Profit-efficiency analysis of forest ecosystem services in the southeastern US

1 Profit-efficiency analysis of forest ecosystem services in the southeastern US 1 2 Andrés Susaetaa§, Ester Gutiérrezb and Sebastián Lozanob 3 a Department of Forest Engineering, Resources and Management, Oregon State University, 4 Corvallis, OR, 97331, USA 5 b Departamento de Organización Industrial y Gestión de Empresas, Universidad de Sevilla, 6 Sevilla, Spain 7 § Corresponding author 8 9 10 Abstract 11 Technical, allocative, and profit efficiency of longleaf pine (Pinus palustris. Mill) forests in 12 the southeastern United States, producing ecosystem services such as timber, tree 13 biodiversity, water, and carbon sequestration, were estimated. This study employed a non-14 parametric two-stage approach involving data envelopment analysis (DEA) and robust linear 15 regression. Utilizing data from the Forest Inventory and Analysis (FIA) program spanning 16 1977-2015 and covering 2,282 forest plots, most longleaf pine forest plots were technically 17 and profit inefficient in ecosystem service production. The inefficiency in profit appeared 18 more attributable to allocative rather than technical inefficiency. Furthermore, the impact of 19 various exogenous variables on inefficiency scores was assessed through robust linear 20 regression. The findings suggested that forest disturbances under private ownership could 21 reduce technical inefficiency. Surprisingly, contrary to stochastic frontier analysis (SFA) 22 results, the robust regression model, considering geographical factors, disturbance, 23 ownership, management, and time in the presence of outliers/influential observations, 24 indicated that disturbances often increased technical inefficiency. Therefore, forest 25 2 management strategies aiming to mimic or replicate the effects of forest disturbances might 1 compromise the efficiency of ecosystem service provision. 2 Keywords: data envelopment analysis; efficiency; ecosystem services; longleaf pine; 3 disturbance; ownership 4 5 6 7 8 1. Introduction 9 The southeastern forests of the United States (US) play a critical role in the nation’s 10 economy. These forests occupy 87 million hectares and provide around 66% of the timber 11 harvested in the US (Oswalt et al., 2019), and support more than 1 million jobs throughout 12 the supply chain (Abt, 2013). They can sequester around 25% of the annual carbon emissions 13 (Han et al., 2007) and generate 34% of the water production in the southern US (Lockaby et 14 al., 2013). Furthermore, they are expected to generate around $14 (through water, carbon and 15 habitat services) for every $1 in timber value (Escobedo and Tilmisina, 2012). 16 In the southeastern US, temperature levels and precipitation are expected to increase 17 throughout the century, with mean annual temperatures possibly increasing over 2°C and 18 precipitation over 10% compared to the 1986-2005 average (Hicke et al.,2021), and with 19 these changes the production of some ecosystem services will be at risk. Elevated 20 temperatures are projected to lead to a decrease in water supply, subsequently exerting a 21 negative impact on forest growth (Lockaby et al., 2013). Climate change is expected to cause 22 changes in the geographic distribution of several species of wildlife and plants, influencing 23 seasonal movement, recruitment, and mortality (Trani Griep and Manley, 2012). 24 Furthermore, climate change can exacerbate the frequency and intensity of natural 25 3 disturbances such as wildfires, pest outbreaks, and windstorms, threatening the sustainability 1 of forestlands and creating ecological change such as the structure of the ecosystem (e.g., 2 changes in species composition, heightened tree mortality, and diminished forest 3 productivity), economic losses, and socioeconomic challenges (Lecina-Diaz et al., 2021). 4 Sustainable forest management is considered a critical strategy to safeguard 5 ecosystem services (Mori et al., 2017). Adaptive management strategies such as forest 6 conversion, changes in rotation age, or thinning regimes are feasible options to conserve and 7 preserve ecosystem services and alleviate climate change impacts on forests (Hanewinkel et 8 al., 2013). Active forest management allows managers and landowners to consider several 9 frequently competing objectives (Uhde et al., 2015). This implies that certain forest 10 management practices can increase the production or availability of one or a bundle of 11 ecosystem services, but they can simultaneously harm the provision or availability of other 12 ecosystem services (Kolo et al., 2020; Schwaiger et al., 2019). Mori and Kitagawa (2014), 13 however, claim that sustainable forest management can provide a win-win solution to address 14 trade-offs between ecosystem services and timber production. 