On the Productivity of Public Forests: A Stochastic Frontier Analysis of Mississippi School Trust...

On the Productivity of Public Forests: A StochasticFrontier Analysis of Mississippi School Trust

Timber Production

Matthew H. Bonds and Danny R. Hughes Q1

This paper presents the results of a stochastic frontier analysis on the technical efficiency of school trusttimber production in Mississippi. The state of Mississippi has a two hundred year history of managingpublic trust lands designated to generate funds for public schools. Local school boards became thetrustees of sixteenth section lands in the 1970s and have since supervised substantial increases in timberreceipts. The majority of the timber management services are contracted to the Mississippi ForestryCommission (MFC)—a state agency responsible for, among other things, overseeing sixteenth sectiontimber management. The school districts and the MFC are legally required to maximize revenuefrom these lands. However, school districts are also legally permitted to outsource forestry servicesto private vendors and do so on a regular basis by recommendation from the MFC. This paper findsthat the average technical efficiency of the sixteenth section lands is 46%, and there is a positiveand statistically significant increase in total timber receipts when a higher proportion of managementservices are outsourced.

Le present article presente les resultats d’une analyse frontiere stochastique de l’efficacite techniquede la production de matieres ligneuses sur les lots reserves aux ecoles publiques dans l’Etat du Mis-sissippi. Cet Etat possede deux cents ans d’histoire en gestion de terres publiques destinees au fi-nancement des ecoles publiques. Les conseils scolaires locaux sont devenus les administrateurs deslots numero 16 dans les annees 1970 et gerent depuis des augmentations substantielles de revenus tiresde la foret. La majorite des services de gestion des matieres ligneuses sont confies a la MississippiForestry Commission (MFC), agence d’Etat chargee, entre autres, de la gestion de la matiere ligneusedes lots numero 16. Les arrondissements scolaires et la MFC sont legalement tenus de maximiserles revenus de ces lots. Les arrondissements scolaires peuvent, en vertu de la loi, confier les servicesforestiers a des entreprises privees, ce qu’ils font regulierement sur recommandation de la MFC. Lesresultats du present article ont montre une efficacite technique moyenne des lots numero 16 de 46% etune augmentation statistiquement significative et positive des revenus totaux tires de la foret lorsqu’unegrande partie des services de gestion etaient impartis.

There is an extensive, and relatively dated, literature on the economic efficiency of na-tional forest timber production in the United States. Relying mostly on simple revenue-cost comparisons, the overwhelming conclusion has been that the U.S. Forest Serviceoperates inefficiently (Clawson 1977; Hyde 1981; Muraoka and Watson 1983, 1986; Leal1995; Fretwell 2001). More recently, there have been more sophisticated efforts of mea-suring forest productivity with data envelopment analysis (DEA) and stochastic frontieranalysis (SFA) (Rhodes 1986; Kao and Yang 1991, 1992; Kao, Chang, and Hwang1993; Carter and Cubbage 1994, 1995; Viitala and Hanninen 1998; Kao 2000; Grebnerand Amacher 2000; Siry and Newman 2001; Zhang 2002). Unfortunately, the complexuse of public forests makes such analyses less than straightforward. For example, the

Canadian Journal of Agricultural Economics 55 (2007) 171–183

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172 CANADIAN JOURNAL OF AGRICULTURAL ECONOMICS

Multiple-Use Sustained Yield Act requires, “the management of all the various renew-able surface resources of the national forests so that they are utilized in the combinationthat will best meet the needs of the American people.” Such needs—such as recreationaluse and timber harvesting—are broad and often conflicting, and therefore the data nec-essary for accurate economic efficiency analyses are difficult to acquire. These multipleobjectives tend to be ignored in these analyses, and may often undermine proper inferencesin these studies.

Fortunately, there is an alternative subject for efficiency analysis of public forests thathas been almost entirely ignored by resource economists: school trust lands (also knownas state trust lands, and sixteenth section lands). These lands are generally managedunder the trust doctrine exclusively for the purposes of generating revenue for publicschools. Moreover, many states manage these via local governments, and therefore thereare many simultaneous operations by which efficiency comparisons can be made. Suchlands, therefore, constitute a treasure trove of research possibilities for efficiency analysisof public land management.

