2015 OUTLOOK AND ANALYSIS LETTER - Nc State Universityresearch.cnr.ncsu.edu/rern/aix/aix2015_outlook_letter.pdf · 2015 OUTLOOK AND ANALYSIS LETTER a report prepared for the National

2015 STATE PARK SYSTEMS’ OUTLOOK AND ANALYSIS LETTER 1

2015 OUTLOOK AND ANALYSIS LETTER

a report prepared for the

National Association of State Park Directors

By

Jordan W. Smith, PhD1 and Yu-Fai Leung, PhD

Department of Parks, Recreation and Tourism Management

1 Address all correspondence to [email protected]

2 2015 STATE PARK SYSTEMS’ OUTLOOK AND ANALYSIS LETTER

OVERVIEW This year’s Outlook and Analysis Letter updates and improves upon the production frontier model developed and refined in previous years (Siderelis and Smith 2013; Siderelis et al. 2012; Smith et al. 2015). In previous years, we measured the technical efficiencies of the states’ park systems using estimation routines and algorithms that assumed a state’s operational efficiencies were temporally invariant (Pitt and Lee 1981). That is, we assumed that operational and discretionary management practices within a state park system did not change over time. The inefficiencies observed in 1990 would be the same inefficiencies observed in 2010. This assumption is tenuous at best and becomes particularly questionable when data are available over a long period of time (Schmidt and Sickles 1984); this is the case with the AIX archive data. Data within the AIX archive describe the production of outdoor recreation at state park systems over the past 31 years. We set out this year to find and fit a statistical specification capable of acknowledging operational efficiencies are likely to change year-over-year. Specifically, explored two time-varying fixed-effects specifications, one which allows inefficiency estimates to vary within individual state park systems (Cornwell, Schmidt, and Sickles 1990) and one which allows inefficiency estimates to vary across state park systems (Lee and Schmidt 1993). Across the two time-varying specifications and our original time-invariant specification, we compared technical efficiency estimates and subsequent inefficiency rankings. Our intent was to determine whether the specification of time-invariant efficiency estimates significantly alters the technical efficiency rankings of individual state park systems. The results suggest no statistically significant differences in efficiency rankings across the three specifications. However, the several anomalies in individual state park systems were noticed. These anomalies suggest that time can plays an important role in the estimation of state park systems’ technical efficiencies. If analysts disregard time and opt to use specifications capturing only long-term average efficiency estimates, they are likely to disregard a substantial amount of information concerning recent trends in state park systems’ ability to produce outdoor recreation opportunities. To illustrate the utility of time-varying specifications, we derive and plot state-level efficiency estimates over the past 31 years. The estimates clearly show substantial heterogeneity across the 50 state park systems. Four general trends in operational efficiencies are observed: 1) steady, long-term improvements; 2) steady, long-term declines; 3) recent rebounds; and 4) recent declines. Each of these trend categories is associated with its own set of management implications. States with steady, long-term improvements will be well poised to address and adapt to unforeseen reductions in state appropriations. These state park systems should be commended for their consistently good decision-making behavior. States with steady, long-term declines need to investigate why they are operating in an increasingly inefficient way. Is it due to stagnant attendance levels, a general unwillingness to invest in capital improvements, an unwillingness to increase employment, or a consistent reluctance to use use-fees to generate revenues. The real reason is likely a mix of all of the above. States experiencing recent rebounds experienced declines in operational efficiencies early on in the observed period of analysis, but have since improved. State park system operators within these states should be commended for their ability to “right the ship” so to speak and alter their organizations’ tendency to make poor decisions. States experiencing recent declines peaked in operational efficiency at some time in the not to distant past, but have since experienced sharp declines in the efficient use of operational expenditures. These states are trending in a negative direction and should carefully examine how and why their organization’s structure is consistently producing poorer outdoor recreational opportunities year over year.


TRENDS AND FORECASTS

GENERAL FORECASTING METHODOLOGY For each of the key variables reported in this outlook and analyses—attendance, operating expenditures, capital expenditures, revenue, labor and acreage—we forecast point estimates ahead for three years. This is accomplished through a weighted linear moving average. Data were estimated using the weighted linear trend over the previous 3 years, t-3. We assigned more weight to the observed data points closer to the year for which estimates are being calculated. Specifically, observed data for the year of estimation, t, was assigned a weight of 3, observed data at t-1 was assigned a weight of 2 and observed data at t-2 was assigned a weight of 1. For example the estimated attendance in 2015 was calculated as: 16

1 ∗ 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑_𝑎𝑡𝑡𝑒𝑛𝑑𝑎𝑛𝑐𝑒!"#$ + 2 ∗ 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑_𝑎𝑡𝑡𝑒𝑛𝑑𝑎𝑛𝑐𝑒!"#$ + 3 ∗ 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑_𝑎𝑡𝑡𝑒𝑛𝑑𝑎𝑛𝑐𝑒!"#$

ATTENDANCE – TRENDS Attendance refers to the total counts of day and overnight visitation to both fee and non-fee areas (Leung et al. 2015). The long-term trends in attendance for all state park systems can be seen in Figure 1. Visitation to the states’ parks systems has risen steadily since the beginning of our sampling period in 1984 when they received a total of 643 million visits. Attendance reached its peak in 2000, when the states’ park systems received 787 million visits; it has since leveled off to around 740 million annual visits. For 2014, attendance to the states’ park systems climbed from the 727 million visits reported in 2013 to 740 million visits; this is a 1.67% increase.

650

650

700

750

800

Tota

l Ann

ual A

ttend

ance

(Milli

ons)

1980 1990 2000 2010

Annual Attendance (Millions) Fitted Median Spline

Figure 1. Total annual attendance to the 50 state park systems.


ATTENDANCE – FORECASTS Attendance is expected to gradually increase over the next three years (Figure 2). Based on recent trends, annual attendance is expected to hover around 740 million visits (736 million in 2015, 736 million in 2016 and 740 million in 2017).

650

700

750

800

Tota

l Ann

ual A

ttend

ance

(Milli

ons)

1980 1990 2000 2010 2020

Annual Attendance (Millions)

Projected Annual Attendance (Millions)

Figure 2. Forecasted annual attendance for the 50 state park systems.


OPERATING EXPENDITURES – TRENDS Operating expenditures are payments made for goods and services to manage a state park system (Leung et al. 2015). The long-term trends in operating expenditures, expressed as 2014 dollars, across all state park systems are illustrated in Figure 3. After controlling for inflation, the data reveal operating expenditures have risen over the past 31 years. On average, inflation adjusted operating expenditures have increased by $23.3 million dollars per year since 1984. More recently however, the states’ park systems’ inflation adjusted operating budgets have declined. For 2014 the states’ park systems’ inflation adjusted operating expenditures decreased to $2.45 billion from the $2.57 billion reported in 2013; this is a 0.05% decrease. [Note this year we report inflation adjusted operating expenditures. In 2014, we reported non-adjusted expenditures.]

2.5

1.5

2.0

3.0

3.5

Tota

l Ann

ual O

pera

ting

Expe

nditu

res

(Billi

ons)

1980 1990 2000 2010

Annual Operating Expenditures (Billions) Fitted Median Spline

Figure 3. Total annual operating expenditures for the 50 state park systems.


OPERATING EXPENDITURE – FORECASTS Recent trends suggests expenditures associated with providing the goods and services required to manage the states’ park systems will continue to decline over the coming years (Figure 4). We expect total operating expenditures for 2015 to be $2.53 billion; this is expected to decrease to $2.49 billion in 2016 and to $2.45 billion in 2017.

1.5

2.0

2.5

3.0

3.5

Tota

l Ann

ual O

pera

ting

Expe

nditu

res

(Billi

ons)

1980 1990 2000 2010 2020

Annual Operating Expenditures (Billions)

Projected Annual Operating Expenditures (Billions)

Figure 4. Forecasted operating expenditures for the 50 state park systems.


CAPITAL EXPENDITURES – TRENDS Capital expenditures are non-recurring expenditures used to improve the productive capacity of a state park system (Leung et al. 2015). Typically, these are for land acquisition, periodic park improvements and construction. The long-term trend in inflation adjusted capital expenditures reveals a relatively stable pattern over the past 31 years (Figure 5) with the exception of a notable spike in 2005. Inflation adjusted capital expenditures have declined steadily since the 2008 recession, as would be expected given large-scale reductions in state appropriations, park-generated revenues and other funding sources tied to the health of the states’ economies (Siderelis and Smith 2013). The states’ park system managers reported capital expenditure of $626 million in 2014, which is slightly below the $632 million reported in 2013; a 0.01% decrease. [Note this year we report inflation adjusted capital expenditures. In 2014, we reported non-adjusted expenditures.]

0.5

1.0

1.5

2To

tal A

nnua

l Cap

ital E

xpen

ditu

res

(Billi

ons)

1980 1990 2000 2010

Annual Capital Expenditures (Billions) Fitted Median Spline

Figure 5. Total annual capital expenditures across the 50 state park systems.


CAPITAL EXPENDITURES – FORECAST Recent trends suggest capital outlays for improving the productive capacity of the states’ park systems will remain relatively stable at around $625 million per year over the next three years (Figure 6). We estimate total capital expenditures to be $619 million in 2015, $628 million in 2016 and $626 million in 2017.

0.5

1.0

1.5

2.0

Tota

l Ann

ual C

apita

l Exp

endi

ture

s (B

illion

s)

1980 1990 2000 2010 2020

Annual Capital Expenditures (Billions)

Projected Annual Capital Expenditures (Billions)

Figure 6. Forecasted annual expenditures across the 50 state park systems.