15 The efficient allocation of forest resources (e.g., timber, nontimber forest products, 16 and other ecosystem services) by considering different management objectives has been 17 thoroughly analyzed since the early 1960s, particularly from an optimization perspective 18 (Kaya et al., 2016). Improving the allocation of forest resources by formulating a resource 19 efficiency policy mix, i.e., a rational collection of instruments, across several governance 20 levels, aimed at encouraging the effective and sustainable use of resources in production and 21 consumption systems– is critical to promoting the sustainable use of forest resources in 22 production and consumption (Wilts and O’Brien, 2019). With the growing societal demand 23 for ecosystem services, it is imperative to determine, to the best possible extent, the best 24 management practices that ensure an efficient allocation of such services. 25 4 Non-parametric approaches developed to estimate production efficiency such as data 1 envelopment analysis (DEA, Charnes et al., 1978) have been applied to evaluate natural 2 resource allocation (Gutiérrez and Lozano, 2022; Masuda, 2016; Whittaker et al., 2015). DEA 3 is a mathematical optimization method that determines the production technology frontier, 4 identifies those production units that perform efficiently, and allows comparison of each 5 unit’s performance relative to the identified efficient units (Cooper et al., 2006). DEA is a 6 data-driven methodology that only requires the observed input and output data, i.e., the 7 amounts of resources consumed by each unit and the amounts of products it produced. From 8 the data, the production possibility set (also known as the DEA technology) is determined. 9 This production possibility set contains all the operating points that are deemed feasible, i.e., 10 the possible combinations of outputs can be produced given the existing inputs. An operating 11 point is said to be inefficient if there exists a feasible operating point that can produce the 12 same amount (or more) of outputs consuming less resources, or if it can produce more outputs 13 consuming the same amount (or less) of inputs. The efficiency score of an operating point 14 measures these potential input and output improvements. If no improvements are feasible 15 then the observed operating point is technically1 efficient. 16 In addition to the technical efficiency, and provided that data on the unit costs and 17 prices of the different inputs and outputs are known, the profit efficiency of any observation 18 can also be determined. Profit efficiency can be defined as the ratio of the profit associated 19 with the observed operating point to the maximum profit that can be attained considering the 20 1 The term technical refers to the DEA technology, i.e., the production possibility set, which implicitly defines what is technically possible in terms of what can be produced with any given amount of resources. Mathematically, the non-dominated subset of the production possibility set is the efficient frontier and contains all the technical efficient operating points. 5 whole production possibility set. For example, an 80% profit efficiency means that the profit 1 generated by the observed operating point is 80% of that of the maximum profit operating 2 point. The difference between profit efficiency and technical efficiency is called allocative 3 efficiency2. 4 The main objective of our paper is to determine, using DEA, the profit and technical 5 efficiency of longleaf pine (Pinus palustris. Mill) forest ecosystems in the production of 6 ecosystem services, in the southeastern United States. We specifically examine carbon 7 sequestration, water production, tree species richness, and timber production. The present 8 study contributes to the scientific literature on the provision of forest ecosystem services by 9 using a weighted additive DEA model and decomposing profit efficiency into technical and 10 allocative efficiency, and as a secondary step in our model, by analyzing the statistical 11 significance of the factors that impact efficiency. Furthermore, the study sheds light on forest 12 management practices that can improve the provision of forest ecosystem services from an 13 efficiency perspective in the region. 14 We have selected longleaf pine – using plot-level Forest Inventory and Analysis (FIA) 15 data from the USDA Forest Service (US Department of Agriculture Forest Service, 2021)– 16 due to the relevance of this forest species in the provision of ecosystem services in the 17 Southeastern United States. Longleaf pine is the core of the North American Coastal Plain, 18 2 It is possible, indeed common in practice, that an observed operating point is technically efficient but not profitably efficient. In that case, although it is not possible for the corresponding production unit to increase its outputs without increasing its inputs also (i.e., technical efficiency), it is nonetheless possible to increase its profit by allocating inputs and outputs differently (i.e., allocative inefficient). Therefore, a profitably efficient observation needs to be both technically and allocatively efficient. 