As an illustration, this paper presents the case of timber production under theMississippi School Trust Program (MSTP). The sixteenth section lands in Mississippi havea more than 200-year history of being managed with the objective to generate revenuesfor public schools and offer an interesting experiment in institutional economics. An SFAis used here to test timber productive efficiency of the lands and measure the returns toprivatizing forest management activities.

THE MISSISSIPPI SCHOOL TRUST PROGRAM: BACKGROUND

The sixteenth section program is rooted in American colonial policies. The GeneralLand Ordinance of 1785 designated townships as 6-mile-by-6-mile square tracts of land,composed of 36 1-square-mile sections. The sixteenth section is approximately in themiddle of the township—in the third row and third column of the square. The ordinancereserved the sixteenth section of every township for the maintenance of public schoolswithin the township. These provisions were maintained under the Northwest Ordinanceand into Mississippi statehood. For details of the legal history of school trust lands inMississippi as well as throughout the United States generally, see Bonds and Pompe(2005) and Souder and Fairfax (1996).

After decades of dismal revenue generation from the school trust lands, an 1895 Mis-sissippi Supreme Court decision in Jones vs. Madison County determined that sixteenthsection land was trust property—the state being the trustee and the inhabitants of thetownships being the beneficiaries (Sixteenth Section Biennial Report, 1997–98).

Jurisdiction over sixteenth section lands has changed numerous times since theircreation, and its history has even been referred to as the “Legacy of Shame” by theMississippi Secretary of State’s Office (Clayton and Spencer 1977; Sixteenth sectionbiennial report, 1998–99). Though the counties of Mississippi had always been legallyrequired to manage the lands exclusively to generate revenue to fund schools, the sourceof some of the inefficiencies may be attributed to the difference between the principals—the local school districts—and the agents. The trustees appear to have had incentives tomanage these lands in conflict with the interests of the schools (e.g., allocating the landto special interests). As State Superintendent of Education, J.R. Preston stated in 1890,

PRODUCTIVITY OF PUBLIC FORESTS 173

“The only uniformity discernible at this distance is that land went and no revenue camein return” (Bond 1931).

In 1948, the General Legislative Investigating Committee reported that timber fromsixteenth section lands had been sold, “at such grossly inadequate prices as to shock theconscience and, in some instances, as to constitute nothing more or less than a donationof this timber to private individuals” (Mississippi Laws of 1948). Legislation was passedin 1958 that required the State Land Commissioner to classify all school lands into twocategories: “Forest” and “Other.” Land classified as Forest was prohibited from beingleased, and its management control was transferred away from the Boards of Supervisorsto the Forestry Commission. In 1978, the Sixteenth Section Land Reform Act was passed,which gave ultimate control of the lands to the Boards of Education where it rests now(MS Code, Sec. 29-3-1).

The county school boards are now required by law to classify the lands according toa finding of their highest and best use for producing the maximum revenue (MS Code,Sec 29-3-33). Management of land classified as Forest is still supervised by the MississippiForestry Commission (MFC) (MS Code, Sec. 29-3-45), and is required to be managed fortimber production, but is typically simultaneously leased to hunting clubs. Each schooldistrict is required to contract with the MFC, which then schedules timber harvestingand sales. Both the MFC and the respective school boards must authorize all timbermanagement activities.

The district school boards are responsible for compensating the MFC for the costsof the timber management (MS Code, Sec. 29-3-47). Fifteen percent of timber receipts foreach district are placed into an escrow fund that is used to cover the costs of managing therespective forests. Excess money that has accumulated in the escrow funds may be releasedto the respective school boards after authorization from the Secretary of State and theMFC. Those funds may be directed to cover a large variety of public school expenditures.In case of insufficient funds for timber management, school boards may deposit moneydirectly into the escrow fund, defer payments to the MFC until sale of timber at a laterdate, or seek assistance via the Forest Resource Development Law of 1974 (MS Code, Sec.49-19-201). In addition to providing need-based grants for timber management to schooldistricts, the Forest Resource Development Law requires that, “the Mississippi ForestryCommission brings all Sixteenth Section Forest Lands to maximum productivity.”

The MFC is responsible for forest management decisions in all of the participatingdistricts, but school boards are legally permitted to outsource the activities to privatevendors (MS Code, Sec. 29-3-49). In practice, the MFC is involved in all forest manage-ment activities and recommends outsourcing in cases when they cannot accommodatethe demand. For projects estimated to exceed $10,000, the MFC must publicly advertisethe project and accept the highest bid over a three-week period. For projects less than$10,000, a public advertisement is not required, and vendors are contacted directly forbid submission.