REVENUE – TRENDS Revenue is money generated from use fees and charges; it includes all revenue from ‘entrance fees’, ‘camping fees’, ‘cabin/cottage rentals’, ‘lodge rentals’, ‘group facility rentals’, ‘restaurants’, ‘concessions’, ‘beaches/pools’, ‘golf courses’ and ‘other’ sources such as donations (Leung et al. 2015). Revenue data within the AIX archive reveal steady year-over-year increases throughout the 30-year sampling frame (Figure 7). This past year (2014), total revenues were reported at $1.10 billion, which is slightly down (-0.05%) from the $1.16 billion reported in (2014).

0.6

0.8

1.0

1.2

1.4

Tota

l Ann

ual R

even

ues

(Billi

ons)

1980 1990 2000 2010

Annual Revenues (Millions) Fitted Median Spline

Figure 7. Total annual revenues generated by the 50 state park systems.


REVENUE – FORECASTS Given the consistency of reporting in annual revenue data, we can be very confident in our forecasted values for the upcoming years (Figure 8). We estimate total revenues generated across all state park systems will be $1.14 billion in 2015, $1.12 billion in 2016 and $1.10 billion in 2017.

0.6

0.8

1.0

1.2

1.4

Tota

l Ann

ual R

even

ues

(Billi

ons)

1980 1990 2000 2010 2020

Annual Revenues (Millions)

Projected Annual Revenues (Millions)

Figure 8. Forecasted revenues generated by the 50 state park systems.


LABOR – TRENDS The labor required to maintain the states’ park systems saw increases from 1984 to the early 2000s (Figure 9). State park system operators reported a high of 56,630 employees in 2002. However since 2002, total employment across the states’ park systems has declined. This is notable given the gradual increases in both attendance and acreage over the same time period. The trends illustrate a persistent demand placed upon state park operators to accommodate more users across larger areas with fewer and fewer personnel. Data from 2014 reveal a slight downturn in the total number of employees. A total of 46,489 positions were reported for 2014, a 0.07% decrease from the 49,997 reported in 2013.

3040

5060

70To

tal A

nnua

l SPS

Em

ploy

ees

(Tho

usan

ds)

1980 1990 2000 2010

Annual SPS Employees (Thousands) Fitted Median Spline

Figure 9. Total labor required to maintain outdoor recreation opportunities provided within the 50 state park systems.


LABOR – FORECASTS Recent trends within the labor data suggest the state park systems will continue to reduce employment levels over the coming years (Figure 10). We expect total employment to be 48,169 in 2015, dropping gradually to 46,489 in 2017.

3040

5060

70To

tal A

nnua

l SPS

Em

ploy

ees

(Tho

usan

ds)

1980 1990 2000 2010 2020

Annual SPS Employees (Thousands)

Projected Annual SPS Employees (Thousands)

Figure 10. Forecasted labor required to maintain outdoor recreation opportunities provided within the 50 state park systems.


ACREAGE – TRENDS Acreage refers to the total acreage within the states’ park systems managed as ‘parks’, ‘recreation areas’, ‘natural areas’, ‘historical areas’, ‘environmental education areas’, ‘scientific areas’, ‘forests’, ‘fish and wildlife areas’ and ‘other miscellaneous areas’ (Leung et al. 2015). The total area managed within the states’ park systems has increased steadily since 1984 with notable expansions in recent years (Figure 11). Specifically, the year 2013 saw a 0.02% increase in acreage over 2012, growing from 1.50 million acres to 1.53 million acres. This past year (2014), the states’ park systems grew notably as total acreage increased to 1.82 million acres; this is a 0.19% increase.

1012

1416

18To

tal S

PS A

crea

ge (M

illion

s)

1980 1990 2000 2010

SPS Acreage (Millions) Fitted Median Spline

Figure 11. Total acreage within the 50 state park systems.


ACREAGE – FORECASTS We expect the total size dedicated to the states’ park systems will continue to increase gradually over the coming years (Figure 12). Based on recent trends, total acreage in 2015 will be 1.67 million acres. In 2016 the size is expected to increase to 1.72 million and in 2016, it is expected to reach 1.82 million.

1012

1416

18To

tal S

PS A

crea

ge (M

illion

s)

1980 1990 2000 2010 2020year

SPS Acreage (Millions)

Projected SPS Acreage (Millions)

Figure 12. Forecasted acreage within the 50 state park systems.


TECHNICAL EFFICIENCY Technical efficiency is a concept and metric developed and frequently used within the field of public administration to assess the ability of organizational units to maximize the production of known outputs while minimizing production costs (Schachter 2007). van der Meer and Rutgers (2006: 3) describe it simply as “the ratio between input and output”. For public resource mangers known outputs include all of the resources that enable their organization to provide desired goods and services to the public. For state park system managers, known outputs can include labor, built infrastructure, parkland and visitor-generated revenues. Park managers have discretionary operating budgets, which they use to maintain each of these output factors. More technically efficient park managers will be able to employ more personnel, maintain more infrastructure, manage more acres of parkland and generate greater revenues with smaller operating budgets. Managers pursue the least costly means of achieving given ends (Simon 1976). Maximizing technical efficiency is relatively simple and logical when the goals and objectives of a public agency/organization are clear and measureable2. This is the case for the nation’s state park systems, where most managers’ primary motivation is to provide the public with high quality outdoor recreation opportunities. Conceptually, we assume all of the states’ park system managers are attempting to maximize public enjoyment of the resources they manage (i.e., maximize attendance) while minimizing costs associated with providing and managing those opportunities (i.e., minimizing operating expenditures)3. This assumption forms the basis of our production frontier model (Siderelis et al. 2012). The production frontier model assumes managers are continually trying to maximize known outputs related to the quality of outdoor recreation provided within their state (i.e., attendance, capital expenditures, revenues, labor and acreage) while minimizing financial costs (i.e., operating expenditures) associated with managing and producing those known outputs. FACTORS OF PRODUCTION IN THE PROVISION OF OUTDOOR RECREATION OPPORTUNITIES We measure managers’ technical efficiency by their ability to minimize the financial costs associated with managing their state’s park system (input factors = operating expenditures) in an effort to obtain the known outputs needed to produce outdoor recreation opportunities (output factors). The known outputs needed to produce outdoor recreation opportunities within a state park system, each of which is directly tied to the operating budgets of the states’ park systems, are:

• Attendance, the total count of day and overnight visitation to both fee and non-fee areas. Attendance is directly tied to operating expenditures under the logical assumption it costs more (less) to provide outdoor recreation opportunities to a greater (smaller) number of individuals;

• Capital expenditures, non-recurring expenditures used to improve the productive capacity of a state park system; typically these are for land acquisition, periodic park improvements and construction. Capital expenditures have a direct, albeit latent, impact on operating expenditures as managers must pay for maintaining improvements paid for as non-recurring capital expenditures (e.g., improvement to transportation infrastructure, trail system development or refinement, etc.);

• Revenue, the monies generated from use fees and other associated charges such cabin and cottage rentals (see Table A1 for full description). Revenues are directly tied to the operating expenditures required to maintain the states’ park systems as a portion of the capital available to be spent on operating expenditures is generated through user fees and other charges;

2 Several scholars from within public administration have argued the use of a simple technical efficiency metric is not always

feasible, especially when agencies/organizations are faced with “dual-mandates” or required to manage for multiple, conflicting uses (Andrews and Entwistle 2013; Grandy 2009).

3 An argument could be made that park managers’ do not only seek to maximize attendance and minimize operating expenditures through their decisions. We acknowledge that managers’ decisions are also influenced by other objectives such as protecting the states’ natural, cultural and ecological resources and providing for the safety of workers and visitors.


• Labor, the total count of full-time, part-time and seasonal employees who maintain, operate and protect a state park system. Labor is directly tied to operating expenditures as more (fewer) employees will require a larger (smaller) pool of dedicated financial resources to maintain a state park system; and

• Acreage, the total area of a state park system including ‘parks’, ‘recreation areas’, ‘natural areas’, ‘historical areas’, ‘environmental education areas’, ‘scientific areas’, ‘forests’, ‘fish and wildlife areas’ and ‘other miscellaneous areas’. Acreage has direct impacts on operating expenditures; larger (smaller) areas are assumed to require more (less) dedicated financial resources to maintain.