6 the World’s 36th Biodiversity Hotspot (Noss, 2016). Furthermore, longleaf pine forests 1 sequester more carbon and are home to higher levels of wildlife compared to other southern 2 pines such as loblolly pine (Kirkman et al., 2013; Samuelson et al., 2014). 3 4 5 6 7 8 2. Literature review 9 Efficiency analysis in the forest sector generally involves two quantitative methods: 10 the parametric stochastic frontier analysis (SFA)3 and the non-parametric data envelopment 11 analysis (DEA). SFA was proposed about the same time as DEA (Aigner et al., 1977) and its 12 main strength is the stochastic treatment of the deviations from the frontier– deviations which 13 are decomposed into a non-negative inefficiency term and a random noise term. However, 14 SFA has not been as widely used as DEA. The reasons for this may be that, as indicated by 15 Olesen and Petersen (2016), the restrictive assumptions generally employed in SFA on the 16 functional form and the distribution characteristics of the inefficiency term, may in some 17 cases, involve an unacceptable functional structure of the stochastic frontier that will 18 potentially violate the purpose of the efficiency analysis. In spite of the deterministic 19 3 Although SFA has been traditionally considered a parametric approach, non-parametric versions of SFA have been developed to handle multiple inputs and outputs, thereby avoiding endogeneity problems (Simar and Wilson, 2022). Non-parametric SFA also helps tackle issues related to the assumptions of the parametric functional form and the stochastic specifications of the error component (Kumbhakar et al., 2007). 7 character of DEA–all deviations from the frontier are attributed to inefficiency, ignoring the 1 presence of noise in the data–its non-parametric nature as well as its ability to include multiple 2 outputs become major arguments that justify its use for efficiency analysis as proposed in this 3 analysis. 4 Salehirad and Sowlati (2005), Sowlati (2005), Gutiérrez and Lozano (2022), and 5 Strange (2021), provided a comparative literature review of SFA and DEA studies in forestry 6 from 1991 to December 2020. The reader is referred to those articles for an in-depth review 7 of forest efficiency studies up to 2020. This literature review demonstrates that DEA has been 8 used in most forestry efficiency related studies. This is likely due to its lack of a specific 9 functional form a priori based on probabilistic distribution, its ability to integrate multiple 10 inputs, outputs, and production technologies using a simple mathematical programming 11 approach, and its ability to handle different types of variables (e.g., non-discretionary 12 variables, undesirable outputs, dual role factors), even in the presence of uncertainty). The 13 vast majority of studies have focused particularly on the wood-based products industry, 14 followed by forest management analyses, while only a small number of studies are dedicated 15 to forest operations (Aalmo et al., 2021; Obi and Visser, 2017a, 2017b, 2018, 2020). 16 Since December 2020, several efficiency-based studies have been published on forest 17 management and primary forest products. For example, Chen and Yao (2021) explored the 18 forestry ecological efficiency using the Malmquist productivity index4 and the super 19 4 The Malmquist productivity index (Färe et al., 1994) is a method to gauge the productivity change of a production unit between two periods and it can be decomposed into an efficiency change term and a technology change term, i.e., from one period to the next, the unit may have increased or decreased its efficiency and the efficient frontier of one period may have shifted reflecting progress or regress in the corresponding DEA technology. 8 efficiency SBM model5 in 31 Chinese provinces from 2014 to 2018. They found spatial 1 differentiation between regions, highlighting efficiency improvements in the southern coastal 2 regions. From the perspective of the wood industry, Banaś et al. (2021) and Krišt’áková et al. 3 (2021) used input-oriented6 (timber production) and output-oriented (lumber and wood 4 panels) DEA models in Poland (1990-2019) and Bulgaria versus Slovakia (8 enterprises, 5 2014-2018), respectively. Susaeta and Rossato (2021) analyzed the efficiency of the Brazilian 6 pulp and paper industry (8 enterprises, 2016) in the production of pulp and bioelectricity using 7 an output-oriented radial7 model. They adjusted the efficiency score using a synthetic 8 indicator, and a truncated linear regression model was conducted to examine the effects of 9 external and related industry factors on the adjusted efficiency score. Lundmark et al. (2021) 10 evaluated improvements in forest bioenergy production efficiency of Sweden’s harvesting 11 products (20 counties, 2008-2014), combining a network DEA model (i.e., the production 12 units consist of different subprocesses, each of which has its own inputs and outputs, and 13 5 The super efficiency SBM model (Tone, 2002) is a non-oriented DEA model – a model that tries to simultaneously reduce inputs and increase outputs as opposed to input-oriented or output-oriented– that allows to rank the technical efficient units by assigning them efficiency scores that can be larger than one–hence the term super-efficiency. 