After a long and tumultuous history, the sixteenth section lands in Mississippi arenow legally being managed to maximize revenue through joint cooperation between theirtrustees—the Boards of Education and the MFC. Total timber receipts from sixteenthsection lands have improved from a real value of about $7 million in 1979 to $22 millionin 2001.1 Despite this marked improvement, the question still remains, how well are thelands being managed relative to their potential? On one hand, profits go to the school


boards’ budgets, providing an incentive for efficiency. On the other hand, the MFC canincrease its budget through higher timber management costs, for which the school boardsare required to compensate, possibly providing a disincentive for efficiency. Which ofthese forces is dominant? These are questions that no productivity analysis has attemptedto answer—neither for Mississippi nor for any other state in the Union. How muchadditional revenue could be generated under an efficient management regime? What isthe opportunity cost to the public schools of employing a monopolistic MFC instead ofcompetitive private vendors?

DATA

Leal (1997) and Fretwell (2001) have suggested that because state trust lands—in contrastto U.S. national forests—tend to generate profits, they constitute a model for public landmanagement. However, the objective of national forests is not to maximize profit, andthe existence of profits on state trust lands is an insufficient bar for inferring their overallefficiency. Despite the tumultuous political history of Mississippi school lands, they havemaintained clear objectives and we may therefore rely on SFA to estimate their productiveefficiency and benefits of privatization.

Data on total forestland acres, expenditures, and timber receipts from 1997 to 2001of every participating school district were collected from the Mississippi Forestry Com-mission. While the districts also receive funds from hunting leases, management of thelands focuses on maximizing timber productivity, with hunting considered an incidentalsource of revenue; the average hunting lease amounts to approximately $5 per acre peryear. We therefore omit hunting revenue from the analysis. The expenditures included inthis analysis are: fertilization, pruning, release, fire-break/road maintenance, firelane con-trol, vegetation and animal control, silvicultural burning, timber marking and technicalassistance. Site preparation, planting—activities that preceded the current managementregime of recent timber harvests—and MFC overhead expenses are not included. Data onthe value of the escrow fund in the 1995–96 were also collected from the MFC for use asinstrumental variables. In addition, soil data from the U.S. Department of Agriculture areused as control variables. The expenditures and receipts were averaged over the five yearperiod with the GDP deflator, and the remaining cross-section includes the 71 districtsin Mississippi for which complete data were available.2 The average real expendituresoutsourced to private vendors were divided by the average real total expenditures paidto the MFC and the private vendors to yield the average cost–share privatized in eachdistrict. Summary Statistics for the data sample can be found in Table 1.

METHODOLOGY

Productive efficiency refers to the complete minimization of economic waste such thateither, for some observed level of output, inputs are minimized, or for some observed levelof inputs, outputs are maximized, or some combination of the two (Coelli et al 1998).The stochastic frontier production function was first proposed in independent papersby Aigner, Lovell, and Schmidt (1977) and Meeusen and van den Broeck (1977). Sincethen, it has been used extensively to measure the productive efficiency of airlines, utilities,and other regulated industries where data have been available. For an overview of theproductivity analysis literature see Kumbhakar and Lovell (2000).


Table 1. Summary statistics n = 72

StandardMean deviation Minimum Maximum

Avg. real timber sales 1997–2001 $295,219.40 $283,320.8 $1,700.28 $1,368,338Avg. real total expenditures

1997–2001$6,533.52 $6,708.44 $40.07 $40,749.82

Average cost share privatized1997–2001

0.13 0.22 0 0.96

Total forestland acres 5,210.41 3,033.49 533 13,450Real escrow fund 1995–1996 $92,601.82 $84,791.13 $463.23 $380,773.1

SFA converts the input–output observations to a production frontier, accounting fortechnical inefficiency and random noise (Coelli et al 1998). While a typical least squaresregression consists of a deterministic component and a random noise component, thestochastic frontier model is based on the premise that a production frontier cannotbe generated from the deterministic component of a least squares linear regression be-cause not all firms operate efficiently. It therefore assumes a distribution of technicalinefficiency—often a half-normal distribution—in addition to the random noise. Thisapproach allows for the estimation of parameters accounting for these differences in thefirms’ efficiencies.