All variables used in our analysis are expressed relative to the total acreage within their respective state park system. Summary statistics for all variables are provided in Table 1. Table 1. Summary statistics for data in the longitudinal panel data set (1984 – 2014) Variable Mean SD Skewness Attendance / Acre a 118.42 135.402 2.65 Attendance (visitor-hours) / Acre a 356.69 407.83 2.65 Operating Expenditures / Acre b 435.68 475.02 2.85 Capital Expenditures / Acre b 180.59 369.34 7.66 Revenue / Acre b 211.54 289.91 3.63 Labor (personnel) / Acre 0.0092 0.0112 2.92 Labor (person-hours) / Acre c 19.21 23.37 2.92 Notes. a Using the assumption each visit is 3.012 hours long; this value was derived by taking the estimated 2.2 billion hours of outdoor

recreation provided by the states’ park systems (Siikamäki 2011) and dividing it by the average annual attendance rates for all the states’ park systems over the past 31 years (730,515,427).

b Operating expenditures, capital expenditures and revenue are adjusted to a 2013 base rate. c Using the assumption each employee works 2,080 hours per year. PRODUCTION FRONTIER MODEL DEVELOPMENT We assume the states’ park system managers are attempting to maximize public enjoyment of the resources they manage (i.e., maximizing known outputs) while minimizing costs associated with providing and managing those opportunities (i.e., minimizing operating expenditures). This allows us to specify a production frontier model by regressing annual operating expenditures on the known output factors needed to produce outdoor recreation opportunities. The production frontier model is expressed as: 𝑦!" = 𝛽!𝑎!" + 𝛽!𝑐𝑥!" + 𝛽!𝑟!" + 𝛽!𝑙!" − 𝑢! + 𝜀!" (1) The dependent variable y refers to the operating expenditures per acre for the jth = 1,…, 50 park system in year t = 1,…,30. The independent variables are a (visitor-hours per acre), cx (capital expenditures per acre), r (revenue per acre) and l (person-hours per acre); these are also indexed to each park system and each year. The individual regression coefficients are expressed as βs. Heterogeneity across the states’ park systems is handled through the inclusion of u, a fixed effect corresponding to each individual panel (state); this coefficient is time-invariant. Finally, ε refers to random error. All variables are transformed to their natural log (ln) before estimation. We fit the model using the xtreg command with the fe (fixed effect) option in the Stata statistical software package. RESULTS Results of applying the production frontier model described above to the longitudinal panel data are shown in Table 2. The model fit the data very well as indicated by the R2 of 0.896. The known output factors associated with producing outdoor recreation opportunities explain 89.6% of the variance in reported operating expenditures. A large proportion of our model’s explanatory power comes from explicitly modeling the heterogeneity across states (panels) through the uj term. This is evident through the high rho (ρ) coefficient which reports the proportion of the variance in the dependent measure


explained solely by within-panel (within-state) effects. Our model yielded a ρ value of 0.572, suggesting just over 57% of the variance in reported operating expenditures over the past 31 years can be explained as observed heterogeneity across the states’ park systems. As shown in Table 2, all of the known input factors are highly significant (p ≤ 0.001). The β coefficients can be interpreted as point elasticities, meaning they indicate the percentage change in operating expenditures given a 1% increase (decrease) in the dependent variable. The β coefficients are also used to calculate average marginal effects, which are the monetary change in operating expenditures corresponding to a 1% increase in a β coefficient’s respective variable. On average, a 1% increase in attendance (visitor-hours) is associated with a 0.308% or $35.91 increase in operating expenditures. More intuitively, we can say that it costs just under $36 for state park system managers to produce an additional 3.57 hours of outdoor recreation within their state’s park system. Similarly, the analysis suggests a 1% increase in capital expenditures is associated with a 0.048 percent increase in operating expenditures. Every $1.80 spent on non-recurring capital expenditures is associated with a concomitant $6.66 increase in costs associated with maintaining existing opportunities for outdoor recreation. Our analysis also suggests a 1% increase in revenue corresponds to a 0.068 percent increase in operating expenditures. Every $2.11 generated by the states’ park systems corresponds to $7.72 in operating expenditures; this is logical given the states’ park systems are quasi-public goods whose operating expenditures are only partially funded by generated revenues (state appropriations, dedicated funds and federal funds are also used to pay for operating expenditures). Finally, our model revealed a 1% increase in labor (person-hours) is associated with a 0.386% increase in operating expenditures. More simply, every 11.52 minutes (MLabor (person-hours)/Acre = 19.21 × 1% × 60 min./hr.) worked by employees of the states’ park systems corresponded to $9.26 in operating expenditures. This finding is intuitive, state park systems with larger labor pools also have larger costs associated with maintaining opportunities within their system. HOW TECHNICALLY EFFICIENT ARE THE STATES’ PARK SYSTEMS? Production frontier analyses, such as our model of technical efficiency, are designed to produce a single ratio between input and output factors (Chambers 1988). The factor over which the manager has control is the input factor, in our case this is operating expenditures. The output factors refer to what is being generated by managers’ decisions, in our case these are the known outputs of attendance, capital expenditures, revenue and labor. The input factor provides the reference for the technical efficiency ratio given it is both singular and the dependent variable in the analysis. The output factor measure is generated by summing the β coefficients for all of the individual output factors. Values of 1.0 indicate an ‘optimal’ technical efficiency in which each additional input factor yields a 100% return across the output factors. Summing the β coefficients generated by our model (Table 2) yields an output factor measure of 0.811, suggesting the nation’s state park system managers are highly efficient at developing and maintaining outdoor recreation opportunities within their systems.


Table 2. Results of the production frontier model fit to the longitudinal panel data set (1984 – 2014)

Independent Variable β a Std. Error t p 95% C.I.

Average Marginal

Effect ($)b U.B. L.B. ln Attendance (visitor-hours) /

Acre 0.308 0.017 17.77 ≤ 0.001 0.274 0.342 35.91

ln Capital Expenditures / Acre 0.048 0.006 7.81 ≤ 0.001 0.036 0.060 6.66 ln Revenue / Acre 0.068 0.009 7.61 ≤ 0.001 0.051 0.086 7.72 ln Labor (person-hours) / Acre c 0.386 0.018 21.12 ≤ 0.001 0.351 0.422 9.26 Constant 6.571 0.104 62.95 ≤ 0.001 6.366 6.775 ρ c 0.572 R2 0.896 Notes. a The β coefficients can be interpreted as point elasticities, meaning they indicate the percentage change in operating

expenditures given a 1% increase (decrease) in the dependent variable. b Average marginal effects are the monetary change in operating expenditures corresponding to a 1% increase in a β coefficient’s

respective variable; they are calculated as 𝑥β × ln(𝑥) where 𝑥 is the variable mean. c The proportion of the variance in the dependent measure explained solely by within-panel (within-state) effects. TECHNICAL EFFICIENCY RANKINGS BY INDIVIDUAL STATE PARK SYSTEMS We noted above the majority of our production frontier model’s explanatory power came from the inclusion of a within-panel (state) estimator (the uj term). In fact, nearly two-thirds of the variance in operating expenditures can be accounted for through the within-panel (state) estimator alone; this is exhibited by the 0.647 rho (ρ) coefficient. These results suggest the high probability of considerable heterogeneity in the technical efficiency across individual state park systems. This between-panel (state) heterogeneity can be characterized by calculating individual technical efficiency scores for each of the states’ park systems. Individual technical efficiency scores are computed through the following equation: 𝑇𝑒𝑐ℎ𝑛𝑖𝑐𝑎𝑙 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦! =

!!"# !!

(2)

Here, uj is simply the estimated fixed effect from Equation 1; it is unique for each of the j = 1,…, 50 park systems. Because uj estimates are derived through the production frontier model for all 50 park systems, they are expressed relative to a theoretical maximum in which the state-level ratio between input and output factors is 1.0. State’s whose park systems yield technical efficiency scores greater than 1.0 are operating above the theoretical maximum. Likewise, states with technical efficiency scores less than 1.0 are operating below the theoretical maximum. We calculated the state-level technical efficiency scores using Equation 2; the results are reported in Table 3. To ease interpretation, we also rank individual states’ park systems by their scores. Generally, the state-level technical efficiency scores are consistent with those we published in 2014 as noted in Column 3 and 6 of Table 3 (Smith and Leung 2014; Smith et al. 2015). The Alaska State Park System continues to be the most efficient at jointly producing the known output factors of attendance, capital improvements, revenue, labor and acreage with minimal operating costs. The South Dakota, Nebraska, New Hampshire and Colorado state park systems round out the top five systems that have most efficiently produced outdoor recreation opportunities over the past 31 years. Several state park systems did see notable changes in their technical efficiency rankings: Hawaii continued to improve, jumping from 31st in 2014 to 25th in 2015; this is up from their 40th position in 2013. The state park systems of Minnesota and Tennessee experienced notable declines, dropping from 33rd to 36th and from 29th to 32nd respectively. The Texas state park system also dropped three spots from 21st to 24th.


Table 3. Individual state park systems’ technical efficiency scores and rankings.

State

Technical Efficiency

Score a 2015 Rank (2014 Rank) State

Technical Efficiency

Score a (2014 Rank) Alabama 0.694 45 (44) Montana 1.070 17 (16) Alaska 1.760 1 (1) Nebraska 1.642 3 (3) Arizona 0.651 48 (48) Nevada 1.040 18 (17) Arkansas 0.758 42 (41) New Hampshire 1.563 4 (4) California 0.658 47 (47) New Jersey 1.016 19 (20) Colorado 1.477 6 (5) New Mexico 0.763 41 (42) Connecticut 1.461 7 (7) New York 0.944 31 (32) Delaware 0.866 37 (37) North Carolina 0.949 29 (30) Florida 0.980 27 (25) North Dakota 1.266 10 (10) Georgia 0.714 43 (43) Ohio 0.995 22 (24) Hawaii 0.984 25 (31) Oklahoma 0.844 39 (38) Idaho 0.937 34 (34) Oregon 0.928 33 (35) Illinois 0.855 38 (39) Pennsylvania 0.796 40 (40) Indiana 1.353 9 (9) Rhode Island 1.165 14 (15) Iowa 1.255 11 (12) South Carolina 1.034 16 (18) Kansas 1.248 12 (11) South Dakota 1.669 2 (2) Kentucky 0.590 49 (49) Tennessee 0.956 32 (29) Louisiana 0.548 50 (50) Texas 1.015 24 (21) Maine 1.176 13 (14) Utah 0.682 46 (46) Maryland 1.016 21 (19) Vermont 1.182 15 (13) Massachusetts 0.983 26 (27) Virginia 0.975 28 (26) Michigan 1.384 8 (8) Washington 1.013 20 (22) Minnesota 0.907 36 (33) West Virginia 1.011 23 (23) Mississippi 0.702 44 (45) Wisconsin 1.506 5 (6) Missouri 0.966 30 (28) Wyoming 0.901 35 (36) Notes. a A score of 1.0 is the theoretical maximum.