6 While non-oriented approaches aim at simultaneously reducing inputs and increasing outputs, input-oriented models prioritize input reduction over output increase. Similarly, output-oriented models prioritize output increase over input reduction. 7 An output-oriented DEA model uses a radial metric if it expands the outputs uniformly, i.e., increasing all outputs by the same multiplicative factor. Similarly, an input-oriented DEA model uses a radial metric if it contracts the inputs uniformly, i.e., reducing all inputs by the same multiplicative factor (Cooper et al., 2006). 9 there exist also intermediate products produced and consumed within the system) to estimate 1 harvesting volumes and a partial equilibrium forest sector model to estimate price effects. 2 They found that inefficiencies in forest management translate into higher prices of forest 3 products and a reduction in other ecosystems services. 4 DEA has also been applied to new areas of interest by, for example, assessing the 5 performance of tourist forests (Li et al., 2021) and of forest ecosystems (Mizuta et al., 2022; 6 Pukkala, 2016; Shepard et al., 2021; Toma et al., 2020). However, few DEA studies have 7 addressed the efficiency of pine forests in the provision of ecosystem services. In the case of 8 the southeastern US, Susaeta et al. (2016a) analyzed the efficiency of loblolly pine forests in 9 the provision of timber, sequestered carbon, and tree species richness under changing climatic 10 conditions. Susaeta et al. (2016b) extended this previous analysis by decomposing efficiency 11 into allocative and profit efficiency. Mizuta et al. (2021) measured the efficiency of soil 12 carbon sequestration in various land uses, including pinelands. Shepard et al. (2021) analyzed 13 the economic and technical efficiency of loblolly pine in timber production considering 14 different levels of fertilization and evidence of drought in Oklahoma. Mizuta et al. (2022) 15 assessed the efficiency in above net primary productivity of loblolly pine in the region. 16 In this study, the DEA analysis presents a new perspective on the efficiency of forest-17 based ecosystem services production that distinguishes it from previous studies by Susaeta et 18 al. (2016a, 2016b) in several ways. Notably, our analysis incorporates water supply as an 19 essential ecosystem service provided by forests. Additionally, we broaden the scope of our 20 efficiency analysis beyond Florida to encompass multiple states in the southeastern US. 21 Furthermore, we conduct a parametric analysis to examine the factors that impact both 22 technical and profit efficiency in the production of ecosystem services. By adopting a more 23 comprehensive approach and accounting for multiple determinants of efficiency, the current 24 16 0 1 n j j CARBON j CARBON CAR kBON slac  = =+  (3i) 0 1 n j j WATER j WATER WA cTER sla k  = =+  (3j) 1 1 n j j  = =  (3k) 00 j TREE TIMBER CARBON WATER j slack , slack , slack , slack     (3l) It should be noted that the components of the directional vector g that are used in the 1 objective function (2) to normalize the slack variables (and make them dimensionless) 2 implicitly weigh those slacks. In that sense, their respective values can reflect the preference 3 and priorities of the corresponding stakeholders. Like all DEA models, the above TI model 4 projects DMU 0 onto a dominating target operating point, one that consumes fewer resources 5 and generates more outputs. The objective function maximizes the sum of these potential 6 enhancements, referred to as 'slacks' in DEA terminology. These input and output slacks are 7 normalized using the directional vector components. The target operating point is calculated 8 as a convex linear combination of the observed DMUs, with the coefficients of the linear 9 combination j  serving as non-negative variables. The resulting target operating point is 10 inherently technically efficient, implying no further improvements are possible. In fact, if 11 DMU 0 itself were technically efficient, no improvements would be attainable, and the DMU 12 17 would project onto itself. Note that the non-discretionary variables are handled as per Banker 1 and Morey (1986)10. 