Stochastic frontier applications to timber production have typically regressed outputsfor a small number of years on inputs for those respective years (Carter and Cubbage 1995;Siry and Newman 2001). This allows analysts to rely on very few years of observations,but has two fundamental problems. First, it assumes that the forests are fully regulated,where inputs for the years observed are constant over every year of the timber productioncycle. However, this assumption negates the use of a panel set, where output for differentyears are regressed on the inputs for those respective years. For a detailed exposition, seeAppendix A. In addition, the assumption of fully regulated forests is strong, and oftenunreasonable.

If production inputs vary over time (i.e., if forests are not fully regulated), an idealstatistical analysis of the production process would involve data on the physical inputs(e.g., number of employees, growing stock volume, meters of roads, logging trucks, etc.), aswell as physical outputs (i.e., volume of timber sales) over the course of the harvest cycle.Unfortunately, such data for the Mississippi School Trust Program are not available.Rather, our data consist of timber receipts and management expenses over a five-yearperiod (1997–2001), which we are able to average over time into a single cross-sectionbecause of sufficient contemporaneous observations (n = 72). Thus, we avoid treating theforests as if they are fully regulated (which they are not), but we rely on a couple of otherassumptions. The first is that timber sales and operating expenses are good proxies forphysical outputs and inputs. Secondly, we assume that the average operating costs andtimber sales in the years observed are equal to the average operating costs and timbersales over the harvest cycle for each district. Violation of either of these assumptionscould bias efficiency estimates.


There are a couple of other issues regarding regressors, or lack thereof, that warrantdiscussion. Timber is not produced in a vacuum, and is vulnerable to random (i.e.,unpredictable) events such as weather crises. Because SFA implements a random errorterm, stochastic normally distributed weather patterns over the five years will not bias thecoefficient estimates. However, if long-term crises (e.g., droughts or hurricanes) strike asingle district or groups of districts disproportionately over the course of the five years, theanalysis may attribute technical inefficiency to what would be better considered omittedvariables. Soil types, which are geographically oriented and may roughly correspondto long term weather variables, are used as regressors here and may mitigate some ofthese potential problems.3 There are five major soil-geographic classifications used here:Southern Mississippi Valley Alluvium; Southern Coastal Plain; Southern MississippiValley Silty Uplands; Alabama, Mississippi, and Arkansas Blackland Prairie; and EasternGulf Coast Flatwoods.

Regressing timber sales receipts on expenditures over the same time period is alsosubject to an endogeneity problem. This model assumes that average timber receipts area function of average expenditures on inputs. Unfortunately, it is also the case here thatexpenditures are derived from the forestry escrow funds that are composed of a portionof the timber receipts. That is, the inputs here (and likely in other studies of public forests)are also a function of the output.

To solve this problem, the real value of the 1995–96 escrow fund is used as an instru-mental variable and a two-stage regression is implemented. The escrow fund accumulatesin value over time in accordance with annual injections that are typically much greaterthan the annual expenditures. The escrow fund in the year previous to 1997 provides auseful instrumental variable because its value is completely independent of subsequenttimber sales, yet constitutes the bulk of the source from which management expendituresare withdrawn from 1997 to 2001. The model for the first stage is:

XEX,i = γ0 + γ1 XEF,i + εi (1)where,

XEX,i is the natural log of the average real value of expenditures for district i from 1997to 2001.

XEF,i is the natural log of the real value of the escrow fund for district i in the 1995–96academic calendar year.

The first stage yieldsXEX,i , which is the predicted value ofXEX,i , produced from theestimates of the first stage, presented in Table 2.

The production function that has been most commonly employed in timber pro-ductivity analysis is Cobb–Douglas (Siry and Newman 2001) primarily because it is easyto estimate and manipulate and requires fewer observations than alternative functionalforms. Both the Cobb–Douglas and the more flexible Translog functional form were con-sidered, with the Translog functional form rejected through log-likelihood testing.4 Thefinal model for the second stage is:

Yi = β0 + β1 XEX,i + β2 XA,i + β3 XPV,i + β4 XSA,i + β5 XSC,i + β6 XSU,i + β7 XSG,i

+ β8 XSCP,i + β9 XSCU,i + vi − ui (2)


Table 2. Stage one: Generating XEX,i

Variable Coefficient estimates

Constant 1.235(1.042)

XEF - Natural log of the real value of the escrow fund fordistrict in the 1995–1996 academic calendar year.