DOES TIME MATTER? MODELING THE TEMPORAL DYNAMICS OF STATE PARK SYSTEMS OPERATING EFFICIENCIES THROUGH ALTERNATIVE STOCHASTIC

FRONTIER SPECIFICATIONS STOCHASTIC FRONTIER SPECIFICATIONS The production frontier model presented above (Equation 1) was developed by Siderelis and his colleagues (2012) to provide an empirically-grounded method of estimating the operating efficiencies of each state park system within the US. The model is a focused application of stochastic frontier analysis. Stochastic frontier analyses were originally introduced in the late 1970s as a method of objectively comparing the firms’ ability to maximize the production of a certain good or service while minimizing financial costs (Meeusen and van den Broeck 1977; Aigner, Lovell, and Schmidt 1977). All stochastic frontier specifications are rooted in the idea no economic agent can exceed an ideal ‘production frontier’ in which they would receive a 100% return in the known output factors of production for each additional unit of input (typically these are operational costs)4. Statistically, stochastic frontier specifications can be most easily understood as a multiple regression equation with a composite error term comprised of both standard noise, for example error that might enter the dataset due to measurement error, and technical inefficiencies. In their simplest form, stochastic frontier specifications can be expressed as: 𝑦! = 𝛼 + 𝛽!! 𝑥!" + 𝜀! , where (3) 𝜀! = 𝑣! − 𝑢! (4) where yj refers to the input factors allocated by operational unit j, 𝛼 is a the intercept, xj refers to the each known output factors n produced by unit j and 𝛽! are coefficients estimated to minimize the composed error term 𝜀!. A fundamental aspect of stochastic frontier specifications is their decomposition of the composed error term into both 𝑣! a non-negative technical inefficiency estimate and 𝑢!, the standard disturbance parameter arising from measurement or specification error. Technical inefficiency estimates are assumed to be one-sided (i.e., distributed following a half-normal, exponential, truncated normal, or gamma distribution) and conditionally dependent upon the composed error term. The conditional dependence of 𝑢! on 𝜀! is handled through a two-step estimation process developed by Jondrow and his colleagues (1982) and refined by Battesse and Coelli (1988). The process involves first estimating all model parameters (𝛼,𝛽! 𝑎𝑛𝑑 𝜀!) through common maximum likelihood estimation5, and then deriving point estimates of inefficiency (i.e., 𝑢!) using the mean or mode of the conditional distribution 𝑓(𝑢!|𝜀!) where the estimated standard disturbance parameters are equal to 𝑦! − 𝛼 − 𝛽!! . 4 It is important to note stochastic frontier models can be used to analyze both production frontiers and cost frontiers. Production frontier models, such as the ones examined here, estimate the maximum quantity of known output factors of production (e.g., generate more attendance) that can be produced for each input factor (e.g., dollars of operating expenditures). Cost frontier models are slightly different in that they assume operational units are attempting to minimize the input factor of production (e.g., production costs) needed to produce a set bundle of outputs at fixed prices. While the statistical estimation of both models is identical, studies of the efficient provision of public goods and services such as health care (Harrison and Sexton 2006; Hollingsworth 2008) and utilities (Renzetti and Dupont 2003) almost exclusively focus on the estimation of production frontiers. 5 Some specifications utilize modified ordinary least squares (Cornwell, Schmidt, and Sickles 1990), iterative least squares (Lee and Schmidt 1993) or generalized method of moments (Schmidt and Sickles 1984) estimation techniques.


STOCHASTIC FRONTIER SPECIFICATIONS FOR PANEL-DATA The above specifications have assumed data are available, for only one time period. However, data on the provision of public goods and services are often available across multiple time periods (typically years). Consequently, the cross-sectional stochastic frontier specification can be extended to capitalize on the availability of more data. Pitt and Lee (1981) were the first to do this, specifying the panel-data equation: 𝑦!" = 𝛼 + 𝛽!! 𝑥!"# + 𝜀!" , where (5) 𝜀!" = 𝑣!" − 𝑢! (6) Pitt and Lee’s specification specified a normally distributed standard error term (𝜀!") and half-normal distributed inefficiency estimates (𝑢!)6 and again inefficiency estimates are conditionally dependent upon the distribution of the standard error term (𝜀!"). This unfortunately means inefficiency estimates are averaged across all panels t for each operational unit n; inefficiency is assumed to be time-invariant. Logically and theoretically however, it is tenuous to assume each organizational unit maintains the same level of operational efficiency year after year. This assumption becomes particularly questionable when data are available over a long period of time (Schmidt and Sickles 1984); this is the case with our dataset describing the production of outdoor recreation at state park systems over the past 31 years. It is illogical to assume North Carolina State Parks have maintained a consistent level of operational efficiency for more than three decades. Some examples of how technical efficiency might change year to year include: 1) the effects of large one-time capital expenditures. A large capital expenditure in one year, such as the construction of a visitor center, will require larger labor pools and operational costs dedicated to maintaining the new facility. Changes in the characteristics and amenities provided by a state park system are likely to affect how park managers allocate time and fiscal resources. Consequently, it is highly likely operational efficiencies would change as the production frontier model readjusts to minimize the residual error. Technical efficiency estimates are dependent upon the mean (or mode) of residual error estimates and those residual errors are estimated using the underlying data; as the data change, so too will the technical efficiency estimates. In this report, we explore two alternative specifications that can be utilized to empirically estimate time-varying efficiency estimates. The first solution developed to overcome the limitations arising from applying cross-sectional stochastic frontier specifications to longitudinal data was proposed by Cornwell and his colleagues (1990). The approach involves replacing the intercept in Equation 5 𝛼 with a flexibly parameterized time-varying and unit-specific intercept. The full specification is expressed as: 𝑦!" = 𝛼 + 𝛽!! 𝑥!"# + 𝑣!" − 𝑢! (7) Then, all unit-specific effects are gathered 𝛼! = 𝛼 − 𝑢! and the equation is re-expressed as: 𝑦!" = 𝛼! + 𝛽!! 𝑥!"# + 𝑣!" (8) We mentioned above that technical efficiencies are estimated in cross-sectional specifications using a two-step process in which the efficiency estimate is derived from the mean (or mode) of the composed error term. Cornwell and his colleagues proposed a similar process for panel data. First, the specification presented in Equation 8 is estimated. Second, the standard error parameters are regressed on a constant,

6 Pitt and Lee’s (1981) specification was later extended using normal-truncated normal distributions by Battesse and Coelli (1988).


time and time squared 𝑣!" = 𝜃!! + 𝜃!!𝑡 + 𝜃!!𝑡! + 𝛼!" . Importantly, this estimation results in a unit- and time-specific error term 𝛼!". The final step in the process is to derive unit- and time-specific inefficiency point estimates; this is completed by subtracting the unit- and time-specific error term from the unit-specific effects estimated in Equation 8. This is expressed as: 𝑢!" = 𝛼! − 𝛼!" (9) The major appeal to Cornwell et al.’s specification is its ability to allow for unit-specific temporal patterns of inefficiency, however its method of obtaining time-specific effects (via a constant, time and time squared) does require the estimation of a relatively large number of parameters (specifically N × 3). The second specification developed to overcome the limitations arising from applying cross-sectional stochastic frontier specifications to longitudinal data was developed by Lee and Schmidt (1993). Lee and Schmidt’s specification also allows for the estimation of unit- and time-specific inefficiency estimates; these are obtained through the use of a set of dummy variables corresponding to each temporal unit within the data (years in our empirical application). Lee and Schmidt’s specification can be specified as: 𝑦!" = 𝛼 + 𝛽!! 𝑥!"# + 𝑣!" − 𝑢!" , where (10) 𝑢!" = 𝑔 𝑡 × 𝑢! (11) Here, g(t) is the set of dummy variables. The specification is computationally less burdensome than Cornwell’s, however it requires the analyst to assume temporal patterns in efficiency are the same across all organizational units. While Cornwall’s specification allows for temporal patterns (e.g., changes in uj from 2012 to 2013 to 2014) to vary within operational units, Lee and Schmidt’s specification assumes those temporal patterns are consistent across units. RESEARCH QUESTIONS Despite the logical assumption a state park systems’ technical efficiency changes over time, all previous empirical applications of our production frontier model (described in Equation 1) have assumed the technical efficiencies of each state park system are invariant across time. This assumption was present in the model’s formation (Siderelis et al. 2012), its use to estimate the effects of distinct ecoregions across the US on the production of outdoor recreation at state park systems (Siderelis and Smith 2013) and its use to estimate shifts in operational expenditures under simulated future policy scenarios (Smith et al. 2015). In this year’s outlook and analysis letter, we revisit the basic production frontier and illustrate how the specification of time-invariant efficiency estimates can lead to a more detailed understanding in the operations of the nation’s state park systems. The specifications developed by Cornwell et al. and Lee and Schmidt each have advantages and disadvantages, Cornwell’s et al.’s specification allows for temporal patterns in efficiency estimates to vary within operational units, but it requires the estimation of a relatively large number of parameters. Alternatively, Lee and Schmidt’s specification is more parsimonious, but it requires temporal patterns in efficiency estimates to be estimated across operational units. Beneficial to both specifications is their ability to estimate unit- and time-specific inefficiency estimates, a necessity when dealing with operational units guided by temporally-dynamic decision-making processes; this is certainly the case across the states’ park systems. The decisions of park operators can be influenced by both endogenous effects, such as the purchasing or transfer of parklands or large one-time allocations to improve recreational facilities or amenities, and exogenous effects, such as


the health of their state’s economy which will directly impact the demand for outdoor recreation. Our analysis is guided by three interrelated research questions:

RQ1. Does the specification of time-invariant efficiency estimates significantly alter the technical efficiency ranking of individual state park systems?