2 3 3.1.1 Profit inefficiency (PI) 4 The maximum profit DEA model is similar to the TI model above just substituting the 5 objective function (2) by 6 0TIMBER CARBON WATER TREE Max p TIMBER p CARBON p WATER q TREE  =  +  +  − (4) and also substituting these other constraints 7 1 n jj j TREE TREE  = = (5a) 1 n jj j TIMBER TIMBER  = = (5b) 1 n jj j CARBON CARBON  = = (5c) 1 n jj j WATER WATER  = = (5d) 10Since they are outside management’s control, non-discretionary variables cannot be treated as discretionary ones. Thus, they do not have an associated slack variable and they appear neither in the objective function of the technical inefficiency model nor in the objective function of the profit maximization model. 18 where TIMBER CARBON WATER p , p , p are the unit price of the three discretionary outputs, 1 TREE q is the unit price of the only discretionary input, π0 is the maximum profit that DMU 2 0 could obtain, provided it operates as indicated by the optimal value of the variables TREE, 3 TIMBER, CARBON and WATER. 4 The PI model described above calculates a target operating point that maximizes 5 profit, determined using input and output prices. Just like in the TI model, this target operating 6 point is computed as a convex linear combination of observed DMUs, ensuring technical 7 efficiency. Unlike the TI model, it is not a requirement for the target operating point to 8 dominate DMU 0. Interestingly, the technically efficient target derived from the TI model is 9 feasible in the PI model, though not necessarily optimal. The corresponding profit might not 10 be the maximum achievable. 11 Following Cooper et al. (2011), the PI of DMU 0 can be computed as 12 ( )   0 0 0 0 0 04 TIMBER CARBON WATER TREE TREE TREE TIMBER TIMBER CARBON CARBON WATER WATER p TIMBER p CARBON p WATER q TREE PI min q g , p g , p g , p g  −  +  +  −  =     (6) and can be expressed as 13 0 0 0 PI TI AI=+ (7) where the residual term AI0 represents the Allocative Inefficiency of DMU 0, i.e., the part of 14 the profit inefficiency that is not due to technical inefficiency but to an inadequate input and 15 output mix that does not respond to the input and output prices faced by the DMU. 16 In order to estimate PI, we assumed a value of $28 per m3 of timber (Timber Mart 17 South, 2022). For carbon sequestration, we used a value of $18 per metric ton of carbon 18 (Forest Trends’ Ecosystem Marketplace, 2021). In the case of water yield, we used the cost 19 of pumping groundwater for the upper Floridian aquifer, $0.07 per mm, as a proxy for the 20 19 price of water (Florida Department of Environmental Protection 2015). A unit price for 1 species richness was ruled out since this variable is a non-discretionary output. 2 The input costs were calculated as the management costs of growing longleaf pine 3 trees. Management costs ($ per ha) were calculated as a function of the silvicultural 4 treatments performed on each single plot. The silvicultural treatments defined in the FIA 5 program were absence of management, site preparation ($324 per ha), artificial regeneration 6 ($166 per ha), natural regeneration ($83 per ha), and fertilizer application ($311 per ha) 7 (Maggard, 2021). Only one of the silvicultural treatments described above was carried out for 8 each plot, and these treatments occurred at the time the plots were recorded. Furthermore, we 9 calculated the cost of establishing trees at age zero for each plot– a proxy for the present 10 planting/regeneration costs–by assuming a value of $0.13 per tree (Maggard, 2021), 11 considering an annual mortality rate of 5% and the age of the plot. 12 13 3.2. Stage 2: Robust multiple linear regression analysis 14 The second stage carries out a regression analysis of those inefficiency scores with 15 the objective of identifying exogenous variables that have an effect on the inefficiency of the 16 DMU. As such, our objective is to determine which external factors are significantly related 17 to the average TI of longleaf pine forest ecosystems; specifically, those that are considered as 18 descriptive measures of the relative performance plots in the sample. 19 Additionally, two non-parametric statistical significance hypothesis tests were 20 conducted. First, the one-sample Wilcoxon signed-rank test (Gibbon, 1971) was employed to 21 compare the average technical inefficiency versus allocative inefficiency across several 22 exogenous variables. Second, a pairwise multiple-comparison Dunn’s test (Dunn, 1964) was 23 utilized, with corrections made using the Benjamini-Hochberg multiple-comparison 24 20 adjustment (Benjamini and Hochberg, 1995), to identify similarities among exogenous 1 variables. 