0.617∗∗∗

(0.095)R2 0.336Adj. R2 0.328

Notes:1. The estimated standard errors are presented below the corresponding estimates.2. ∗∗∗ Significant at the 1% level.

where,

Yi is the natural log of the average real value of revenues from 1997 to 2001XEX is the predicted value of the natural log of the average real value of expenditures

from 1997 to 2001XA is the natural log of forestland acresXPV is the average real cost–share privatized from 1997 to 2001XSA is a soil dummy (SD) variable for Southern Mississippi Valley AlluviumXSC is an SD variable for Southern Coastal PlainXSU is an SD variable for Southern Mississippi Valley Silty UplandsXSG is an SD variable for Eastern Gulf Coast FlatwoodsXSCP is an SD variable for Southern Coastal Plain and Blackland PrairieXSCU is an SD variable for Southern Coastal Plain and Southern Mississippi Valley Silty

Uplandsvi is a random disturbance term that is i.i.d. N(0, σ 2

v), independent of ui

ui is a technical inefficiency term that is an i.i.d. truncation at 0 of N(0, σ 2u)

Equation (2) is estimated through maximum likelihood estimation, with the like-lihood function maximized in terms of the variance parameters, σ 2 = σ 2

v + σ 2u and

γ = σ 2u/σ

2. Estimates of the efficiency of the i th producer are predicted as TEi =E[exp(−ui)|(vi − ui)], which is interpreted as the degree to which output fallsshort of its potential given a specific technology and level of inputs. Estimatesfor returns to scale are calculated by summing the estimated coefficients for thefactor inputs, which are the average expenditures, XEX, and forestland acresXA;the variables for the soil and for the cost–share privatized are considered explanatoryvariables that are independent of the inputs.

EMPIRICAL RESULTS AND DISCUSSION

The results of the stochastic frontier test indicate that the average district in Mississippiis operating at 46% technical efficiency (Table 3), implying revenues could more thandouble without increasing costs, if timber were produced perfectly efficiently. In addition,the coefficient for returns to scale here is 1.155, which is comparable to the findingsby Carter and Cubbage (1995), who have returns to scale estimates of 1.130. Though


Table 3. Parameter estimates for the frontier production function

Variable OLS ML

Constant −0.586 2.215∗

(1.626) (1.148)XEX - Predicted value of the natural log of the average real value of

expenditures from 1997 to 20010.754∗∗∗ 0.696∗∗∗

(0.180) (0.090)XA - Natural log of forestland acres 0.596∗∗∗ 0.459∗∗∗

(0.170) (0.159)XPV - Average real cost–share privatized from 1997 to 2001 1.380∗∗∗ 0.989∗∗

(0.522) (0.340)XSA - Soil type—Southern Mississippi Valley Alluvium 1.070 0.672

(0.841) (0.986)XSC - Soil type—Southern Coastal Plain 1.240∗ 1.191

(0.719) (0.984)XSU - Soil type—Southern Mississippi Valley Silty Uplands 1.517∗∗ 1.337

(0.742) (1.007)XSG - Soil type—Eastern Gulf Coast Flatwoods 1.708∗ 1.913∗∗

(0.888) (0.983)XSCP - Soil type mixed—Southern Coastal Plain and Blackland

Prairie1.293∗ 1.488

(0.722) (1.014)XSCU - Soil type mixed—Southern Coastal Plain and Southern

Mississippi Valley Silty Uplands1.103 0.950

(0.709) (0.996)R2 0.587 –Adj. R2 0.526 –Log-likelihood – −75.966Mean technical efficiency – 0.456Elasticity of scale 1.35 1.155

Notes:1. The estimated standard errors are presented below the corresponding estimates.2. ∗∗∗ Significant at the 1% level.3. ∗∗ Significant at the 5% level.4. ∗ Significant at the 1% level.

these figures have been interpreted to reveal increasing returns to scale, an F-test revealsthat the elasticity of scale coefficient presented here is not significantly different from1.5 We therefore cannot reject the null hypothesis that Mississippi school trust timber isproduced at constant returns to scale, implying that revenues may be directly proportionalto management expenses.

The coefficient estimates for acres and expenditures are positive and significant atthe 1% level. The SF and OLS coefficient estimates for the private vendor share are 0.989and 1.380, respectively, and are positive and significant at the 5% and 1% levels. Thissuggests, for example, that if a district increases the portion of its activities outsourced by10%, holding costs constant, revenue would be expected to rise by around 10%.