We address this research question by comparing the mean and standard deviations of technical efficiency coefficients generated using: 1) a time-invariant fixed-effect specification (Schmidt and Sickles 1984); 2) a time-varying within-unit fixed-effect specification (Cornwell, Schmidt, and Sickles 1990); and 3) a time-varying across-unit fixed-effect specification (Lee and Schmidt 1993). We also compare the state-specific technical efficiency rankings for the entire panel-dataset (1984-2014) against the state-specific technical efficiency rankings for 2014. Our intent is to determine if specification significantly affects the ranking of individual state park systems. Biased technical efficiency estimates, and subsequently rankings, could lead to inefficient

RQ2. Does the specification of time-invariant efficiency estimates significantly alter coefficient estimates corresponding to the known output factors stipulated in our production frontier model?

We compare the coefficient estimates corresponding to the known output factors of production (attendance, capital expenditures, revenue, labor and acreage) generated from: 1) the time-invariant fixed-effect specification; 2) the time-varying within-unit fixed-effect specification; and 3) the time-varying across-unit fixed-effect specification. We also estimate the average marginal effects associated with each coefficient to illustrate how specification can alter monetary estimates directly affecting state park system operators’ decision making. Average marginal effects are the monetary change in operating expenditures corresponding to a 1 percent increase in a coefficient’s respective variable.

RQ3. How has the technical efficiency of individual state park systems changed over the past 31 years?

This final research question is exploratory and meant to illustrate how individual state park systems are trending in the operational efficiencies. Using simple growth rate statistics, we summarize both long-term (the past 31 years) and recent (2014 only) trends in technical efficiency estimates generated from both the time-varying within-unit fixed-effect specification and the time-varying across-unit fixed-effect specification. RESULTS DOES THE SPECIFICATION OF TIME-INVARIANT EFFICIENCY ESTIMATES SIGNIFICANTLY ALTER THE TECHNICAL EFFICIENCY RANKING OF INDIVIDUAL STATE PARK SYSTEMS? We present a comparison of the technical efficiency rankings generated using three fixed-effect specifications:

• the time-invariant equation (TI) developed by Schmidt and Sickles (1984); • the time-varying within-unit (TV-WU) equation of Cornwell, Schmidt and Sickles (1990); and • the time-varying across-unit (TV-AU) equation developed by Lee and Schmidt (1993).

The technical efficiency rankings generated by each specification are presented in Table 4; maximum differences within individual states across the three specifications are shown in the final column. A visual comparison of the rankings suggests for the vast majority of states, the choice to use either a time-invariant specification or a time-varying specification does not substantially alter technical efficiency rankings. We utilized two test statistics, Friedman’s nonparametric two-way analysis of variance and


Kendall’s coefficient of concordance, to determine if the rankings were significantly different. Both tests are a measure of the agreement between k sets of rankings (Gibbons and Chakraborti 2011). The results of the both tests across all ranking are reported in Table 3. None of the rankings derived from long-range technical efficiency estimates (i.e., TI, TV-WU1984-2014 and TV-AU1984-2014) were significantly different from one another.

Table 3. Friedman’s nonparametric two-way analyses of variance (F), Kendall’s coefficients of concordance (K), and associated p-values across all rankings Ranking

Ranking TI TV-WU1984-

2014 TV-WU2014

TV-WU1984-

2014

F = 0.50 K = 0.10 p = 0.480

— —

TV-WU2014 F = 0.72 K = 0.14 p = 0.396

F = 0.50 K = 0.01 p = 0.480

—

TV-AU1984-

2014 and TV-AU2014

F = 0.80 K = 0.02 p = 0.777

F = 0.32 K = 0.01 p = 0.572

F = 0.32 K = 0.01 p = 0.573

While the tests for differences were not statistically significant, it should be noted that several states’ rankings varied notably across the three specifications. Consider Florida for example, its state park system was ranked near the middle of the pack at 27th when using the TI specification. However, Florida’s ranking improved to 23rd when the TV-WU specification was specified, but moved a full 10 slots down to 33rd when the TV-AU specification was specified. Another prime example is the Texas state park system. Texas was ranked 24th when the TI specification was used, but improved to 21st under the TV-WU specification and dropped to 32nd under the TV-AU specification. These uncommon disparities in ranks are likely attributable for two reasons. For the TV-WU specification, they are likely attributable to notable deviations in technical efficiency year over year. This is logical given the technical efficiency scores are calculated as function of time under the TV-WU specification (see Equation 8 above). For the TV-AU specification, the disparities in rankings arise, most likely, from these states having estimated trends in technical efficiency that deviate notably from the population average; a visual inspection of the trend in efficiency for both the anomalies seen within Florida and Texas are shown in Figures 13 and 14 below. A visual comparison of the rankings estimated with both the TV-WU1984-2014 specification and the TV-WU2014 specification (middle columns in Table 4) suggest states’ technical efficiency scores and rankings do change dramatically over time. The tests for significant differences between the long-term technical efficiency rankings and the most recent technical efficiency rankings support the lack of significant differences (Table 3; TI-TV-WU2014: p = 0.396; TI-TV-AU2014: p = 0.777)7.

7 No tests were conducted between the TV-AU1984-2014 rankings and the TV-AU2014 because the TV-AU specification assumes

all organizational units follow the same temporal trend in inefficiency, consequently making rankings invariant across time.


Despite the lack of a statistical difference in technical efficiency scores and subsequent rankings, states’ ranking between the two specifications differed by nearly eight spots (Table 4). We have noted several authors (Belotti et al. 2013; Ahn, Lee, and Schmidt 2001; Ahn, Lee, and Schmidt 2006) have raised concerns over the assumption technical efficiency can be temporally invariant; these results validate their concerns. Washington State, for example, has had an average ranking of 18 over the past 31 years, but last year it was in 42nd place, a difference of 24 places. Similarly, North Dakota and Texas are currently 23 spots off, and in both cases below, their 31 year average. These results suggest time plays a critical role in

.5.5

5.6

.65

.7Te

chni

cal E

ffici

ency

1984 1989 1994 1999 2004 2009 2014

Average Technical Efficiency from TI(1984−2014)Average Technical Efficiency from TV−AU(1984−2014)Yearly Technical Efficiency from TI(1984−2014)Yearly Technical Efficiency from TV−AU(1984−2014)

.5.5

5.6

.65

.7Te

chni

cal E

ffici

ency

1984 1989 1994 1999 2004 2009 2014

Average Technical Efficiency from TI(1984−2014)Average Technical Efficiency from TV−AU(1984−2014)Yearly Technical Efficiency from TI(1984−2014)Yearly Technical Efficiency from TV−AU(1984−2014)

Figure 13. Technical efficiency trends for Florida State Parks relative to the average for all systems.

Figure 14. Technical efficiency trends for Texas State Parks relative to the average for all systems.


estimating the efficiency of individual state park systems. If analysts disregard time and opt to use specifications capturing only long-term average efficiency estimates, they are likely to disregard a substantial amount of information concerning recent trends in state park systems’ ability to produce outdoor recreation opportunities. We return to this discussion when we explore temporal trends within individual state park systems below.


Table 4. Individual state park systems’ technical efficiency (TE) scores and rankings.