2 Because the TI scores do not take values in the unit interval and TI scores naturally 3 contain outliers and high leverage points, this robust approach, even when the observations 4 deviate from the assumptions of the model, is appropriate to increase the reliability and 5 accuracy of statistical modeling (Maronna et al., 2006). The specification of the multiple 6 linear regression model is as follows: 7 TIj=β0+∑βkSTATEjk +∑βlMANAGEMENTjl 10 l=6 5 k=1 + β11OWNERSHIPj + β12DISTURBj+β13ZTIMEj+uj, j=1, …n (8) where STATE represents the location of the forest plots in the different states, 8 MANAGEMENT reflects the evidence of the following types of management per forest plot: 9 cutting, site preparation, artificial regeneration, natural regeneration, fertilizer application, 10 and absence of management; OWNERSHIP represents if the forest plot is under private or 11 public ownership; DISTURB reflects whether the plot shows any level of damage cause by 12 disturbances such as wildfires, storms, floods, drought, diseases, insects or animals, and; 13 ZTIME is a standardized continuous variable that represents the time of the FIA observation 14 associated to the forest plot. 𝛽 represents the coefficients to be estimated and u is the error 15 associated with each forest plot. Table 1 shows the summary statistics of the variables 16 employed in this model. The multiple linear regression analysis is performed using R code 17 (Maechler et al., 2022), using an extension of the maximum likelihood method (M-18 estimation), which is robust to the presence of outliers and feasible with both continuous and 19 categorical exogenous variables. Finally, in addition to the present DEA study, we also 20 employ stochastic frontier analysis to determine technical and profit efficiency (SFA, Section 21 A.1 and A.2, Appendix A), providing a complementary perspective on our findings. 22 21 1 4. Results 2 4.1. Efficiency assessment 3 Most of the forest plots were not efficient in the production of ecosystem services. In 4 the case of TI, we can see that the majority of the forest plots were in the range of 1.90-3.81, 5 with the exception of those plots located in western FL and south AL-MS, which showed 6 higher TI values (3.81-5.71)11 (Figure 2). Since the component of the directional vector g 7 used for normalizing the input and output slacks corresponds to the average of the observed 8 values, this means that for most forest plots, the total enhancement in the provision of timber, 9 water, carbon sequestration, and tree density could amount to 190-381% of the average plot. 10 Opposite results were found when using SFA, with an average of only 3.3% of the production 11 of ecosystem services lost to due to technical inefficiency (Table B.1, Appendix B) 12 Insert Figure 2 13 In general, longleaf pine plots were more technically inefficient in private ownership, 14 with an absence of disturbances and with evidence of natural regeneration (Figure 3). 15 However, from an allocative perspective, plots in public ownership, with presence of 16 disturbances and with evidence of cutting, were more inefficient (Figure 3). From a 17 profitability perspective, the majority of the longleaf plots were highly inefficient, within the 18 PI range of 19.36-29.04, except for some plots located predominantly in GA, SC and NC, 19 which showed lower PI estimates (Figure 2). The relatively high values of PI obtained, much 20 higher than the corresponding TI values, indicated, according to equation (7), that there is 21 11 Note that while the absolute value of the TI scores depends on the specific values of the components of the directional vector (which function as normalization coefficients), their labelling as low or high above is qualitive (subjective) and based on their relative values. 22 significant profit inefficiency and that it mainly has an allocative character more than a 1 technical origin. SFA estimates supported these findings, indicating that forest plots are 2 highly inefficient in terms of profitability. The estimated SFA profit inefficiency was 1.48 3 (148%) suggesting that most of the profit inefficiency is due to allocative reasons (Table B.2, 4 Appendix B). 5 There is evidence that medians of TI (private versus public), AI (private versus 6 public), TI (presence of disturbance-absence of disturbance), AI (presence of disturbance-7 absence of disturbance), AI (managementabsence of management) distributions were 8 statistically different at the 0.001 significance level (Wilcoxon signed-rank test, Figure 3). 9 However, non-differences were shown between management practices with respect to AI. 10 Significant TI differences were observed between “cutting” and each other practices, between 11 “nothing” and “site preparation”/”natural regeneration”/ ”artificial regeneration” and 12 between “fertilization” and “site preparation”. Significant differences were not detected 13 between the rest of other pairs of management practices (Table 2). 14 Insert Figure 3 and Insert Table 2 15 It can be noted that a non-homogeneous pattern arose between states across the 16 management, ownership, and disturbance variables, namely, a right-skewed TI distribution 17 (Fig. 4a-4c), a left-skewed PI distribution (Fig. 5a-5c), and right-skewed and left-skewed AI 18 distribution (Fig. 6a-6c)12. Therefore, extreme values far from the median values occurred. 