depending on the distribution assumed for u i and are coded in software such as Limdep and STATA.

24. Summary Comparison of DEA v/s SFA Approaches DEASFA Non-parametric method  Cannot test hypotheses Parametric method  Can test hypotheses Uses mathematical programmingUses maximum likelihood econometric estimation Does not accommodate noise (noise is effectively part of the efficiency score) Specifies noise (separates noise from efficiency scores) Can accommodate multiple outputs and multiple inputs Typically can only accommodate single output with multiple outputs Functional form is not specifiedFunctional form needs to be specified

25. Overview of Study Sample and Variables Study Focus: Efficiency of solid waste management (a subject of major environmental significance and legislation in Wales) Study sample: 299 Welsh Small and Medium-sized manufacturing Organizations (SMES) in 19 industries who responded to a BRASS survey in 2003 Study Variables:  Output: Ln (Proportion of total solid waste recycled)  Inputs: (a) Ln (Total recycling cost expended per ton) (b) Ln(Organization size i.e.,#employees))  Variables use to explain inefficiencies: Dummy indicators (0,1) of waste auditing, waste monitoring, publication of environmental policies, use of local support groups

26. SFA Results (Base Model) Model Parameters: Constant 0.031 *** Ln (Treatment cost per ton of solid waste) -0.002*** Ln (Number of Employees) -0.010 *** Model Statistics: Lambda 0.000 Log-Likelihood -527.27 Wald Chi 2 (Prob. > Chi 2 ) 460280.49(.000)

27. SFA Results -- 2 Model of Predictors of Variance of Inefficiency Scores (this section of the model is re-estimated as part of the original model): Constant 2.493 *** Firm Monitors Waste 0.159 Firm Audits Waste -0.418 * Firm Publishes Environmental Policy 0.192 Firm Uses Local Business Support Group -0.495 ***

28. Rank Correlations of SFA with DEA Efficiency Rankings SFA technical efficiency score rankings were correlated (using Kendall’s Tau) with the DEA efficiency score rankings for two different DEA approaches:  CCR approach (correlation is.87)  Slack-based CCR approach (correlation is.87) Thus our confidence that SFA and DEA provide similar efficiency rankings of the Welsh SMEs is very high  this is encouraging given the different assumptions underlying these two approaches

29. Summary of Findings SFA was used to obtain technical efficiency scores for 299 Welsh SMEs and the two inputs specified were both found to be significant The SFA scores correlate with those obtained by DEA  increasing our confidence in our estimates of the SMEs efficiency rankings Some initial evidence that waste monitoring and use of local business support groups may impact efficiencies of the SMEs Further research: We are focusing on panel data collection of SME inputs and outputs to answer important questions like:  Which industries have been improving their efficiencies faster over time?  Which waste management practices have the most impact over time?  Can more sophisticated input and output models be developed for the rankings?  Can the model be succesfully applied to other waste management approaches?  How do SMEs compare to larger firms? Different countries?