Time-invariant fixed-effect specification

(TI) Time-varying within-unit fixed-effect specification (TV-WU) Time-varying across-unit fixed-effect specification (TV-AU)

State TE Score (uj) Rank Historical TE

Score (uj1984-2014) Rank ΔTI

Most Recent TE Score

(uj2014) Rank ΔTI Historical TE



(uj2014) Rank ΔTI Alabama 0.236 45 0.261 46 1 0.670 41 4 0.238 45 0 0.220 45 0 Alaska 1.166 1 1.463 1 0 1.532 2 1 1.150 1 0 1.065 1 0 Arizona 0.172 48 0.243 48 0 0.476 45 3 0.155 48 0 0.144 48 0 Arkansas 0.324 42 0.334 43 1 0.441 46 4 0.343 41 1 0.318 41 1 California 0.182 47 0.299 44 3 0.313 48 1 0.184 47 0 0.170 47 0 Colorado 0.991 6 1.108 5 1 0.954 25 19 0.977 7 1 0.904 7 1 Connecticut 0.980 7 1.062 7 0 1.034 17 10 1.017 5 2 0.942 5 2 Delaware 0.457 37 0.435 41 4 0.883 31 6 0.475 38 1 0.439 38 1 Florida 0.581 27 0.689 23 4 1.228 9 18 0.561 33 6 0.519 33 6 Georgia 0.264 43 0.296 45 2 0.771 39 4 0.276 43 0 0.255 43 0 Hawaii 0.585 25 0.694 22 3 1.266 8 17 0.645 22 3 0.597 22 3 Idaho 0.537 34 0.589 36 2 0.878 33 1 0.552 35 1 0.511 35 1 Illinois 0.444 38 0.566 37 1 0.887 30 8 0.489 37 1 0.452 37 1 Indiana 0.904 9 0.940 9 0 0.998 21 12 0.927 9 0 0.858 9 0 Iowa 0.829 11 0.928 10 1 1.139 11 0 0.876 10 1 0.811 10 1 Kansas 0.823 12 0.912 11 1 1.062 13 1 0.851 12 0 0.787 12 0 Kentucky 0.073 49 0.040 49 0 0.084 49 0 0.083 49 0 0.077 49 0 Louisiana 0.000 50 0.019 50 0 0.000 50 0 0.000 50 0 0.000 50 0 Maine 0.764 13 0.864 13 0 1.217 10 3 0.784 14 1 0.725 14 1 Maryland 0.617 21 0.688 24 3 1.045 15 6 0.621 24 3 0.575 24 3 Massachusetts 0.584 26 0.642 30 4 0.893 29 3 0.622 23 3 0.575 23 3 Michigan 0.926 8 1.011 8 0 1.319 6 2 0.938 8 0 0.868 8 0 Minnesota 0.504 36 0.609 32 4 0.433 47 11 0.499 36 0 0.462 36 0 Mississippi 0.247 44 0.258 47 3 0.531 43 1 0.267 44 0 0.248 44 0 Missouri 0.566 30 0.642 29 1 0.989 22 8 0.609 27 3 0.563 27 3 Montana 0.672 17 0.757 16 1 0.951 26 9 0.701 17 0 0.649 17 0 Nebraska 1.094 3 1.165 3 0 1.497 3 0 1.118 3 0 1.035 3 0 Nevada 0.642 18 0.773 15 3 1.059 14 4 0.655 20 2 0.606 20 2 New Hampshire 1.016 4 1.078 6 2 1.022 19 15 1.069 4 0 0.987 4 0 New Jersey 0.629 19 0.732 19 0 1.289 7 12 0.649 21 2 0.601 21 2 New Mexico 0.328 41 0.446 40 1 0.833 36 5 0.321 42 1 0.297 42 1 New York 0.557 31 0.592 35 4 1.045 16 15 0.590 29 2 0.546 29 2 North Carolina 0.572 29 0.649 27 2 0.982 23 6 0.618 26 3 0.572 26 3 North Dakota 0.840 10 0.874 12 2 0.851 35 25 0.874 11 1 0.809 11 1 Ohio 0.609 22 0.686 25 3 1.077 12 10 0.655 19 3 0.607 19 3


Table 4 (continued). Individual state park systems’ technical efficiency (TE) scores and rankings.

Time-invariant fixed-effect specification

(TI) Time-varying within-unit fixed-effect specification (TV-WU) Time-varying across-unit fixed-effect specification (TV-AU)

State TE Score

(uj) Rank Historical TE



(uj2014) Rank ΔTI Historical TE



(uj2014) Rank ΔTI Oklahoma 0.433 39 0.504 38 1 1.011 20 19 0.440 39 0 0.407 39 0 Oregon 0.537 33 0.639 31 2 0.879 32 1 0.585 30 3 0.541 30 3 Pennsylvania 0.389 40 0.465 39 1 0.862 34 6 0.434 40 0 0.402 40 0 Rhode Island 0.748 14 0.709 20 6 0.943 27 13 0.814 13 1 0.754 13 1 South Carolina 0.702 16 0.756 17 1 1.589 1 15 0.704 16 0 0.651 16 0 South Dakota 1.110 2 1.191 2 0 1.470 4 2 1.123 2 0 1.039 2 0 Tennessee 0.550 32 0.602 34 2 0.757 40 8 0.574 31 1 0.531 31 1 Texas 0.586 24 0.699 21 3 0.496 44 20 0.573 32 8 0.530 32 8 Utah 0.229 46 0.339 42 4 0.801 37 9 0.216 46 0 0.200 46 0 Vermont 0.741 15 0.802 14 1 1.025 18 3 0.716 15 0 0.663 15 0 Virginia 0.577 28 0.605 33 5 0.908 28 0 0.600 28 0 0.556 28 0 Washington 0.624 20 0.735 18 2 0.615 42 22 0.656 18 2 0.607 18 2 West Virginia 0.596 23 0.655 26 3 0.771 38 15 0.619 25 2 0.573 25 2 Wisconsin 1.010 5 1.109 4 1 1.412 5 0 1.015 6 1 0.939 6 1 Wyoming 0.522 35 0.647 28 7 0.956 24 11 0.558 34 1 0.517 34 1 Mean 1.20 1.20 1.92 7.76 Notes. a A score of 1.0 is the theoretical maximum.


DOES THE SPECIFICATION OF TIME-INVARIANT EFFICIENCY ESTIMATES SIGNIFICANTLY ALTER COEFFICIENT ESTIMATES CORRESPONDING TO THE KNOWN OUTPUT FACTORS STIPULATED IN OUR TECHNICAL EFFICIENCY SPECIFICATION? Results from the time-invariant fixed-effect specification developed by Schmidt and Sickles (1984) and utilized in previous studies using the AIX archive (Siderelis et al. 2012; Siderelis and Smith 2013; Smith et al. 2015) are reported in Table 5, Panel A. Panels B and C report results from both of the time-varying specifications. All of the specifications suggest the output factors of production are positive and highly significant; as would be logically expected. A comparison of all three specifications also suggests little variation in estimated coefficients. The maximum variation in the output factors of production variables was seen in the lnRevenues/Acre variable and it was less than one-half of one-hundredth of a point (βTV-

WU - βTV-AU = 0.046). The range of this variation is not intuitive, so we converted each estimated coefficient to its average marginal effects (Column 8 of Table 5) to ease interpretation. The maximum differences in estimated average marginal effects are highlighted in Table 6. The differences are quite small, less than $5 per acre; this suggests that while the time-varying specifications may be more ‘realistic’ and capable of capturing the dynamic equilibrium within state park systems’ operations, their estimated coefficients do not deviate in any managerially significant way. More simply put, we do not believe a state park system managers’ decision making will be swayed by knowing that it actually costs $40.24 to produce 3.57 hours of outdoor recreation (AME[TV-WU]lnAttendance(visitor-hours)/Acre) instead of $35.91 (AME[TI]lnAttendance(visitor-hours)/Acre). Consequently, we believe these findings provide some external validity to the results and managerial implications reported in previous production analyses using the AIX archive (Smith et al. 2015; Siderelis et al. 2012; Siderelis and Smith 2013).


Table 5. Results of the technical efficiency specification fit to the longitudinal panel data set (1984 – 2014)

Panel A. Time-invariant fixed-effect specification (Schmidt and Sickles 1984)


Average Marginal


Acre 0.308 0.017 17.77 ≤ 0.001 0.274 0.342 35.91

ln Capital Expenditures / Acre 0.048 0.006 7.81 ≤ 0.001 0.036 0.060 6.66 ln Revenue / Acre 0.068 0.009 7.61 ≤ 0.001 0.051 0.086 7.72 ln Labor (person-hours) / Acre c 0.386 0.018 21.12 ≤ 0.001 0.351 0.422 9.26 Constant 6.571 0.104 62.95 ≤ 0.001 6.366 6.775 σu 0.33 σv 0.24

Panel B. Time-varying within-unit fixed-effect specification (Cornwell, Schmidt, and Sickles 1990)


Average Marginal


Acre 0.327 0.018 17.96 ≤ 0.001 0.292 0.363 40.24

ln Capital Expenditures / Acre 0.049 0.006 8.58 ≤ 0.001 0.038 0.060 6.70 ln Revenue / Acre 0.103 0.012 8.85 ≤ 0.001 0.080 0.125 9.28 ln Labor (person-hours) / Acre c 0.291 0.018 15.79 ≤ 0.001 0.255 0.328 6.99 σu 0.37 σv 0.20

Panel C. Time-varying across-unit fixed-effect specification (Lee and Schmidt 1993)


Average Marginal


Acre 0.313 0.053 5.88 ≤ 0.001 0.209 0.418 37.04

ln Capital Expenditures / Acre 0.034 0.019 1.85 0.064 -0.002 0.071 6.21 ln Revenue / Acre 0.040 0.028 1.44 0.150 -0.014 0.094 6.63 ln Labor (person-hours) / Acre c 0.421 0.058 7.31 ≤ 0.001 0.308 0.534 10.25 σu 0.35 σv 0.23 Notes. a The β coefficients can be interpreted as point elasticities, meaning they indicate the percentage change in operating

expenditures given a 1% increase (decrease) in the dependent variable. b Average marginal effects are the monetary change in operating expenditures corresponding to a 1% increase in a β coefficient’s

respective variable; they are calculated as 𝑥β × ln(𝑥) where 𝑥 is the variable mean.