19 12 While all these activities are indeed conducted under private ownership (see Fig. 4d), the level of management, in relative terms, appears to be relatively low. Around 34% of the private forest plots demonstrated evidence of forest management. Notably, cutting stands out as the primary activity, accounting for 24% of the forest plots, followed by fertilization 23 Considerable disparities were evident among the different groups of variables. The state of 1 NC and the treatment with artificial regeneration were the subgroups with low levels of TI/PI 2 values, and where the dispersion of AI was observed. 3 At the state level, the TI values of all levels of ownership, management, and 4 disturbance were non-homogeneous with the exception of SC (ownership), FL and NC 5 (management), and GA and MS (disturbance). Approximately 75% of forest plots located in 6 AL and MS in private ownership showed a TI value lower than 4.0 (Figure 4a). With the 7 exception of FL, forest plots with evidence of disturbances were technically less inefficient 8 in providing ecosystem services than those without evidence of disturbance (e.g., wildfires, 9 storms, floods, drought, diseases, insects, animals) (Figure 4c). TI between management and 10 ownership variables behaved similarly when cutting was used as treatment by public and 11 private ownership (Figure 4d). Furthermore, TI appeared to be higher in publicly owned plots 12 with evidence of site preparation. 13 In the case of PI, different patterns also emerged in 14 ownership/management/disturbance by state identifying upper and lower extreme points 15 (Figure 5a, 5b, 5c). NC and SC, however, are states where the extreme values were located 16 in the upper tail of the distributions. The pattern discrepancy was even sharper when the plots 17 showed evidence of natural regeneration, other preparation, and site preparation (Figure 5e) 18 and in the case of ownership (Figure 5f) for all levels of disturbance. Most of the plots showed 19 a PI value greater than 25.0 in the presence of disturbance, with the exception of NC (Figure 20 5c). Furthermore, disturbances also generated higher levels of PI only in forest plots located 21 (3.8%) and artificial regeneration (2.4%). Conversely, site preparation and natural regeneration are scarcely observed under private ownership. 24 in AL and GA. From an economic perspective, compared to public ownership, roughly 75% 1 of privately owned longleaf plots were less inefficient in the absence of forest management 2 and with evidence of natural regeneration, fertilizer application, and site preparation (Figure 3 5d). Furthermore, compared to public ownership, natural regeneration, fertilizer application, 4 and site preparation decreased PI levels of PI in privately-owned forest plots. 5 6 Insert Figure 4, Figure 5 and Figure 6 7 4.2. Regression analysis 8 The global precision of the estimated model is evaluated by calculating the adjusted 9 R2 and the standard error statistics, indicating a good fit to the proposed model (Table 3). The 10 most important predictor of TI in the provision of ecosystem services was the geographical 11 location of the plots. The estimates of the coefficients were significantly positive in all states 12 with respect to the baseline (SC) indicating that the plots located in SC have lower TI scores, 13 i.e., they are more efficient from a technical point of view. Furthermore, we found that those 14 states farther from SC were technically more inefficient in the production of ecosystem 15 services. For example, the average TI value of the plots in MS was twice higher than the 16 average TI value in SC, which was the largest effect in TI. Furthermore, the smallest 17 difference is observed in NC with an average TI 0.47 higher than that of SC. The negative 18 signs of coefficient of SFA model suggest that forest plots in FL, GA and NC show to be 19 more efficient in the provision of ecosystem services than those located in SC (Table B.1, 20 Appendix B). 21 The estimate of land ownership revealed that, on average, the TI under private forest 22 ownership is 0.71 higher than under public forest ownership. In addition, the positive 23 coefficient effect of the disturbance variable indicated that forest plots with damage tend to 24 be more inefficient in the provision of ecosystem services. The SFA approach revealed that 25 25 private forest plots were more inefficient in providing ecosystem services compared to those 1 under public ownership, as indicated by the positive sign of ownership. Conversely, forest 2 plots that have been damaged were less inefficient in the provision of ecosystem services, as 3 implied by the negative sign of disturbance (Table B.1, Appendix B). 