There are several possible explanations for the inefficiency of the School Trust Pro-gram and potential advantages of outsourcing. Private vendors keep their revenues and


therefore have an incentive to minimize the costs of operation for a given set of activities.In addition, their receipts are based on the services they sell, which are determined bytheir ability to underbid their competitors. In short, private vendors have an incentive tooperate efficiently. In a competitive market, we would expect the prices charged by privatevendors to be equal to their marginal cost of production.

Alternatively, the MFC has a monopoly of forest management services on SchoolTrust lands. Payment to the MFC for any services provided to the school districts is guar-anteed regardless of price or quality of service. But they are paid only for their cost ofproduction, and therefore have no economic incentives to lower costs or improve services.Arano and Munn (2006) determined that industrial timber producers in Mississippi man-age their land six times as intensively as the sixteenth section lands. In fact, School Trustland management closely resembles that of nonindustrial timber producers in Mississippiwho are not considered to be profit maximizers.

The SFA determined only one soil to be significantly different from SMVM-SMVSMmix, which was the Eastern Gulf Flatwoods, which can be found in southern Mississippiand, according the USDA, is 90% covered in forests. The coefficient estimate is 1.913,indicating that timber from the Eastern Gulf Flatwoods region produce nearly three timesthe value per expenditure as the SMVM-SMVSM soil.

CONCLUSION

Here, we consider the Mississippi School Trust Program, which has a long and veryinteresting history of timber production. Our results indicate that boards of educationalong with the MFC could improve revenues for public schools through two routes.First, the statistically significant coefficient estimate of 0.99 on the privatization variableindicates that private outsourcing is associated with twice as much revenue per expen-diture as the activities of the MFC. In the period observed, the average proportion ofoutsourced timber management costs was 13%. Assuming complete substitutability be-tween activities of the MFC and of the private vendors, these results imply that schooldistricts could increase their revenues by 87% without incurring additional costs sim-ply by privatizing the remaining timber management activities. Moreover, the averagetechnical efficiency score for each school district is about 46%, implying that each dis-trict could more than double their revenues without increasing costs, or alternatively,halve their costs, while maintaining the same revenues. Combined, these results implythat timber production on school trust lands are generating as little as one fourth ofthe revenue that would be expected from a perfectly efficient competitive timber market.Given that timber production already generates over $35 million dollars annually forMississippi public schools, such a potential increase in efficiency could have significantconsequences.

Mississippi School Trust timber production represents a specific case of a moregeneral issue regarding the management of public resources. How can the returns to theirintended beneficiaries be maximized? There have been a number of efforts to addressthis general question by measuring the efficiency of timber production on public lands(Rhodes 1986; Kao and Yang 1991, 1992; Kao, Chang, and Hwang 1993; Viitala andHanninen 1998; Kao 2000; Grebner and Amacher 2000; Siry and Newman 2001; Zhang2002). However, for most public lands, such an analysis is difficult because of their


multiple, pecuniary and nonpecuniary uses. School Trust Lands are unique in that theyare managed under the trust doctrine, and with a single legal objective: to maximizerevenue for the purposes of funding public schools. They are therefore well positionedto shed light on the efficiency of public land management. Specifically, we find thatprivatization of management activities may improve overall efficiency; such a conclusionis harder to draw when the objectives are more complex. “In a sense there are threemajor public land systems [in the U.S.]: the national forests, the BLM [Bureau of LandManagement] lands, and the state trust lands,” (Nelson 1996); yet school trust lands havereceived minimal attention from resource economists. We suggest that school trust landsoffer rich possibilities for research on public land management.

NOTES1Deflated with the GDP deflator, base year =1996.2The GDP deflator was chosen over a timber price index for two reasons: a) The objective of revenuemaximization is not conditional on the source of the revenue; b) Data on timber classification wasnot available. It should be noted that the efficiency scores determined from SFA are unit invariant.3The soil types can be found from the Major Land Resource Area Soil Map of Mississippifrom the U.S. Department of Agriculture, http://www.mo15.nrcs.usda.gov/technical/mlra_image_ms.html.4The coefficient estimates produced by the Translog form were not found to be statistically signif-icant at the 10% level, except for average expenditures, which was negatively signed. We attributethese results to the severe multicollinearity detected in the Translog data. Typically, this can bemitigated through the use of panel data; however, the nature of timber production and the lengthof our panel constrains the analysis to a simple cross-sectional model, which is discussed in furtherdetail in Appendix.5F-statistics equal 0.387 and 1.346 for the SF and OLS estimates, respectively.6This assumption is not necessary to generate the eventual conclusions, but makes the analysissimpler.