HOW HAS THE TECHNICAL EFFICIENCY OF INDIVIDUAL STATE PARK SYSTEMS CHANGED OVER THE PAST 31 YEARS? Results from analyses focused on the previous two research questions, RQ1 and RQ2, suggest even though time-varying specifications may be more theoretically consistent with the actual shifting operational systems across the states’ park systems, they do not generate managerially meaningful or statistically significant differences in either system specific estimates of technical efficiency or in the estimated ratio between input and output factors of production. So do the time-varying specifications hold any utility for state park system managers or outdoor recreation researchers? Potentially. The TV-WI specifications developed by Cornwell, Schmidt and Sickles (1990) allows for the estimation and display of unit-specific temporal trends in technical efficiency. These temporal trends are useful for describing the general trend in individual state park systems’ ability to efficiently produce outdoor recreation opportunities for the public. Are certain states trending upward and delivering more acreage, labor and investments in capital improvements? Conversely, are certain states starting to lag and become less efficient over time? If time-variable specifications can illustrate the magnitude of these trends, then they are useful for national leadership and training efforts such as those facilitated by the National Association of State Park Directors (e.g., Attarian 2015). Figure 15 displays the annual technical efficiency estimates generated from the time-varying within-unit fixed-effects specification (TV-WU). The estimates clearly show substantial heterogeneity across the 50 state park systems. Four general trends in operational efficiencies are observed: 1) steady, long-term improvements; 2) steady, long-term declines; 3) recent rebounds; and 4) recent declines. Each of these trend categories is described below and the states within each category are listed in Table 6.

1. Steady, long-term improvements. These states have gradually improved their ability to efficiently produce outdoor recreation over the past 31 years. While this does not imply these states are currently more efficient than those in the other trend categories described below, it does suggest park operators in these states have improved their ability to maximize the production of outdoor recreation opportunities given limited operational budgets. It is likely these states will be best poised to address and adapt to unforeseen reductions in state appropriations. These state park systems should be commended for their consistently good decision-making behavior.

2. Steady, long-term declines. Over time, these states have become less efficient in their ability to

efficiently produce outdoor recreation. Potential reasons for this might be gradual increases in state-appropriated operating budgets that do not result in a concomitant growth in the output factors of production. For example, a state legislature might have gradually increased appropriations to their state park system while simultaneously limiting the purchasing of new parklands or limiting the ability of park management to leverage usage fees (both of which are output factors of production). Consequently, the state park system would become increasingly inefficient over time. This situation is unlikely however. More realistically, increasingly inefficient operations are attributable to multiple factors that might include: stagnant attendance levels, a general unwillingness to invest in capital improvements, an unwillingness to increase employment and a consistent reluctance to use use-fees to generate revenues.

3. Recent rebounds. These states experienced declines in operational efficiencies early on in the

observed period of analysis, but have since improved. State park system operators within these states should be commended for their ability to “right the ship” so to speak and alter their organizations’ tendency to make poor decisions. As with the states experiencing steady, long-term improvements, the recent rebound states are will be well suited to address and adapt to unforeseen reductions in state appropriations.


4. Recent declines. These states peaked in operational efficiency at some time in the not to distant past, but have since experienced sharp declines in the efficient use of operational expenditures. The reasons for these recent declines are likely to vary by state. Some state park systems might have experienced a one or two year period during which they substantially reduced the size (acreage) of their park system via land transfers. A rapid reduction in size, and relatively consistent operating budgets, would result in a notable decrement to the technical efficiency metric. Regardless of the cause, these states are trending in a negative direction and should carefully examine how and why their organization’s structure is consistently producing poorer outdoor recreational opportunities year over year.

Table 6. The time-varying within-unit fixed-effect specification (TV-WU) revealed four general trends in state park systems’ operational efficiencies Trend States Steady, long-term improvements

• Alabama • Arkansas • Illinois • Kansas • Massachusetts • Mississippi • New Jersey

• New York • Rhode Island • Utah • Virginia • West Virginia • Wisconsin • Wyoming

Steady, long-term declines

• Colorado • Minnesota

• Oregon • Texas

Recent rebounds • Arizona • California • Delaware • Florida • Georgia • Hawaii • Idaho • Indiana • Iowa • Kentucky • Maine • Maryland • Michigan

• Missouri • Montana • Nebraska • Nevada • New Mexico • North Carolina • Ohio • Oklahoma • Pennsylvania • South Carolina • South Dakota • Tennessee • Vermont

Recent declines • Alaska • Connecticut • Louisiana

• New Hampshire • North Dakota • Washington

Note.


0.2

.4.6

.51

1.5

2

.1.2

.3.4

.5

.2.3

.4.5

.25

.3.3

5.4

.91

1.1

1.2

1.3

.91

1.1

1.2

.2.4

.6.8

1

.4.6

.81

1.2

0.2

.4.6

.8

.4.6

.81

1.2

.4.6

.81

.4.6

.81

.9.9

51

.8.9

11.

1

.6.8

11.

2

0.0

5.1

.15

.2

0.0

2.0

4.0

6

.6.8

11.

2

.4.6

.81

.5.6

.7.8

.9

.91

1.1

1.2

1.3

.4.6

.81

.1.2

.3.4

.5

.4.6

.81

.7.8

.91

11.

5

.6.8

11.

2

.6.8

11.

2

.51

1.5

0.5

11.

5

0.5

1

.4.6

.81

.7.8

.91

.6.8

11.

2

.2.4

.6.8

1

.4.6

.81

.2.4

.6.8

.2.4

.6.8

1

.51

1.5

1.1

1.2

1.3

1.4

1.5

.5.6

.7.8

.5.6

.7.8

.2.4

.6.8

.7.8

.91

.5.6

.7.8

.9

.6.6

5.7

.75

.8

.2.4

.6.8

11.

11.

21.

31.

4

.4.6

.81

1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014

1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014

1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014

1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014

1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014

1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014 1984 1994 2004 2014

1984 1994 2004 2014 1984 1994 2004 2014

Alabama Alaska Arizona Arkansas California Colorado Connecticut Delaware

Florida Georgia Hawaii Idaho Illinois Indiana Iowa Kansas

Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi

Missouri Montana Nebraska Nevada New Hampshire New Jersey New Mexico New York

North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina

South Dakota Tennessee Texas Utah Vermont Virginia Washington West Virginia

Wisconsin Wyoming


APPENDIX A AN OVERVIEW OF THE AIX All analyses in this report utilize data collected from the Annual Information Exchange (AIX), a data collection and reporting system contracted to NC State University by the National Association of State Park Directors (NASPD). The AIX system is intended primarily for use by state park system operators and staff for: identifying program, facility and personnel needs; formulating budgetary requests for state legislatures; and comparing their programs with those of other states. Data collected by the AIX system include:

• an inventory of the number, acreage and type of areas managed by each state park system; • an inventory of the number and type of facilities managed by each state park system; • annual attendance counts broken down by fee-areas, non-fee areas, day-use areas and overnight

use areas; • annual capital and operating expenditures by each state park system; • annual revenue generated by source (e.g., entrance fees, cabin rentals, etc.) for each state park

system; and • an inventory of the number and type of personnel positions required to maintain each state park

system, this includes salary ranges and an inventory of employee benefits. Each year, the AIX project team prepares a Statistical Report of State Park Operations, which details the data collection process and provides detailed definitions and descriptions of the reported data (Leung et al. 2015). Individuals or organizations interested in utilizing data in the AIX system should contact the AIX Project Team lead, Dr. Yu-Fai Leung at [email protected]. VARIABLES PULLED FROM THE AIX To conduct the analyses described in this report, we generated a longitudinal panel data set of key data collected through the AIX. The variables we utilize in our analyses are described in Table A1. Each variable is reported annually for each state park system between the years 1984 and 2014. The AIX archive contains data back to 1979. However, poor data collection and/or archiving standards for data prior to 1984 prohibit their use. MODIFICATIONS TO ORIGINAL DATA Missing Data – Due to inconsistent data collection standards across state park systems, not all data are present in the AIX archive for each year. TableA2 shows the breakdown of missing data by state. Only a small proportion of data are missing, mostly for capital expenditures. We used linear interpolation to fill missing values and create a fully balanced dataset8. Inflation – We adjusted all monetary variables (operating expenditures, capital expenditures and revenue) to a 2014 base rate to compensate for inflation. The adjustments were made using the Consumer Price Index for all Urban Households (www.bls.gov)9. Aggregation – To complete the trend analysis for all state park systems, we collapsed the data by year across all states10.

8 The Stata14 .do file is saved as “/interpolation.do”. 9 The Stata14 .do file is saved as “/cpi_conversion.do”. 10 The Stata14 .do file is saved as “/create_yearly_totals.do”.


Table A1. Variables from the AIX archive used to construct the longitudinal panel data set (1984 – 2014) Variable Definition Location in annual AIX Excel

spreadsheets Attendance The total counts of day and overnight visitation to both fee and non-fee areas. Table 3 – L3:L52 Operating Expenditures

Payments made for goods and services to manage a state park system. Operating expenditures are funded through park generated revenue, general funds, dedicated funds, federal funds, and other funds such as interagency transfers and money generated through temporary leases.

Table 5 – G3:G52

Capital Expenditures

Non-recurring expenditures used to improve the productive capacity of a state park system. Typically, these are for land acquisition, periodic park improvements, and construction. Capital expenditures are funded through park-generated revenue, state appropriations, dedicated funds, bonds, federal funds, and other sources such as gifts, grants, and transfers.

Table 5 – Q3:Q52

Revenue Monies generated from use fees and charges; this includes all revenue from ‘entrance fees’, ‘camping fees’, ‘cabin/cottage rentals’, ‘lodge rentals’, ‘group facility rentals’, ‘restaurants’, ‘concessions’, ‘beaches/pools’, ‘golf courses’, and ‘other’ sources such as donations.