4 Only natural regeneration and the use of other types of management prescriptions 5 such as fertilizers are significant in the model of TI, in both cases increasing the inefficiency 6 in the provision of ecosystem services in longleaf pine plots compared to the absence of forest 7 management. In the case of the SFA, natural regeneration along with artificial regeneration 8 and site preparation also increased inefficiency (Table B.1, Appendix B). The time predictor 9 indicates that the provision of ecosystem services has become more inefficient over time. 10 Insert Table 3 11 5. Discussion 12 The present DEA findings showed that most of the longleaf pine forest plots were 13 technically inefficient in providing ecosystem services. Susaeta et al. (2016a) used a 14 standard output-oriented DEA model to maximize ecosystem services and found similar 15 results for loblolly pine in the region. Their study indicated that approximately 66% of 16 loblolly pine plots were inefficient in providing timber, tree species richness, and carbon 17 sequestration. Our results indicated that the provision of forest ecosystem services could be 18 increased to a larger extent, reflecting a five-fold increase in inefficiency compared to that 19 of loblolly pine. 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Econ. 155, 59–69. 11 12 38 List of Tables and Figure captions 1 Table 1. Summary and statistics of variables employed in the two-stage analysis. 2 Table 2. Dunn’s statistic (with Benjamini-Hochberg correction for p-values). 3 Table 3. Robust regression results of technical inefficiency. 4 Figure 1. Location of the forest plots 5 in the southeastern US (numbers between parenthesis represent the number of forest plots per state). 6 Figure. 2. Profit, technical and allocative inefficiencies of longleaf pine plots 7 . Figure 3. Average technical inefficiency/allocative inefficiency per ownership group, 8 disturbance group and management group. 9 Figure 4. Violin plot (combination of boxplot and density trace) of technical inefficiency 10 grouped into different exogenous variables (state, ownership, management and disturbance). 11 Figure 5. Violin plot (combination of boxplot and density trace) of profit inefficiency grouped 12 into different exogenous variables (state, ownership, management and disturbance). 13 Figure 6. Violin plot (combination of boxplot and density trace) of allocative inefficiency 14 grouped into different exogenous variables (state, ownership, management and disturbance). 15 ) ) 39 Table 1. Summary and statistics of variables employed in the two-stage analysis. First-stage DEA: inputs and outputs Variable (units) Mea n Max Min Std. Dev. Global Moran’s I statistic (ZI-score)c Local Geary’s C statistic (ZC-score)c Inputs Total annual precipitation (mm)a 1425 .2 2971.5 772.0 281.3 0.12 (27.1)*** 0.89 (6.9)*** Site productivity (m3/ha/yr)a 4.2 14.0 0.5 1.8 0.10 (21.2)*** 0.85 (10.1)*** Average annual minimum temperature (ºC)a 13.1 18.6 7.6 1.9 0.33 (69.5)*** 0.54 (41.5)*** Average annual maximum temperature (ºC)a 26.0 31.0 19.7 1.7 0.34 (72.8)*** 0.49 (40.8)*** Plot age (years)a 44.2 113.0 1.0 22.8 0.05 (11.8)*** 0.96 (3.7)*** Tree density (trees/ha)b 633. 6 6167.0 4.7 736.3 0.06 (13.9)*** 0.94 (2.0)** Outputs Timber production (m3/ha)b 76.0 470.4 0.1 66.7 0.07 (16.1)*** 0.95 (2.1)** Carbon sequestered (C ton/ha/year)b 6.7 168.0 0.5 11.0 0.01 (2.6)*** 1.01 (-0.2) Water yield (ton)b 5381 .1 12531.7 945.2 1,310.9 0.10 (22.3)*** 0.91 (5.9)*** Richness (1-10 level)ae 2.2 10.0 1.0 0.98d Richness frequency 1 [36%]; 2 [33%]; 3 [16%]; 4 [7%]; 5 [4%]; 6 [2%]; 7 [1%]; 8 [0.3%]; 9 [0.2%]; 10.0 [0.04%) Second-stage multiple linear regression: exogenous variables OWNERSHIP (1=private; 0=public) 0.69 1 0 DISTURB (1=disturbance; 0=no disturbance) 0.41 1 0 STATE AL (Alabama) 0.13 1 0 FL (Florida) 35.8 1 0 40 GA (Georgia) 19.2 1 0 MS (Mississippi) 7.5 1 0 NC (North Carolina) 6.7 1 0 SC (South Carolina) 17.6 1 0 MANAGEMENT cutting 0.22 3 1 0 site preparation 0.00 7 1 0 natural regeneration 0.01 8 1 0 fertilization 0.04 8 1 0 no management 0.70 6 1 0 a Non-discretionary; b Discretionary; c Standard deviation calculated under the assumption of randomization; d Index of qualitative variation; e The number of different forest species per forest plot ranges from 1 to 10; *** significant at the 0.001 significance level; ** significant at the 0.01 significance level; values between parenthesis represent standard errors. 41 Table 2. Dunn’s statistic (with Benjamini-Hochberg correction for p-values). Art. Reg Cutting Fert Nat.reg Nothing Cutting -3.09*** - - - - Fert 1.98 2.98*** - - - Nat.Reg -0.6 3.67*** 1.91 - - Nothing -2.34*** 4.59*** -0.82 -2.53*** - Site Prep 0.06 3.69*** 2.37** 0.75 2.83*** *** significant at the 0.001 significance level; ** significant at the 0.01 significance level. 48 Fig. 6. Violin plot (combination of boxplot and density trace) of allocative inefficiency grouped into different exogenous variables (state, ownership, management and disturbance). Horizontal lines represent the first quartile, second quartile and third quartile of the dataset. a) b) c) d) e) f)