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MS Code, Sec. 49-19-201. 1974. Forest resources development program. MS Forestry Resources.www.mscode.com/free/statutes/29/003/0201.htm.Mississippi State Law, 1906. P. 55 In The distribution of unconditional federal land grants (sixteenthsections) to the financial support of the public schools of the state of Mississippi, L.N. Davis. 1950.M.A. thesis, Mississippi Southern College, MS. Q5Mississippi Laws of 1948. Ch. 497, Sec. 12. P. 150 in The distribution of unconditional federal landgrants (sixteenth sections) to the financial support of the public schools of the state of Mississippi,L.N. Davis. 1950. M.A. thesis, Mississippi Southern College, MS.


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APPENDIX

Due to data constraints, many econometric analyses of timber production regress outputfrom a given year on input in that year, assuming the production function,

YT = f

(H∑

h=0

xhT

)(A1)

where the subscript on each variable represents the year of activity and the superscriptrepresents the age-class. YT is units of output in year T , x h

T is units of inputs in year Tinto stands of age-class h.

In reality, forests require many years for inputs to be converted to outputs. A “true”model would have output in year T as a function of inputs into the same stand over thecourse of the harvest cycle,

YT = f

(H∑

h=0

xhT−H+h

)(A2)

where x hT−H+h represents units of inputs into the stands of age-class h in year T−H+h,

and H is the length of the harvest cycle in years. For example, if the harvest cycle is 35years, the timber yield in 1999 is a function of the inputs into the seedling stand (age class0) in 1964, the yearling stand (age class 1) in 1965, the two year old stand in 1966, etc. . .

The specification in Eq. (A1) implicitly assumes that inputs in year T into stands ofage-class h are equal to inputs in year T − H + h into stands of age-class h: xh

T = x hT−H+h ,

for all h. That is, the inputs into each age-class are constant over time.


Inputs can be decomposed, xhT = ch

T ahT = ch

T−H+h ahT−H+h = x h

T−H+h , for all h. Where

chT represents inputs per acre of age-class h at time T , and ah

T represents acres of age-classh at time T . For simplicity, we can assume inputs per acre of each age-class are constantover time,6 ch

T = chT−H+h = ch , for all h, implying that the area allocated to each age-class

must also be constant over time, ahT = ah

T−H+h = ah for all h. That is, the area of theseedling stand in 1964, a0

64, is equal to the area of the seedling stand in 1965, a065, as well

as that of 1999, a099. But, it is also the case that, ah

T = ah+tT−H+t = ah+t

T−H+t, for all h and t.For example, the area of seedling stand in 1964, a0

64, is equal to the area of the yearlingstand in 1965, a1

65, and the two year old stand in 1966, a266, because they are the same

stand. Therefore, we can conclude, ah = ah+tT−H+t = a, for all h and t. That is, a0

64 = a065 =

a099 = a1

65 = a266; the area of all age-class stands at all time periods are equal. And because

the cost per acre is constant for each age-class over time, expenditures in each year areimplicitly assumed to be constant. That is, the model that is implicitly implemented is:

YT = f

(H∑

h=0

ch a

)(A3)

The inputs may vary among age-classes in a particular year, but there is no variationbetween years. Therefore, using a panel with output and inputs that vary across yearsviolates the assumptions necessary to regress outputs of a given year on inputs of thatyear.

Queries

Q1 Author: Please provide affiliations for authors.

Q2 Author: Reference Davis (1950) is not cited in the text. Please check.

Q3 Author: Reference MS Code Sec. 29-3-33 is not cited in the text. Please check.

Q4 Author: Reference MS Code, Sec. 29-3-115 is not cited in the text. Please check.

Q5 Author: Reference Mississippi State Law,1906 is not cited in the text. Please check.

Q6 Author: Reference Muroake and Watson (1983) is not cited in the text. Please check.

Q7 Author: Reference Muroake and Watson (1986) is not cited in the text. Please check.

Q8 Author: Please check for the completeness and correctness of the referenceand also reference is not cited in the text.

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