Table 5 – DA3:DA52

Labor The total count of full-time, part-time, and seasonal employees who maintain, operate, and protect a state park system. Table 6 – U3:U52 Acreage The total acreage within each state park system; this includes ‘parks’, ‘recreation areas’, ‘natural areas’, ‘historical areas’,

‘environmental education areas’, ‘scientific areas’, ‘forests’, ‘fish and wildlife areas’, and ‘other miscellaneous areas’. Table 1 – AN3:AN52


Table A2. Missing data in the longitudinal panel data set (1984 – 2014) Variable State AL AK AZ AR CA CO CT DE FL GA HI ID IL Attendance 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 2 (6%) 0 (0%) 0 (0%) 2 (6%) 2 (6%) 2 (6%) Operating Expenditures 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 1 (3%) 0 (0%) 0 (0%) Capital Expenditures 0 (6%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 1 (3%) 0 (0%) 0 (0%) 0 (0%) 7 (23%) 0 (0%) 4 (13%) Revenue 0 (0%) 3 (10%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 4 (13%) 0 (0%) 0 (0%) Labor 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) Acreage 0 (0%) 0 (0%) 1 (3%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 1 (3%) 0 (0%) State IN IA KS KY LA ME MD MA MI MN MS MO MT Attendance 0 (0%) 1 (3%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 1 (3%) 0 (0%) 0 (0%) Operating Expenditures 0 (0%) 1 (3%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 1 (3%) 0 (0%) 1 (3%) 0 (0%) 0 (0%) Capital Expenditures 1 (3%) 3 (10%) 0 (0%) 0 (0%) 1 (3%) 1 (3%) 0 (0%) 0 (0%) 0 (0%) 1 (3%) 4 (13%) 0 (0%) 3 (10%) Revenue 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 1 (3%) 0 (0%) 0 (0%) Labor 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 1 (3%) 1 (3%) 0 (0%) 0 (0%) Acreage 1 (3%) 1 (3%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 2 (6%) 0 (0%) 1 (3%) State NE NV NH NJ NM NY NC ND OH OK OR PA RI Attendance 1 (3%) 0 (0%) 2 (6%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) Operating Expenditures 0 (0%) 1 (3%) 0 (0%) 0 (0%) 1 (3%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 2 (6%) Capital Expenditures 0 (0%) 0 (0%) 3 (10%) 1 (3%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 1 (3%) 0 (0%) 2 (6%) 5 (16%) Revenue 0 (0%) 1 (3%) 1 (3%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) Labor 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 1 (3%) Acreage 0 (0%) 0 (0%) 1 (3%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 1 (3%) 0 (0%) 0 (0%) State SC SD TN TX UT VT VA WA WV WI WY Total % Attendance 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 13 8.39 Operating Expenditures 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 8 5.16 Capital Expenditures 0 (0%) 0 (0%) 3 (10%) 2 (6%) 0 (0%) 0 (0%) 1 (3%) 0 (0%) 1 (3%) 3 (10%) 3 (10%) 53 34.19 Revenue 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 10 6.45 Labor 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 3 1.94 Acreage 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 9 5.81


REFERENCES Ahn, S. C., Y. H. Lee, and P. Schmidt. 2001. “GMM Estimation of Linear Panel Data Models with Time-

Varying Individual Effects.” Journal of Econometrics 101 (2): 219–55. doi:10.1016/S0304-4076(00)00083-X.

———. 2006. “Stochastic Frontier Models with Multiple Time-Varying Individual Effects.” Journal of Productivity Analysis 27 (1): 1–12. doi:10.1007/s11123-006-0020-8.

Aigner, D., C. A. K. Lovell, and P. Schmidt. 1977. “Formulation and Estimation of Stochastic Frontier Production Function Models.” Journal of Econometrics 6 (1): 21–37. doi:10.1016/0304-4076(77)90052-5.

Andrews, R., and T. Entwistle. 2013. “Four Faces of Public Service Efficiency.” Public Management Review 15 (2): 246–64. doi:10.1080/14719037.2012.725760.

Attarian, A. 2015. State Park Leadership School Curriculum Guide. Raleigh, NC: National Association of State Park Directors.

Battese, G. E., and T. J. Coelli. 1988. “Prediction of Firm-Level Technical Efficiencies with a Generalized Frontier Production Function and Panel Data.” Journal of Econometrics 38 (3): 387–99. doi:10.1016/0304-4076(88)90053-X.

Belotti, F., S. Daidone, G. Ilardi, and V. Atella. 2013. “Stochastic Frontier Analysis Using Stata.” The Stata Journal 13 (4): 719–58.

Chambers, R. G. 1988. Applied Production Analysis: A Dual Approach. Cambridge, United Kingdom: Cambridge University Press.

Cornwell, C., P. Schmidt, and R. C. Sickles. 1990. “Production Frontiers with Cross-Sectional and Time-Series Variation in Efficiency Levels.” Journal of Econometrics 46 (1–2): 185–200. doi:10.1016/0304-4076(90)90054-W.

Gibbons, J. D., and S. Chakraborti. 2011. Nonparametric Statistical Inference. 5th ed. Statistics: Textbooks and Mongraphs. Boca Raton, FL: CRC Press.

Grandy, C. 2009. “The ‘efficient’ Public Administrator: Pareto and a Well-Rounded Approach to Public Administration.” Public Administration Review 69 (6): 1115–23. doi:10.1111/j.1540-6210.2009.02069.x.

Harrison, J. P., and C. Sexton. 2006. “The Improving Efficiency Frontier of Religious Not-for-Profit Hospitals.” Hospital Topics 84 (1): 2–10. doi:10.3200/HTPS.84.1.2-10.

Hollingsworth, B. 2008. “The Measurement of Efficiency and Productivity of Health Care Delivery.” Health Economics 17 (10): 1107–28. doi:10.1002/hec.1391.

Jondrow, J., C. A. Knox Lovell, I. S. Materov, and P. Schmidt. 1982. “On the Estimation of Technical Inefficiency in the Stochastic Frontier Production Function Model.” Journal of Econometrics 19 (2–3): 233–38. doi:10.1016/0304-4076(82)90004-5.

Lee, Y. H., and P. Schmidt. 1993. “A Production Frontier Model with Flexible Temporal Variation in Technical Efficiency.” In The Measurement of Productive Efficiency: Techniques and Applications, edited by H. O. Fried, C. A. Knox Lovell, and S. S. Schmidt, 237–55. New York: Oxford University Press.

Leung, Y. -F., J. W. Smith, A. Miller, and C. Serenari. 2015. Statistical Report of State Park Operations: 2013-2014 - Annual Information Exchange for the Period July 1, 2013 through June 30, 2014. Raleigh, NC: Department of Parks, Recreation and Tourism Management, NC State University.

Meeusen, W., and J. van den Broeck. 1977. “Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error.” International Economic Review 18 (2): 435–44. doi:10.2307/2525757.

Pitt, M. M., and L. -F. Lee. 1981. “The Measurement and Sources of Technical Inefficiency in the Indonesian Weaving Industry.” Journal of Development Economics 9 (1): 43–64. doi:10.1016/0304-3878(81)90004-3.

Renzetti, S., and D. Dupont. 2003. “Ownership and Performance of Water Utilities.” Greener Management International 2003 (42): 9–19. doi:10.9774/GLEAF.3062.2003.su.00004.


Schachter, H. L. 2007. “Does Frederick Taylor’s Ghost Still Haunt the Halls of Government? A Look at the Concept of Governmental Efficiency in Our Time.” Public Administration Review 67 (5): 800–810. doi:10.1111/j.1540-6210.2007.00768.x.

Schmidt, P., and R. C. Sickles. 1984. “Production Frontiers and Panel Data.” Journal of Business & Economic Statistics 2 (4): 367–74. doi:10.1080/07350015.1984.10509410.

Siderelis, C., R. L. Moore, Y. -F. Leung, and J. W. Smith. 2012. “A Nationwide Production Analysis of State Park Attendance in the United States.” Journal of Environmental Management 99: 18–26. doi:10.1016/j.jenvman.2012.01.005.

Siderelis, C., and J. W. Smith. 2013. “Ecological Settings and State Economies as Factor Inputs in the Provision of Outdoor Recreation.” Environmental Management 52 (3): 699–711. doi:10.1007/s00267-013-0083-z.

Siikamäki, J. 2011. “Contributions of the US State Park System to Nature Recreation.” Proceedings of the National Academy of Sciences 108 (34): 14031–36. doi:10.1073/pnas.1108688108.

Simon, H. A. 1976. Administrative Behavior: A Study of Decision-Making Processes in Administrative Organization. New York: Free Press.

Smith, J. W., and Y. -F. Leung. 2014. National Association of State Park Director’s Report: 2014 Outlook and Analysis. Raleigh, NC: Department of Parks, Recreation and Tourism Management, NC State University.

Smith, J. W., Y. -F. Leung, E. Seekamp, C. Walden-Schreiner, and A. B. Miller. 2015. “Projected Impacts to the Production of Outdoor Recreation Opportunities across US State Park Systems due to the Adoption of a Domestic Climate Change Mitigation Policy.” Environmental Science & Policy 48 (April): 77–88. doi:10.1016/j.envsci.2014.12.013.

Documents

2015 OUTLOOK AND ANALYSIS LETTER - Nc State Universityresearch.cnr.ncsu.edu/rern/aix/aix2015_outlook_letter.pdf · 2015 OUTLOOK AND ANALYSIS LETTER a report prepared for the National